5 famous thought experiments

The 15 Most Mind-Blowing Thought Experiments Of All Time

Via medium.com

If you are the type of person who wants clear, solid answers, then thought experiments may drive you a little bit crazy. When considering thought experiments, sometimes you will have to become comfortable with a paradox, where two seemingly contradictory things may be true at the same time. Other times you will end up with a thought experiment that is not solvable because the answer lies beyond human understanding.

No matter the frustrations with these issues, thought experiments are useful to stretch the mind in ways that most people rarely do and geniuses do all the time.

When Albert Einstein was a lowly patent clerk, the job was so easy for him to do. It was so boring that he finished his work quickly each day and then spent the rest of the time staring out the window and considering his thought experiments. This effort led him to a whole new way of seeing the universe, a deeper understanding of the relationship between time and space, and ultimately the creation of his Special Theory of Relativity. He became a renowned genius for his original thinking, which sometimes took many decades for scientific proof to become available that supported his theories.

If you fancy yourself a kind of genius or if you just want to have some fun thinking about strange things; here are fifteen types of thought experiments that are mind-blowing. If you come up with a new unique answer then you may be the next Einstein!

15. The Zen Koan

Via johanjanssen.deviantart.com

Zen is a form of Buddhism. A koan is a type of question or statement that allows you to ponder it and yet it does not have a definitive answer. One of the most famous ones is “If a tree falls in a forest and there is no one there to hear it. Does it make any sound?” If you consider sound as the vibration of air molecules then the tree falling would definitely vibrate the air molecules surrounding it.

However, if you consider a sound more deeply the concept becomes more complex. The sound comes from the interpretation of the vibration of the air molecules that has a vibratory effect on the tiny parts of the ear, the little hairs, the small bones, and the eardrum. This vibration then causes a signal to be sent to the brain, which the brain interprets as a sound. In this analysis of a sound, it requires a participant for the sound to exist.

To further explore the nature of a sound is to consider the question of where exactly is the sound? Is it near the tree, in the surrounding air, in the ear, or in the brain of the person perceiving it? A completely deaf person standing nearby a tree that falls would not hear any sound, although he or she might feel the vibration of the tree as it struck the ground. A sound cannot simply be a vibration because even though a deaf person can feel possibly feel it, they cannot hear it.

14. The Origin Question

Via NPR.org

This is one of the oldest thought experiments that humankind has pondered for ages since the time of Ancient Greece. It is “Which came first, the chicken or the egg?” This question goes far beyond the origin of poultry because it could just as easily be asked about the universe. If the universe was created from the “Big Bang,” where did the singularity that created the Big Bang come from?

The reason why this is so perplexing it that it comes from our experience. We see that something always arises from something else. A chicken must come from an egg. It does not just spontaneously burst into existence. A religious person might say that God created the chicken and every other animal on Earth all at once and out of nothing. A Darwinian scientist would say all living creatures developed from some primordial ooze.

In 2016, R&D magazine reported that a team of scientists led by Craig Venter, Ph.D. were able to create a simple synthetic life form by using DNA created in a test tube, proving that it is possible. Dr. Venter and his colleagues have been working on this technique since 2010. This simple microbe had 473 genes as compared to a human that has over 20,000. This means maybe a bacterium came first before the egg that eventually became a chicken.

Also during 2016, the Financial Times reported that other scientists at Bath University created a viable offspring without needing to fertilize an egg. This means it is possible to have a chicken without first needing the egg. So, we are back to the same dilemma, which came first?

13. Are You Real or a Copy of Yourself?

Via i.ytimg.com

Plutarch from Ancient Greece is noted as the one who first proposed this thought experiment. There was a ship from Theseus. Over many years of use, parts of the ship began to wear out. The people of Athens kept the ship in good repair. As each part wore out, it was replaced by a new part. Over time, all the parts of the ship had been completely replaced. Is this still the ship from Theseus? If all the old parts were found in a junkyard and assembled into a ship would it be the ship of Theseus?

Let’s take this a step further. Over a period of approximately seven years’ time, every cell in the human body has been replaced by a new one serving the same function as the previous one. If every cell in your body is different, are you still the same person?

Imagine there was a transporting device, like the kind featured on “Star Trek,” with one big difference. This transporter does not send your particles from one part of space to another. Instead, it takes the information about your body down to the tiniest, exact detail and makes a copy, including your memory and consciousness. This device builds an exact copy of you at the distant location. Everyone who encounters this new you thinks it is exactly the same as the old you. You also feel the same. In order to do this transportation, the original you is destroyed in the process. Is the new you the same person? If you looked, acted, and felt exactly the same, would you still be you?

12. Could a Monkey Write a Shakespeare Play?

Via shakesdrama.blogspot.com

The infinite monkey theorem is a thought experiment that says, if you had an infinite amount of monkeys that were trained to type on a keyboard, given an infinite length of time, eventually, one of them would type a Shakespeare play by typing at random. In fact, one would type all of Shakespeare’s work. Moreover, many would type copies of any finite work like a Shakespeare play an infinite number of times.

Even though the probability of a monkey typing Shakespeare is extremely low, it is not zero. Given enough time of say, hundreds of trillions of times the age of the universe, a monkey would randomly type Shakespeare. Even if the chance is only one out of a googolplex (this is a number of 1 followed by one hundred zeros), infinity is forever and larger.

There is mathematical proof of this theorem. The probability of two completely independent events occurring at the same time is the combination of the probability of both separate events occurring. For example, if the chance of it raining in one place today is 0.5 and the chance of having an earthquake in another place is 0.000005. Then, the probability of rain in one place combined with an earthquake in the other place is 0.5 times 0.000005, which equals 0.0000025.

If a keyboard has 50 keys, the chance of typing a single letter is one out of fifty. If a monkey is typing at random the chance of typing the word “banana” is (1/50) × (1/50) × (1/50) × (1/50) × (1/50) × (1/50). This equals the chance of one out of 15,625,000,000 for the monkey to type banana. The chance is small, but no matter how small a chance is, if infinite time is applied the chance is never zero.

11. Brain in a Jar

Via Pinterest.com

Before the “Matrix” films, there was a thought experiment called the “brain in a jar” (sometimes called the “brain in a vat”). This experiment removes a human brain and keeps it alive in a jar. The scientist uses a computer to provide electrical/chemical impulses to the neurons of the brain in the jar that simulate what a brain normally experiences while inside a living human body.

If the computer was sophisticated enough to both provide stimulus to the brain in the jar and react to the brain’s activity in the same ways as if it was still inside the skull of a living human being, then the brain, from its perspective, would not be able to tell that it was in a jar and would have experiences that to the brain seem exactly like reality.

This kind of philosophical examination of our definition of reality brings up the possibility that we are all existing in some form of an illusion that we have no true way of knowing whether it is real or not. We may only be able to determine that we are real; however, everything else is our perception of reality and may not have a true independent existence. At least, there is no sure way to prove the independent existence of anything else to ourselves, since our perceptions are all we have available to use.

10. Time Travel Paradox

Via USmagazine.com

If a time machine existed that allowed a person to travel back in time and they used it to go back to kill their own grandfather, how could that person still exist? This is called the grandfather paradox or an alternative version is the Hitler paradox.

In the Hitler Paradox, a person using a time machine to travel back in time to kill Hitler before he rises to power would have then removed the reason that made the time travel necessary, since Hitler would no longer exist.

One way that quantum scientists used to explain how to avoid the time travel paradox is by using an infinite number of multiple universes. Gong back in time and killing your own grandfather would only kill him in a parallel universe that is identical to the one you come from, with the sole exception that there is no grandfather and therefore no you in it. By the way, the photo is Hitler as a baby. If you could go back in time, would you be able to kill a baby who was at that time just an innocent child?

9. As Above, So Below

Via alphacoders.com

The very largest things in the universe, called the “macrocosm”, are very similar to the very small, called the “microcosm.” This idea was first proposed by Hermes Trismegistus. The macrocosm is the universe. The microcosm is oneself. As the microcosm compares to something larger, it also becomes the macrocosm to something smaller. From the level of atomic particles, a person is a macrocosm.

Scientists, who study particle physicists, continue to look for the fundamental building blocks of the universe. Until the splitting of the atom was possible, it was assumed that the atom was the smallest unit of the universe. After the atom was split, so many new particles were discovered. In contemporary times, the large Hadron collider in Switzerland continues to find new particles of smaller sizes and with different configurations. The tiniest building blocks of the universe have yet to be discovered and perhaps they do not even exist, if everything can be both infinitely small and infinitely large at the same time.

8. Holographic Universe and Fractals

Via Pininterest.com

Related to the “As Above, So Below” thought experiment, is the idea of a holographic universe. The thought experiment about the holographic universe notes that everything in the universe is contained and replicated on a different scale in any smaller piece of it. Just like each part of a laser-made hologram contains the entire image, the holographic universe theorem says that everything is simply a fully contained copy of everything else. The only difference is scale.

Another way to think about this is the idea of fractals. Fractals are mathematical expressions that repeat themselves based on simple rules. As you zoom in on a fractal you see the same pattern repeated, just the same as if you zoom out. The pattern is the same no matter what scale is used. A thought experiment from fractal mathematics is that it is impossible to measure a coastline with 100% accuracy. As the scale of measurement becomes smaller, the edges of the coastline become more varied, thereby increasing its overall length. The only way to measure a coastline is by using an approximation at a certain scale.

7. Unexpected Hanging Paradox

Via wolframmathworld

In this thought experiment, a prisoner on death row is told he will be hanged one day next week between Monday and Friday and he will not know the day of the hanging in advance. This means that he cannot be hanged on Friday because if he is alive on Thursday he will know in advance of his hanging on Friday, which is the last day of the week it is possible for the hanging.

He cannot be hanged on Thursday because if he is alive on Wednesday he will know that since he cannot be hanged on Friday, he will be hanged on Thursday. Since he cannot know this in advance Thursday is also not a day he can be hanged.

This same logic continues to show he cannot be hanged on any day because he will know in advance when he will be hanged. This even applies to Monday because if all the other days are not possible then Monday is the only possible day, and if Monday is the only day left he knows he will be hanged on that day in advance.

The prisoner feels confident in his logic and knows there is no day of the week that is possible for him to be hanged. Monday comes and he is not hanged; however on Wednesday at noon, to his surprise, he is hanged.

6. Time Dilation

Via Study.com

In Einstein’s Special Theory of Relativity, he predicted the phenomena of time dilation. Time dilation is an effect on time as one accelerates to move closer to the speed of light. More time passes for something moving at a slower speed than for something moving at higher speeds. There is also a gravitational effect on time. Things move slower for those closer to a gravitational force like the Earth compared to those further away from the gravitational force.

The strange thing about this phenomena is that Einstein imagined that “time was relative” before there was any way to prove it.

In Einstein’s famous scientific paper that he published on special relativity during 1905, he concluded that when two synchronized clocks that keep perfect time were used and one was taken away from Earth and then brought back, the one that stayed on Earth would have moved at a faster rate of speed and the one brought back would be lagging behind in time.

Decades later, this theory was tested using atomic clocks, which are extremely accurate and the theory was proven correct. One clock stayed on Earth and the other was taken into orbit around the Earth. The one that returned was slightly behind in time when compared to the one that remained on Earth. Einstein’s theory has been proven many times. Atomic clocks on satellites run slightly slower than the same atomic clocks on Earth, so they have to be adjusted for the difference.

5. Runaway Trolley Dilemma

Via Business Insider

In this thought experiment, developed by Philippa Foot in 1967, you come across a set of train tracks. On one set of tracks that the runaway trolley is going down there are five people tied to the tracks who are unable to move. On another set of connected side-tracks, there is one person tied to the tracks. A fast trolley is approaching. It is going too fast to stop in time. There is a switch that will divert the trolley onto one set of tracks or the other. There is no time to do anything but either throw the switch or do nothing. What do you do?

Do you let the trolley kill the five people or do you throw the switch to kill only one to save the five others? What if the one person tied to the tracks alone is your own child?

Another variant has a fat man standing nearby who is large enough to stop the trolley before it hits the five people. Do you push the fat man into the way to save the five that are tied to the tracks? Surprisingly, most would pull the switch to save a net of five of the six lives, but few would push the fat man onto the tracks to save four others. There is a perceived moral difference between the two acts, even though the net number of deaths is the same. However, this decision is reversed if the fat man is the villain who is responsible for tying the people to the tracks.

4. Deterministic Universe

It the theory of the deterministic universe everything has a cause and an effect. There is nothing that happens without a related cause that creates it. Another way to think about this is the idea of fate or karma. Fate is something that happens, which cannot be prevented by the person it happens to. Karma is the effect from something done in the past, Buddhists believe in reincarnation, so for them, karma can last for more than a single lifetime.

From a Buddhist point of view, this explains what bad things happen to seemingly good people or innocent children. They may not have done anything to deserve the bad consequences in this particular life, but they must have done something bad in a past life to bring the bad karma in this life.

A deterministic universe contradicts with the idea of free will. If fate is pre-determined then there is no such thing as making any choice. Choices are just an illusion, which brings the person to the same end result, no matter what they do.

3. Allegory of the Cave

Via SteveSanders.online

This was a thought experiment developed by the Greek philosopher Plato and presented in Plato’s work as a conversation between Plato’s brother and his mentor Socrates. In this thought experiment, Plato has Socrates explain that some people have lived all their lives in a cave held in place by chains and facing a blank wall. They watch the shadows on the wall of things passing by the front of a fire, which is behind them. They create names for the shadows. Some of the shadows’ appear at the same time as when they get water and food. For them, the shadows are the reality. They do not even have a desire to leave the cave because they have not known any other way of life.

In the dialogue written by Plato, Socrates says that a philosopher is like a person freed from the cave. The philosopher sees the true nature of reality, not the manufactured reality of the shadows that are thought to be the reality by those held in the cave.

2. Flatland

Via panoramio.com

Similar to the allegory of the cave is the thought experiment of Flatland. Flatland was a satirical novel written by an English school teacher named Edwin Abbott. In Flatland, everyone lives in two dimensions. The leader of Flatland is a Square. The Square tries to convince the King of the one-dimensional Lineland, which is a group of lustrous dots, that there is more than one dimension. The King tries to kill the Square rather than listen to what he considers nonsense. The Square escapes back to Flatland.

When a three-dimensional object passes through Flatland, the Sphere, it first appears in Flatland as a dot, then changes into a circle, which widens and then shrinks back from a circle to a dot and then disappears. This leads the Square to discover the third-dimension of Spaceland, which he visits.

The Square has dreams of other dimensions, including Pointland, which is a single dot who believes there is nothing in the universe except him. The Square also dreams of higher dimensions and he tells the Sphere and others in Spaceland about his dreams. He is forced to return to Flatland when he is thrown out of Spaceland for trying to spread his crazy ideas about other dimensions.

In Flatland, he is imprisoned for his heretical beliefs. After seven years in prison, the Square writes a book of his memoirs and experiences in other dimensions hoping those in future generations will read it and be able to see beyond their two-dimensional existence.

1. Schrödinger’s Cat

This is one of the most famous thought experiments in physics invented during 1935 by the Austrian physicist Erwin Schrödinger as his argument against the theory of Quantum Superposition that was proposed by other scientists at that time.

Quantum Superposition theory states that at a quantum level, a particle may be in an undetermined state that is sort of in-between states of existence, which collapses into a certain state only upon being observed.

Schrödinger thought this Quantum Superposition proposition was ridiculous and used his cat thought experiment to demonstrate his reasoning.

In the Schrödinger’s Cat thought experiment, you think of putting a cat in a sealed box along with a vial that contains a tiny bit of radioactive material that has a 50% chance of decaying within one hour’s time. Also, you put a Geiger counter in the box that is connected to a hammer and a vial of poison gas. If the Geiger counter detects radioactive decay, then the hammer falls, breaking the glass vial with the poison gas and the cat is killed. Regardless of the macabre nature of this thought experiment, there is no way to know if the cat is dead or alive without opening the box.

Under the Quantum Superposition theory, the cat would be in an undetermined state of dead/alive or alive/dead until the researcher opened the box after one hour had passed. This is what Schrödinger thought was absurd. Clearly, the cat is either dead or alive and because the poison gas kills almost instantly. The cat is never in a state of both being dead and alive at the same time.

Schrödinger’s logic is correct for larger objects such as a cat; however, he was dead wrong when it comes to actions of particles at a quantum level. Research since then has shown quantum particles have the ability to fade in and out of states of reality and simultaneously maintain the probabilistic state of two contrary conditions at the same time until an observation is made.

The observation causes the quantum field to collapse and the state of the particle can then be determined by the researchers. In spite of Schrödinger’s skepticism, quantum research is uncovering strange and unusual things happening at a quantum level, which do not exist in larger forms. Luckily, no cats had to be killed to prove this.

Sources: alternativephysics.org , rdmag.com , ft.com , iflscience.com

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9 Philosophical Thought Experiments You Should Know About

Thought experiments are imaginative devices that can help us better understand philosophy. They are a useful tool in education and entertainment and can be a great way to apply complex concepts to practical situations. Since philosophy looks at questions about life, you can make a thought experiment for nearly any philosophical idea. Learn about some of the most popular ones commonly used in philosophical discussions.

The Trolly Problem

The trolly problem is an ethical thought experiment. It first appeared in philosopher Philippa Foot's 1967 paper, "Abortion and the Doctrine of Double Effect." To start off the thought experiment, imagine you have control of a railway switch. There is an out-of-control trolley headed your way. Up ahead, the tracks of the railway branch into two different paths. On the first track, there is a group of five people; on the other track, there is one person. If you stand, watch, and do nothing, the trolley will head down the first track and kill five people. However, your control allows you to switch the path of the trolley. This way, it heads down track two and kills one person instead of five. The dilemma in this situation is whether or not to flip the switch. A utilitarian answer would be to flip the switch and kill one instead of five.

Selective Surgery

Imagine you are a doctor in the future, and an ill patient comes into your practice. The patient's symptoms lead you to the diagnosis that their heart is failing. Without treatment, the patient is going to die. In your office, the patient passes out. Fortunately, the patient can be saved with surgery that will give them a synthetic heart. The patient can live what you consider to be a good life after this surgery. However, as you are preparing the patient for surgery, a small card falls out of their pocket. The card says for religious reasons; the patient does not want any synthetic organs. Now you must make a decision. If you do not install the heart, the patient will die. However, if you install the heart, the patient will survive at the cost of you violating their wish to have no synthetic organs.

At the heart of this thought experiment is a choice between honoring someone's individual rights and honoring an outside moral code . This is a relevant topic today in bioethics. Philosophers who advocate strongly for personal rights would argue that doing the transplant is wrong. While philosopher John Locke wasn't exposed to this thought experiment, he is someone who expressed the importance of individual rights and consent. According to Locke, individual consent is a fundamental part of creating a political society. In his view, doing the transplant on an unconsenting individual would be wrong.

The Bad Father

A thought experiment that tests loyalty against ethical principles is the bad father. In the thought experiment, there is a son who holds honesty as the highest value. However, his father is not an honest man. One day, his son catches him stealing from a local farmer. In this situation, the son must make a choice. He could turn his father in for breaking the law and stealing. Or the son might feel an ethical obligation to keep silent about his father's crime. While you might find this question silly, ask yourself the implications this scenario has on a larger scale. Would it be better for children to stay loyal and protect their parents or better for them to alert the authorities when their parents stray from the law?

This thought experiment is a variation of the thought experiments proposed by the ancient Greek philosopher Plato. He wrote a dialogue called Euthyphro, where Euthyphro takes his father, Socrates, to court. Euthypro argues taking his father to court is the right thing to do and the pious thing to do. However, Socrates disagrees with Euthypro about his impiety charges and gets into a debate with Euthypro about philosophical questions of universal justice, goodness, and piety. At the core of the philosophical thought experiment is the question of what happens when there is a conflict between our personal lives and the impersonal tenets we believe justice demands. The thought experiment brings old philosophical questions about justice to life.

Prisoners Dilemma

The prisoner's dilemma is a game that was created as a model of human cooperation. The experiment shows how people choose to cooperate or how they don't. The mathematician Albert Tucker is credited with formalizing the thought experiment. Today, a wide array of disciplines use the thought experiment, including philosophy, psychology, economics, and political theory.

For the experiment, imagine a cop arrests both Chris and Cindy for robbing a bank. They are in separate cells where they cannot communicate. Both want to be free and care more about their personal freedom than the freedom of their accomplice. A clever prosecutor will use their desire for freedom to his or her advantage. The prosecutor will tell each person separately that if they confess and their accomplice remains silent, they will drop all charges against them and their testimony to ensure their accomplice does serious time. If they both confess, the prosecutor will ensure they both get early parole. If they both remain silent, they will have to settle for sentences on firearms possession charges. The dilemma for the prisoners is that if they both confess, the outcome is worse than it would have been if they had both remained silent.

The prisoner's dilemma compares individual and group rationality. It shows there can be conflict between individual and collective interests. Conclusions drawn from the Prisoner's Dilemma have been used in modern-day philosophical discussions about arms races and the use of limited natural resources.

The Chinese Room

A thought experiment about artificial intelligence is the Chinese room, designed by philosopher John Searle. He asks us to imagine a situation where someone who only knows the English language is sitting alone in a room. They have instructions for changing rows of Chinese letters. Anyone outside the room would think the person inside the room understood Chinese since they would see them sorting through Chinese characters. However, this is not the case. The person inside the room just understands the instructions. Searle made this thought experiment to show that artificial intelligence cannot have a human-like mind. His thought experiment stresses that while there is understanding, there is not comprehension. 

The Experience Machine

A thought experiment that will make you question the value behind experience, is Robert Nozick's Experience Machine. The experiment is from his book Anarchy State and Utopia . Imagine that there is a machine that will give you any experience you desire. You could enter the machine and have an experience that you were eating the world's best cookie or that you were an astronaut. While you are in the experience machine, you are floating in a tank with electrodes attached to your brain. The question here is if you should plug into this machine to preprogram your life experiences. While in the tank, you wouldn't know that you were in the tank, making the experience even more real. The thought experiment brings questions about the meaning of life. What is the purpose of life if we are plugging into a machine? Will plugging into a machine satisfy all of our desires?

The Ship of Theseus

The Ship of Theseus is a thought experiment that questions whether an object that has all of its components replaced or rearranged is in fact the original object. This paradox was recorded by Plutarch, Theseus, who asks if a ship that was fully restored and replaced completely, down to every single wooden part, was the same ship. Later, other philosophers expanded on this idea. Thomas Hobbes asked if the original planks of the first ship were entirely replaced and then the original planks were used to build another ship, if the second ship would be the original ship. The thought experiment asks questions about what the essence of an object is. The Greek philosopher Heraclitus attempted to solve this paradox. To do this, Heraclitus thought of a river that has water replenishing it. According to Heraclitus, this is the same river. However, Plutarch disagreed and claimed the nature of a river to scatter and then come together means you never step into the same river twice.

Original Position

Ever thought the system was unfair? The original position is a thought experiment centering around achieving a better form of justice. Developed by John Rawls, the thought experiment asks us to imagine that we are in a situation where we do not know our actual life. This way, we are behind what Rawls calls a veil of ignorance. This veil prevents us from knowing the political or economic system that we live under and the laws that are in place.  From this position, we are then asked, with a group of other people behind the veil of ignorance, to look at a list of classic forms of justice. We must draw conclusions from different social and political philosophies. Then, we have to choose a system of justice that we believe would be best for everyone under this veil. This thought experiment calls us to question our beliefs about justice. It forces us to confront the flaws of our political and economic systems.

The Beetle in the Box

The Beetle in The Box thought experiment is also known as the Private Language Argument. Philosopher Ludwig Wittgenstein developed the thought experiment to challenge the way we look at introspection and how it informs the language we use. The thought experiment starts by imagining a group of individuals, each holding a box. The boxes contain what each individual calls their beetle. Nobody can see into anyone else's box. Everyone describes their beetle to each other. However, each person only sees and knows their own beetle. According to Wittgenstein, the descriptions are unimportant. This is because, over time, the individuals would understand the word beetle as the thing in a person's box. While the thought experiment might sound silly, it makes the comparison that human minds are like a beetle. We can never know what is in another individual's mind.

Why Use Thought Experiments?

Thought experiments help us explore philosophical concepts in a more practical way. For example, the trolly problem forces us to confront how we would apply our ethics in a situation. The point of thought experiments isn't to arrive at a specific answer. Instead, thought experiments force us to reason through our ideas and give us insight into solving complex questions. When you come up with an answer to a thought experiment, why you arrived at your answer is just as important as the answer itself.

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Albert Einstein used to ponder these 5 mind-melting questions for fun. Can you figure them out?

• Albert Einstein was well known for his thought experiments involving complex scientific ideas.
• Often he used real-world examples that helped non-scientists grasp his theories of relativity.
• He started pondering one of them, about chasing a beam of light through space, when he was 16.

Albert Einstein , one of the greatest minds of the 20th century, forever changed the landscape of science by introducing revolutionary concepts that shook our understanding of the physical world.

One of Einstein's most defining qualities was his remarkable ability to conceptualize complex scientific ideas by imagining real-life scenarios. He called these scenarios Gedankenexperiments , which is German for thought experiments.

Despite the name, Einstein's mental exercises incorporated data from actual experiments.

Here are a few thought experiments that demonstrate some of Einstein's most groundbreaking discoveries, including his special and general theories of relativity .

What would happen if you chased a beam of light as it moved through space?

Einstein started wondering about this when he was just 16 years old. 

If you could somehow catch up to the light and travel as fast as it is going, Einstein reasoned, you would be able to observe the light frozen in space. But since he knew light was a wave composed of changing magnetic and electric fields, it couldn't truly be still.   

"One sees in this paradox the germ of the special relativity theory is already contained," Einstein wrote in his " Autobiographical Notes ." This "special" theory applies to certain relationships between space and time, and he further explored it with another thought experiment involving trains and light.

Can 2 people experience the exact same event differently? 

Imagine you're standing on a train while your friend is standing outside the train, watching it pass by. If lightning struck near both ends of the train, your friend would see both bolts flash at the same time.

But on the train, you are closer to the bolt of lightning you're moving toward. So you see this lightning first because the light has a shorter distance to travel.

The setup for this experiment is a bit complicated and involves angled mirrors and poles. But the result is that time behaves differently for someone moving than for someone standing still. 

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It cemented Einstein's belief that time and space are relative and simultaneity — two events happening at the same time — depends on your perspective. This is a cornerstone of Einstein's special theory of relativity.

How does your space-traveling twin age compared to you?

Let's say you have a twin who was born at almost the exact same time as you.

But almost immediately, your twin boards a spaceship and launches into space to travel through the universe at nearly the speed of light. 

Since, according to Einstein's special theory of relativity, time moves slower the closer you reach the speed of light, your twin in the spaceship would age more slowly.

When the spaceship landed back on Earth, you would be celebrating your 65th birthday, while your twin hadn't even turned 10 yet, based on an estimation from Omni Calculator.

Is your elevator accelerating or floating in space?

Imagine you are in a windowless elevator, unable to see what's happening outside. Without visual cues, you don't know if you're in a stationary elevator on Earth or in space being hauled upwards. Gravity's tug and upward acceleration in zero gravity both pull you to the floor.  

The physics of both events is the same, Einstein decided, based on the "principle of equivalence." Similarly, if your elevator were to plummet far and fast, you would float as though you were in space.

Now consider Einstein's previous assertion that time and space are relative. If motion can affect time and space (like with the train experiment) and gravity and acceleration behave the same, that means gravity can actually affect time and space. 

If you put a bowling ball on a trampoline, it will depress the fabric. Place marbles close by, and they will roll toward the ball. Objects with huge mass can affect space-time in a similar way. 

The ability of gravity to warp space-time is a key part of Einstein's general theory of relativity, which he published a decade after the special theory and expanded upon it.

Can particles communicate faster than the speed of light?

Einstein wasn't the biggest cheerleader for quantum theory. In fact, he argued back and forth with physicist Niels Bohr over certain occurrences that he believed violated fundamental laws of physics.

One of Einstein's thought experiments had to do with quantum entanglement, which he called " spooky action at a distance ."

Imagine you have a two-sided coin that you can easily split in half. You flip the coin. Without looking at the outcome, you hand one side to your friend and keep the other side for yourself. Then your friend gets on a rocket ship and travels across the universe.

When you look at your coin, you see you're holding the heads side of the coin. Instantly you know that your friend, who is billions of light years away, has the tails side.

Einstein's version of this thought experiment is more complicated than coins and involves entangled particles that share a wave function. Both particles have the potential to be in two possible states, spin up and spin down. Measuring one gives you information about the other, no matter how far apart they are.

It's a bit like if your half of the coin was neither heads nor tails until you looked at it. Since the coin wasn't double-sided, you know your friend has tails when you have heads. But Einstein thought particles behaved more like real coins. They had some inherent property that made them "spin up" or "spin down" all along.

Other scientists have proven him wrong in the decades since. In 2022, three physicists won the Nobel Prize for demonstrating spooky action at a distance.

Watch: Physicist breaks down the science behind 10 iconic Marvel scenes

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Thought Experiments

Thought experiments are basically devices of the imagination. They are employed for various purposes such an entertainment, education, conceptual analysis, exploration, hypothesizing, theory selection, theory implementation, etc. Some applications are more controversial than others. Few would object to thought experiments that serve to illustrate complex states of affairs, or those that are used in educational contexts. The situation is different, however, with respect to the appropriation of imagined scenarios to investigate reality (very broadly conceived to include things like electrons, tables, rain, beliefs, morals, people, numbers, universes, and even divine beings). It is this use of thought experiments that attracts most of the attention inside and outside of philosophical discourse. Significant is the overlap here with many other central philosophical topics, such as the nature of the imagination, the importance of understanding in contrast to explanation, the role of intuition in human cognition, and the relationship between fiction and truth. Moreover, thought experiments are interdisciplinary in two important respects. Firstly, not only philosophers study them as a research topic, but also historians, cognitive scientists, psychologists, etc. Secondly, they are used in many disciplines, including biology, economics, history, mathematics, philosophy, and physics (although, interestingly, not with the same frequency in each).

Most often thought experiments are communicated in narrative form, frequently with diagrams. It is important to distinguish between the imagined scenarios that are featured in thought experiments, on the one hand, and the narratives that establish those scenarios in people’s mind, on the other. Once a scenario is imagined it may assume a life on its own, and this explains partly the creative power of a good thought experiment. Experimental results may obtain that actually run counter to the narrative that initiated the discussion of an imagined scenario. Besides, thought experiments should be distinguished from thinking about experiments, from merely imagining any experiments to be conducted outside the imagination, and from psychological experiments with thoughts, though there may be some overlap. They should also be distinguished from counterfactual reasoning in general, as they seem to require a palpable element, which explains the impression that something is experienced in a thought experiment (i.e., being seen, felt, heard, etc.; not literally, of course). In other words, though many call any counterfactual or hypothetical situation a thought experiment (see, e.g., Rescher 1991), this appears too encompassing.

It is a quite different matter as to whether there is a logical structure common to all of thought experiments. Based on such considerations of logical structure, a taxonomy has been proposed according to which all thought experiments fall into two classes: “Necessity Refuters” and “Possibility Refuters” (see Sorensen 1992, 132–160). Such proposals especially fuel the debate about identity conditions of thought experiments. What modifications to logical structure does a thought experiment tolerate before it ceases to exist and a new one is born? In other words, how much emphasis on propositional characteristics is appropriate in the analysis of thought experiments?

Looking at the development of the discussion about thought experiments over the past thirty years, it is fair to say that thought experiments were primarily an important topic in the philosophy of science and the philosophy of philosophy (“metaphilosophy”), before the scope widened up at a later point. There is a simple reason for that path. At the core of the discussion sits a relatively simple epistemological challenge that is presented in a particularly powerful manner by numerous thought experiments that the history of science has to offer. They suggest that we can learn about the real world by virtue of merely thinking about imagined scenarios. But how can we learn about reality (if we can at all), just by thinking? This is the central question. Are there really thought experiments that enable us to acquire new knowledge about nature without new empirical data? If so, where does the new information come from, assuming that it takes new information to learn anything new about the world by means of thought experiments? Finally, how can we distinguish good from bad instances of thought experiments? These questions seem urgent with respect to scientific thought experiments, because many “recognize them as an occasionally potent tool for increasing our understanding of nature” (Kuhn 1977, p. 241). “Historically their role is very close to the double one played by actual laboratory experiments and observations. First, thought experiments can disclose nature’s failure to conform to a previously held set of expectations. Second, they can suggest particular ways in which both expectation and theory must henceforth be revised” (Kuhn 1977, p. 261). Yet, questions surrounding the epistemological challenge that certain scientific thought experiments pose, are equally urgent with respect to thought experiments outside of the natural sciences. This is especially true with respect to philosophy itself. Philosophy offers numerous examples of thought experiments that play a role similar in importance to some scientific thought experiments. And this fact provokes in turn further inquiries into the relationship between the natural sciences and philosophy, especially with respect to phenomena that implicate both the natural sciences and philosophy, such as the mind and free will (see, e.g., Wilkes 1988; Young 2013).

If scientific practice has room for thought experiments, then the question arises as to why we would want philosophical methodology to be more discriminatory in this respect. One reason that is often offered is that results of scientific thought experiments may be subjected to further empirical testing. Obviously, this can’t be done for philosophical thought experiments. But, it seems difficult to accept a categorical separation of science and philosophy along these lines. The 17th century saw some of the most brilliant practitioners of thought experimentation in Galileo, Descartes, Newton, and Leibniz, all of whom pursued the project of “natural philosophy.” And in our own time, the creation of quantum mechanics and relativity are almost unthinkable without the crucial role played by thought experiments, most of which relate to important philosophical issues that arise from these scientific theories. Besides, much of ethics, philosophy of language, and philosophy of mind is based on the results of thought experiments in a way that seems very similar to scientific thought experiments (though some might contest this), including Searle’s Chinese room, Putnam’s twin earth, and Jackson’s Mary the colour scientist. Philosophy, even more than the sciences, would be severely impoverished without thought experiments. These observations partly explain why it has been argued that a more “unified” account of thought experiments is desirable (see Boniolo 1997; Cooper 2005, pp. 329–330; Gähde 2000). Of course, it is important not to downplay the significant differences between the sciences and philosophy. But an account of thought experiments seems more powerful if it can do justice to the fact that not only in the sciences we find many of them.

There have been several attempts to define “thought experiment” along the lines of traditional conceptual analysis (see, e.g., Picha 2011; McComb 2013), but likely it will be better to leave the term loosely characterized, so as not to prejudice the ongoing investigation. Of course, we need to have some idea as to what thought experiments are to guide a proper philosophical analysis (see Häggqvist 2009), but this does not mean that we need to begin with a technical definition, specifying necessary and sufficient conditions. In fact, many of the most important concepts we deal with remain rather loosely defined when philosophical inquiry begins, e.g., religion or democracy. Luckily, there are plenty of examples to refer to in order to circumscribe our subject matter well enough. As well as those already mentioned, there are Newton’s bucket, Heisenberg’s gamma-ray microscope, Einstein’s elevator, Leibniz’s mill, Parfit’s people who split like amoebas, and Thomson’s violinist. Everyone is probably familiar with some of these. Less familiar thought experiments include the mouse that breaks into the tabernacle of a medieval Roman Catholic Church building to feed on the consecrated wafers kept in there (see Fehige 2018). Roman Catholic Christians believe that a consecrated wafer is the “body of Christ”. The “substance” of the wafer, understood in terms of Aristotelian categories, is believed to be replaced. In its place is the “substance” of Christ’s body after consecration by a priest. Only the Aristotelian “accidents” of the wafer remain intact (smell, colour, texture, etc.). Does the mouse eat the “body of Christ” (if any human actually does)? If not, then the “body of Christ” seems to be less than an objective reality; if yes, the “body of Christ” must be able to do good in the absence of a believing human soul. Another example less known is “the dome” thought experiment, which is to prove indeterminism in Newtonian physics. Imagine a mass sitting on a radially symmetric surface in a gravitational field. Guided by Newton’s laws of motion one comes to realize that the mass can either remain at rest for all times, or spontaneously move in an arbitrary direction (see Norton 2008). This thought experiment triggers a number of very interesting questions concerning the nature of Newtonian theory, the meaning of “physical”, and the role of idealizations in physics. And, of course, does it show what it claims? (see Malament 2008).

This entry continues with an overview of the characteristics of thought experiments in light of examples in Section 1. Section 2 reviews several taxonomies for classfying thought experiments and Section 3 sketches a history of philosophical inquiry into the nature of thought experiments. Section 4 covers several views representing the current state of the debate. The entry concludes by highlighting some trends in discussions surrounding the so-called laboratory of the mind.

1. Important Characteristics of Thought Experiments

2. taxonomies of thought experiments, 3. the history of thought experiments, 4.1 the skeptical objection, 4.2 the intuition–based account, 4.3 the argument view, 4.4 conceptual constructivism, 4.5 experimentalism, 4.6 the mental–model account, 5. going forward, other internet resources, related entries.

Theorizing about thought experiments usually turns on the details or the patterns of specific cases. Familiarity with a wide range of examples is crucial for commentators, and the list is very long (see, e.g., Stuart et al. 2018, pp. 558–560) We will provide a few here. One of the most beautiful early instances (found in Lucretius, De Rerum Natura 1.951–987; see Bailey 1950, pp. 58–59) attempts to show that space is infinite: if there is a purported boundary to the universe, we can toss a spear at it. If the spear flies through, it isn’t a boundary after all; if the spear bounces back, then there must be something beyond the supposed edge of space, a cosmic wall that stopped the spear, a wall that is itself in space. Either way, there is no edge of the universe; thus, space must be infinite.

This example nicely illustrates many of the most common features of what it means to engage in the conduct of thought experiments: we visualize some situation that we have set up in the imagination; we let it run or we carry out an operation; we see what happens; finally, we draw a conclusion. The example also illustrates the fallibility of thought experiments. Since the time of Lucretius, we’ve learned how to conceptualize space so that it could be both finite and unbounded. Imagine a circle, which is a one-dimensional space. As we move around, there is no edge, but it is nevertheless finite. The universe might be a three-dimensional version of this topology. It is, therefore, true that we must try to be mindful of unexpected limitations due to “physical scale effects” (Klee 2008), or other such things, when imagining counterfactual scenarios.

Figure 1. “Welcome to the edge of the Universe”

Often a real experiment that is meant to be the analogue of a thought experiment is impossible to be carried out as such due to physical, technological, ethical, or financial limitations (see, e.g., Sorensen 1992, pp. 200–202); but physical unrealizability needn’t be a defining condition of thought experiments. Rather, the main point is that we seem able to get a grip on nature just by thinking, and therein lies the great interest for philosophy. That was the position of Ernst Mach (see Mach, 1897 and 1905; for a most instructive assessments of his views see Kühne 2006, pp. 165–202, and Sorensen 1992, pp. 51–75). Thought experiments are on a spectrum of different kinds of experiments. They allow us to tap into a great store of “instinctive knowledge” picked up from past experience. We will get back to Mach’s theory further down. His account of thought experiments remains one of the major theories of how thought experiments work. One of Mach’s favourite examples is due to Simon Stevin (see Mach, 1883, pp. 48–58). When a chain is draped over a double frictionless plane, as in Fig. 2a, how will it move? Add some links as in Fig. 2b. Now it is obvious. The initial setup must have been in static equilibrium. Otherwise, we would have a perpetual motion machine; and according to our experience-based “instinctive knowledge,” says Mach, this is impossible. We do not have to perform the experiment in the real world, which we could not do, anyway, since it would require a perfectly frictionless plane. Nevertheless the outcome seems compelling.

Figure 2. “How will it move?”

Judith Thomson provided one of the most striking and effective thought experiments in the moral realm (see Thomson 1971). Her example is aimed at a popular anti-abortion argument that goes something like this: A fetus is an innocent person. All innocent persons have a right to life. Abortion results in the death of a fetus. Therefore, abortion is morally wrong. In her thought experiment, Thomson asks you to imagine a famous violinist falling into a coma. The society of music lovers determines from medical records that you and you alone can save the violinist’s life by being hooked up to him for nine months. The music lovers break into your home while you are asleep and hook the unconscious (and unknowing, hence innocent) violinist to you. You may want to unhook him, but you are then faced with the following argument put forward by the music lovers: The violinist is an innocent person. All innocent persons have a right to life. Unhooking him will result in his death. Therefore, unhooking him is morally wrong. However, the argument, even though it has the same structure as the anti-abortion argument, does not seem convincing in this case. You would be very generous to remain attached for nine months, but you are not morally obligated to do so. The parallel with the abortion case is evident. Thomson’s thought experiment is effective in distinguishing two concepts that had previously been run together: “right to life” and “right to what is needed to sustain life.” The fetus and the violinist might each have the former, but it is not evident that either has the latter. The upshot is that even if the fetus has a right to life (which Thomson does not believe but allows for the sake of the argument), it may still be morally permissible to abort. Those opposed to Thomson’s view have two options. They can either dismiss her thought experiment as a useless fiction. In fact, thought experiments as a method in ethics have their critics (see, e.g., Dancy 1985). Alternatively, they can provide a different version of the same scenario to challenge the conclusion. It is a very intriguing feature of thought experiments that they can be “rethought” (see Bokulich 2001). Real experiments are frequently open to reinterpretation, too. In this respect there does not seem to be a principled difference between the two classes of experiments.

Like arguments, thought experiments can be criticized in different ways. Perhaps the set up is faulty; perhaps the conclusions drawn from the thought experiment are not justified. Similar criticisms can arise in real experiments. Counter thought experiments are perhaps another form of criticism. They do not target the premises or conclusions involved in a particular thought experiment but question the phenomenon, i.e. the non-propositional heart of an imagined scenario (see Brown 2007). For example, Daniel Dennett is convinced that Frank Jackson’s Mary thought experiment is poor evidence to oppose physicalism in philosophy of mind. In Jackson’s version, Mary, who knows everything physics and the neurosciences can possibly know about colours but grew up in a colourless environment (seeing only black, white and grey things), allegedly learns something new when she sees a red tomato for the first time. Now she knows what it is like to experience red. This is an argument for qualia as something over and above the physical. Instead of a red tomato, Dennett, in his version of the thought experiment, presents Mary with a bright blue banana. In his version of the story (which seems just as plausible as Jackson’s), Mary balks and says she is being tricked, since she knows that bananas are yellow, and this, says Mary, is a consequence of knowing everything physical about colour perception. Mary does not learn anything new when she sees coloured objects for the first time, so there is no case against physicalism after all. Jackson’s initial thought experiment was very persuasive, but Dennett’s seems equally so, thus, undermining Jackson’s argument, although there is greater resistence to the conclusion of the latter than the former! Dennett complains a great deal about the ongoing “Mariology”, as he calls the continuing acceptance of Jackson’s thought experiment as a poweful case against physicalism.

Clearly, thought experiments are characterized by an intriguing plasticity, and this raises the interesting question of what it is that preserves the identity of a thought experiment. Replacing a red tomato with a blue banana might still leave us with the same thought experiment––slightly revised. But, at what point do we get a new thought experiment? This is not merely a question about conceptual vagueness. It helps to facilitate a discussion of the intuitively most plausible view about the cognitive efficacy of thought experiments, according to which this power depends on their being arguments, in a fairly strict sense of argument. John D. Norton holds such a view, which will be discussed below. In light of cases where the discussion of one and the same thought experiment played an important role in settling a dispute, the following problem arises: how can one and the same thought experiment support opposing views about a particular matter if the arguments that correspond to the different versions of the thought experiment that were entertained by the disputing parties are significantly different? The dilemma is: we could say that if there is more than one argument then there is more than one thought experiment involved in the dispute. But if that is true then the disputing parties simply talked past each other. One party presented an argument that the other party ignored while presenting their own. Alternatively, we can say that one thought experiment can correspond to many different arguments. But, if that is true then it becomes unclear in what non-trivial sense thought experiments are supposed to be identical with arguments (see Bishop 1999, and the response by Norton 2004, 63–64).

The plasticity of thought experiments coheres with another feature of thought experiments, namely that they seem to have “evidential significance only historically and locally, i.e., when and where premises that attribute evidential significance to it […] are endorsed” (McAllister 1996, p. 248).

Many taxonomies can be found in the literature. They are not mutually exclusive. We will present three of them. The first follows the type of purpose thought experiments serve. A very rudimentary version of it can be found in Mach (1897 and 1905). Such a classification makes sense, because an “imaginary experiment should be judged on its specific purpose” (Krimsky 1973, p. 331). Thought experiments are conducted for diverse reasons (see, e.g., DeMay 2006; Sorensen 1992, pp. 7–15), and this in a variety of areas, including economics (see, e.g., Herfeld 2019; Thoma 2016), education (Helm and Gilbert 1985; Helm et al. 1985, Klassen 2006; Sriraman 2006; Stonier 1990), history (see, e.g., Maar 2014; Reiss 2009), literature (see, e.g., Davies 2007; Elgin 2004), mathematics (see, e.g. Brown 1991 [2011], pp. 90–97; Glas 1999), morality (see, e.g., Hauerwas 1996; Wilson 2016), as well as the natural sciences (see Krimsky 1973), the socio-political realm (see, e.g. Roberts 1993: Thaler 2016), and theology (see, e.g., Gregersen 2014; Fehige 2024). Thought experiments may be used to entertain. This is probably true of short stories or novels which some argue qualify as thought experiments if certain conditions apply (see, e.g., Davenport 1983). Some thought experiments fulfil a specific function within a theory (see Borsboom et al. 2002). Others are executed because it is impossible to run the experimental scenario in the real world (see, e.g., Sorensen 1992, pp. 200–202). Sometimes thought experiments help to illustrate and clarify very abstract states of affairs, thereby accelerating the process of understanding (see Behmel 2001). Again others serve as examples in conceptual analysis (see Cohnitz 2006). And, then there are those that matter in the process of theory discovery (Praem and Steglich–Peterson 2015). The thought experiments that have received most of the attention are taken to provide evidence for or against a theory, putting them on a par with real-world experiments (see, e.g., Gendler 2004). The different ways to use thought experiments, of course, do not exclude one another. Most obviously, for example, a thought experiment can both entertain and make a case against a theory.

A second taxonomy classifies thought experiments in terms of their logical structure (see Sorensen 1992, pp. 132–166). The idea is to divide all thought experiments into two types of “alethic refuters”: “Although there are a number of ways to classify thought experiments, a refutation format scores the most points when judged by familiarity, specificity, and simplicity. According to this scheme, thought experiments aim at overturning statements by disproving one of their modal consequences. Modalities are operators that are applied to propositions to yield new propositions. There are deontic modalities ( permissible, forbidden ), epistemic modalities ( know, believe ), and alethic modalities ( possible, necessary ). The alethic modalities are the best–known and more–basic modality. Hence, we won’t miss anything by concentrating on them” (Sorensen 1992, p. 135). One type of thought experiment “is designed to refute a statement by showing that something ruled out as impossible by that statement is really possible after all” (Sorensen 1992, p. 135). The most discussed examples in the metaphilosophical discussion on thought experiments is of such a type, namely the Gettier scenarios (see Grundmann & Horvarth 2014; Saint-Germier 2019). They are designed to refute the claim that all knowledge is justified, true belief. They serve as a “necessity refuter.” The other type collects examples of “possibility refuters”. They don’t affirm “the possibility of the thought experiment’s content”. Instead, they establish “copossibilities”. A wonderful example is the scenario of an omnipotent God who faces the task of creating a stone too heavy for that God to lift. It seems God cannot succeed. The notion of divine omnipotence causes some headache here.

A third taxonomy (see Brown 1991, chapter 2), which has not gone unchallenged (see Norton 1993b), is more limited than the first two insofar as it focuses largely on the class of those thought experiments that are taken to function in theory choice, which is the use of thought experiments that has been receiving most of the attention. According to this taxonomy, the main division is constructive vs. destructive and resembles Karl Popper’s distinction between apologetic and critical thought experiments. Popper actually distinguishes between three types of thought experiments: heuristic (to illustrate a theory), critical (against a theory) and apologetic (in favour of a theory) (see Popper 1959). His case in favour of a critical and against an apologetic use of thought experiments is very limited. He focuses exclusively on quantum physics and doesn’t really say much to address the primary epistemological challenge presented by the success of critical thought experiments.

Among destructive thought experiments , the following subtypes can be identified: the simplest of these is to draw out a contradiction in a theory, thereby refuting it. The first part of Galileo’s famous falling bodies example does this. It shows that in Aristotle’s account, a composite body (cannon ball and musket ball attached) would have to fall both faster and slower than the cannon ball alone. A second subtype is constituted by those thought experiments that aim to show that the theory in question is in conflict with other beliefs that we hold. Schrödinger’s well-known cat paradox, for instance, does not show that quantum theory (at least on some interpretations) is internally inconsistent (see Schrödinger 1935, p. 812; translation: Trimmer 1980, p. 328): “A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The q-function of the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.” This thought experiment shows that quantum theory (as interpreted by Bohr) is in conflict with some very powerful common sense beliefs we have about macro-sized objects such as cats––they cannot be both dead and alive in any sense whatsoever. The bizarreness of superpositions in the atomic world is worrisome enough, says Schrödinger, but when it implies that same bizarreness at an everyday level, it is intolerable. There is a third subtype of negative thought experiments, namely when, in effect, a central assumption or premise of the thought experiment itself is undermined. For example, as we have seen above, Thomson showed with her thought experiment that “right to life” and “right to what is needed to sustain life” had been run together. When distinguished, the argument against abortion is negatively affected.

A fourth sub-type of negative thought experiments are “counter thought experiments” (see Brown 2007). Norton very usefully introduces a related idea: “thought-experiment/anti-thought-experiment pairs” (see Norton 2004, pp. 45–49). Above, we have already encountered this subtype in our discussion of Lucretius’ spear-thought experiment, and with Dennett’s reply to Jackson’s much discussed Mary the colour scientist thought experiment. Here we would like to add one more example, namely Mach’s counter thought experiment against absolute space. In his Principia Mathematica , Newton offers a pair of thought experiments as evidence for absolute space. One is the bucket thought experiment with water climbing the wall (see Fig. 3), the other is about a pair of spheres joined by a cord that maintained its tension in otherwise empty space (see Fig. 4). The explanation for these phenomena, argues Newton, is absolute space: the bucket and the joined spheres are rotating with respect to space itself. In response, Mach modifies the scenario and argues, contra Newton, that the two spheres would move toward one another thanks to the tension in the cord, and if we rotated a very thick, massive ring around a stationary bucket, we would see the water climb the bucket wall. (For further discussion of Mach’s counter thought experiment to Newton’s see Kühne 2006, pp. 191–202). In short, the point of Mach’s counter thought experiments is to describe the phenomena of the thought experiments’ scenarios differently, that is, to declare that different things would happen. Mach’s counter thought experiment undermines our confidence in Newton’s thought experiments. Absolute space might be a plausible explanation of the phenomena in Newton’s thought experiments, but now, in light of Mach’s counter thought experiment, we’re not so sure of the phenomena itself and thus of the idea of absolute space.

Figure 3. Stages in the bucket experiment

Figure 4. Two spheres held by a cord in otherwise empty space

To be effective, counter thought experiments needn’t be very plausible at all. In a court of law a jury would convict provided guilt is established “beyond a reasonable doubt.” A common defence strategy is to provide an alternative account of the evidence that has just enough plausibility to put the prosecution’s case into some measure of doubt. That is sufficient to undermine it. A counter thought experiment need only do that much to be effective, and in this sense it operates like a “necessity refuter” in Sorensen’s sense.

In addition to destructive ones, there is a second type, the constructive thought experiments . Unsurprisingly, there are many ways they could provide positive support for a theory. One of these is to provide a kind of illustration that makes a theory’s claims clear and evident. In such cases thought experiments serve as a kind of heuristic aid. A result may already be well established, but the thought experiment can lead to a very satisfying sense of understanding. In his Principia Mathematica , Newton provides a wonderful example showing how the moon is kept in its orbit in just the same way as an object falls to the earth (see Ducheyne 2006, pp. 435–437). He illustrates this by means of a cannon shooting a cannon ball further and further (see Fig. 5). In the limit, the earth curves away as fast as the ball falls, with the eventual result being that the cannon ball will return to the spot where it was fired, and, if not impeded, will go around again and again. This is what the moon is doing. We could arrive at the same conclusion through calculation. But Newton’s thought experiment provides that elusive sense of understanding. It’s a wonderful example of the “aha effect” that is typical of many powerful thought experiments.

Figure 5. “The shot heard around the world”

Thomson’s violinist showed that abortion could be morally permissible even when the fetus has a right to life. Similarly, Einstein’s elevator showed that light will bend in a gravitational field, because according to the principle of equivalence, there is no difference between such a frame of reference and one that is accelerating in free space; the laws of physics are the same in all. Suppose then, an observer is inside an elevator sealed off from the outside so that the observer cannot tell whether he is in a gravitational field or accelerating. If it were accelerating, and if a light beam were to enter one side, then, due to the elevator’s motion, the beam would appear to drop or curve down as it crossed the elevator. Consequently, it would have to do the same thing if the elevator was in a gravitational field. Therefore, gravity ‘bends’ light.

Maxwell’s demon showed that entropy could be decreased: The second law of thermodynamics implies that heat won’t pass from a cold body to a hot one. In classical thermodynamics this law is quite strict; but in Maxwell’s kinetic theory of heat there is a probability, though extremely small, of such an event happening. Some thought this a reductio ad absurdum of Maxwell’s theory. To show how it is possible to violate the second law, Maxwell imagined a tiny creature who controls a door between two chambers. Fast molecules from the cold box are let into the hot box, and slow molecules from the hot are allowed into the cold. Thus, there will be an increase in the average speed in the hot box and a decrease in the average speed of molecules in the cold. Since, on Maxwell’s theory, heat is just the average speed of the molecules, there has been a flow of heat from a cold body to a hot one.

Parfit’s splitting persons shows that survival is a more important notion than identity when considering personhood (for a critical discussion see Gendler 2002a). We say they “show” such and such, but, “purport to show” might be better, since some of these thought experiments are quite contentious. What they have in common is that they aim to establish something positive. Unlike destructive thought experiments, they are not trying to demolish an existing theory, though they may do that in passing. To repeat an important point: in principle, given the fact that thought experiments can be rethought (see Bokulich 2001), and that the evidential significance is dependent on historical and local accomplishments (see McAllister 1996), it cannot be irrelevant to identify the intention of the thought experimenter, if one wants to determine the type of a thought experiment: “An imaginary experiment should be judged on its specific purpose” (Krimsky 1973, p. 331).

The practice of thought experiments is not an invention of modern science. That fact may be obscured by the dominance of scientific examples in the lively discussions about thouht experiments today. The Pre-Socratics “invented thought experimentation as a cognitive procedure and practiced it with great dedication and versatility” (Rescher 2005, p. 2). “There is no ancient Greek term corresponding to what we nowadays refer to as a thought experiment, and presumably ancient philosophers did not have our modern notion of a thought experiment. But there is no doubt that they did use thought experiments. In fact, they often employed them in ways similar to those of contemporary philosophers, that is, both for defending their own theories as well as for refuting the theories of their opponents ” (Ierodiakonou 2018, p. 31). (See also Becker 2018; Diamond 2002, pp. 229–232; Fuhrer 2009; Glas 1999; Ierodiakonou 2005; Ierodiakonou and Roux (eds.) 2011; Irvine 1991; Rescher 1991 and 2005, pp. 61–72). The situation is similar with respect to medieval natural philosophy, although there are further nuances to be considered (see King 1991). According to Edward Grant, during the late Middle Ages “the imagination became a formidable instrument in natural philosophy and theology in ways that would have astonished ancient Greek natural philosophers, especially Aristotle” (Grant 2007, p. 201). But this doesn’t mean that we have reason to think of Aristotle as an opponent of the conduct of thought experiments tout court . On the contrary, “Aristotle uses thought experiments for argumentative persuasion and in places where, due to the obscure nature of the subject matter or the counterintuitive nature of the thesis they are meant to support, insight cannot be readily communicated by appeal to observational facts” (Corcilius 2018, p. 73). With a few exceptions that involved problems of motion, “the scholastics” of the medieval period made no meaningful effort to transform their hypothetical conclusions into specific knowledge about the physical world. They did, however, assume that although these hypothetical conclusions were naturally impossible, God could produce them supernaturally if he wished. Special attention received also a class of medieval thought experiments that does not rely on counterfactuals but depends on theological assumptions to study matters non-theological, namely those thought experiments involving angels, whose existence were affirmed at that time (see Perler 2008). Angels are gone by now (see Clark 1992), but not thought experiments. While most thought experiments involving angels have Christianity as their context, there is evidence of the practice of thought experiments also in the context of Islam and Judaism (see McGinnis 2018; Fisch 2019). In fact, the case has been made “that Ibn Sina is the first philosopher in the Aristotelian tradition, and thus perhaps the first in Western philosophy overall, to try to identify the psychological processes that go into postulating a hypothetical scenario. Ibn Sina also exhibits an interest in accounting for why, and to what extent, such psychological acts are thought to carry weight in our study of nature” (Kukkonen 2014, p. 434).

Ernst Mach is commonly credited with introducing the word “thought experiment” ( Gadankenexperiment ) and thereby coining a term for philosophical discussion (recently done, for instance, by Krauthausen 2015, p. 15). “ This view is incorrect, however! […] it can be substantiated that it was used […] already in 1811” (Witt-Hansen 1976, p. 48; see also Buzzoni 2008, pp. 14–15; 61–65; Kühne 2005, pp. 92–224; Moue et al. 2006, p. 63). The conceptual history of “thought experiment” goes back at least to the Danish “Tankeexperiment,” as it was used by Hans-Christian Ørsted. We can go back even further and find in the work of the German philosopher-scientist Georg Lichtenberg (1742–1799) a tacit theory of “experiments with thoughts and ideas.” These experiments help to overcome habits of thought that can inhibit scientific progress, and make possible an enlightened philosophy (see Schildknecht 1990, pp. 21; 123–169; Schöne 1982). Lichtenberg’s “aphoristic experiments” (see Stern 1963, pp. 112–126) reflect “that Lichtenberg’s scientific preoccupations are the formal and thematic prolegomena to his work as a literary artist” (Stern 1963, p. 126). Lichtenberg’s reflections on thought experimentation resemble those of Popper and Thomas S. Kuhn, and it is plausible to think of him as one important figure of the very first period in the history of philosophical inquiry into thought experiments (see Fehige and Stuart 2014).

Accordingly, the modern history of the philosophical investigation into thought experiments can be divided into four stages: in the 18th and 19th century the awareness of the importance of thought experiments in philosophy and science emerges. In addition to Lichtenberg and Hans-Christian Ørsted, special mention should be made of Novalis (see Daiber 2001). The topic reemerges in a more systematic manner at the beginning of the 20th century with little relation to the attempts made at the first stage. The stakeholders of the second stage were Pierre Duhem, Mach, and Alexius Meinong (see Duhem 1913, pp. 304–311; Mach, 1883, pp. 48–58, 1897 and 1905; Meinong 1907). A third stage, probably due to the rediscovery of the importance of scientific practice for a proper understanding of science, followed in the first part of the second half of the 20th century. Again, the contributions of this stage bear little relation to the two previous stages. While the third period has seen a number of noteworthy contributions (Cole 1983; Dancy 1985; Dennett 1985; Fodor 1964; Helm and Gilbert 1985; Helm et al. 1985; Krimsky 1973; McMullin 1985; Myers 1986; Poser 1984; Prudovsky 1989; Rehder 1980a,b; Yourgrau 1962 and 1967), the protagonists of this period were Alexandre Koyré, Kuhn and Popper. The ongoing philosophical exploration of thought experiments began in the 1980s, and marks the fourth stage. Arguably, it has been the most prolific one of all four stages. With some very important sign-postings in place (Horowitz and Massey (eds.) 1991; Sorensen 1992; Wilkes 1988), the ongoing discussion took off in light of a debate between James Robert Brown and John D. Norton (see for a concise statement of each position Brown 2004 and Norton 2004), which many have found useful to establish a contrast with their own alternative accounts of thought experiments. These views “represent the extremes of platonic rationalism and classic empiricism, respectively” (Moue et al. 2006, p. 69). They will be described below.

4. Current Views on Thought Experiments

At this point it is important to recall the key epistemological challenge described in the introduction: how can we learn about the real world through merely thinking about imagined scenarios? This challenge sits at the center of the discussion about thought experiments even though we must note that not all of the work discussed below focuses on it directly. Still, this section describes six views that can be seen as responding in some way to this challenge: The Skeptical Objection, The Intuition-Based Account, The Argument View, Conceptual Constructivism, Experimentalism, and The Mental-Model Account.

Of course, particular thought experiments have been contested. But for the most part, the practice of thought experiments in the sciences has been cheerfully accepted. Pierre Duhem, the great historian of physics, is almost alone in what has been understood as an outright condemnation of scientific thought experiments (see Duhem 1913, pp. 304–311). A thought experiment is no substitute for a real experiment, he claimed, and should be forbidden in science, including science education. However, in view of the important role of actual thought experiments in the history of physics — from Galileo’s falling bodies, to Newton’s bucket, to Einstein’s elevator — it is unlikely that anyone will feel or should feel much sympathy for Duhem’s strictures. We hasten to add that Buzzoni (2018) questions the validity of this reading of Duhem, and argues that already Mach’s reception of Duhem’s views suggests a more nuanced reading of Duhem’s position.

Philosophers can be as critical as Duhem when it comes to thought experimenting in their own field (see Peijnenburg; Atkinson 2003; Thagard 2014; Wilson 2016). At least thought experiments in science, the skeptic claims, can be tested by physical experiment. However, this is clearly false, since frictionless planes and universes empty of all material bodies cannot be produced in any laboratory. True, the results of philosophical thought experiments cannot be even approximately tested. But, skeptics say little about why thought experiments enjoy such popularity in philosophy. We are inclined to say that skeptics underestimate the importance of thought experiments for the creative mind in any field. Also, one mustn’t forget that the cognitive power of real world experiments isn’t a self-evident matter either.

Few are outright skeptics, however. Many take a more ambiguous stance. Sören Häggqvist, for example, has developed a normative model for philosophical thought experiments (see Häggqvist 1996 and 2009). Surprisingly, none of the commonly accepted philosophical thought experiments satisfies his model. And the process of identifying successful thought experiments is only the first step in addressing the central epistemological challenge posed by thought experiments. It gets much messier once we begin to ask exactly how reliable “successful” thought experiments are. Granted, there is some justice in worrying about the reliability of philosophical thought experiments (see, e.g., Klee 2008). This might be true for ethics (see Dancy 1985, Jackson 1992; Wilson 2016), conceptual analysis (see Fodor 1964), and the philosophy of mind: “A popular strategy in philosophy is to construct a certain sort of thought experiment I call intuition pump. […] Intuition pumps are often abused, though seldom deliberately” (Dennett 1985, p. 12). The claim by Dennett and others is that thought experiments too often rest on prejudice and faulty common sense; they are inherently conservative, while real science will likely result in highly-counterintuitive outcomes. Dennett believes that thought experiments rest on naive “folk concepts,” which is why they can be so misguided. It is far from clear that this is a fair charge. Everything involved in Galileo’s thought experiment that produced the principle of relativity could be called “folk concepts.” If we are inside a ship and perform a number of experiments, such as walking about, tossing a ball, watching birds fly about, we could not tell whether we are at rest in port or sailing over a smooth sea. The upshot is that nature behaves the same either way; the laws of nature are the same in any inertial frame. This result is profound and is still with us in Einstein’s relativity, whether it is folk physics or not.

Frequently discussed is the skeptical challenge raised by Kathleen Wilkes. She expresses a deep suspicion of scenarios such as Derek Parfit’s people splitting like an amoeba (see Parfit 1987; Gendler 2002a). Wilkes wants philosophy “to use science fact rather than science fiction or fantasy” (Wilkes 1988, p. 1), and therefore to refrain from using thought experiments because they are “both problematic and positively misleading” (Wilkes 1988, p. 2). She claims that thought experiments about personal identity in particular often fail to provide the background conditions against which the experiment is set (see Wilkes 1988, p. 7). She thinks we would not know what to say if we encountered someone who split like an amoeba. She insists that a legitimate thought experiment must not violate the known laws of nature. We do agree with Wilkes that underdetermination can be a problem. But instead of dismissing thought experiments in philosophy we should consider it a crucial factor in assessing the quality of a thought experiment (see Rescher 2005, pp. 9–14). That is to say that the more detailed the imaginary scenario in the relevant aspects is, the better the thought experiment (see Brendel 2004, pp. 97–99; Häggqvist 1996, p. 28).

We also agree that the inferences drawn in thought experimenting are highly problematic if the hypothetical scenario “is inadequately described” (Wilkes 1988, p. 8). But Wilkes seems to think that the lack of description is unavoidable, which supposedly amounts to a reason against philosophical thought experiments on personal identity because persons are not natural kinds. This makes it impossible to fill in necessary information to make the thought experiment work given its unavoidable underdetermination. Wilkes thinks that “whenever we are examining the ranges of concepts that do not pick on natural kinds, the problem of deciding what is or what is not ‘relevant’ to the success of the thought experiment is yet more problematic than the same question as it arises in science; and, unlike the scientific problem, it may not even have an answer in principle” (Wilkes 1988, p. 15). She adds that scientific laws — especially those describing biological kinds like human beings — “are not disjoint and independent, detachable from one another […]. They are interrelated, to varying degrees of course” (Wilkes 1988, p. 29). This implies, for example, that “a full psychophysiological account of the processes of human perception must at some stage link up with part at least of linguistic ability; for we typically see things under a certain description, and that description may be a very sophisticated one” (Wilkes 1988, p. 29). These considerations have her rule out experiments that challenge the human monopoly of personhood. No thought experiment, claims Wilkes, is well conceived if it involves non-human animals or computers as persons. But also those thought experiments can be ruled out which involve the “fission or fusion of humans” because it is not theoretically possible. “The total impact of the sum of laws that group us together as human beings (a natural kind category) precludes our splitting into two […] or fusing with someone else” (Wilkes 1988, p. 36).

One can ascertain here all too well the inherent difficulties in thinking about personal identity and the limited benefit some thought experiments might have for what is deemed the proper metaphysics of personal identity. Nevertheless, good reasons have been given in favour of the use of thought experiments about personal identity (see Beck 2006; Kolak 1993; Hershenov 2008). We also feel that the problems about thought experiments on personal identity reveal more about the intricate nature of the subject than about the usefulness of philosophical thought experiments. And, disregarding other shortcomings in Wilkes’ skepticism (for further discussion of Wilkes’ views see Beck 1992; Brooks 1994; Focquaert 2003; Häggqvist 1996, pp. 27–34), her suggestion that thought experimental scenarios would have to satisfy current scientific knowledge about the relevant entities featured in a thought experiment is highly implausible. We learn a great deal about the world and our theories when we wonder, for instance, what would have happened after the big bang if the law of gravity had been an inverse cube law instead of an inverse square. Would stars have failed to form? Reasoning about such a scenario is perfectly coherent and very instructive, even though it violates a law of nature.

To some extent we should share Wilkes’s concern that thought experimenting seems to be constrained only by relevant logical impossibilities and what seems intuitively acceptable. This is indeed problematic because intuitions can be highly misleading and relevant logical impossibilities are fairly ungrounded if they cannot be supplemented by relevant theoretical impossibilities based on current science in order to avoid the jump into futile fantasy. But in order to dismiss thought experimenting as a useful philosophical tool one has to show that intuition cannot be a source of knowledge and that an epistemic tool should be useless because there is a serious chance it can fail. Timothy Williamson has argued that we should forget about intuition as a cushion in the philosophical armchair (see Williamson 2004a,b, 2008, pp. 179–207, and 2009; see also Schaffer 2017). The importance of intuitions in philosophy has been neglected in the past (see Williamson 2004b, p. 109–110), and for too long intuition didn’t receive the attention it deserves (see, e.g., DePaul and Ramsey (eds.) 1998). Besides the traditional divide between empiricists, rationalists and skeptics, it is not only a very non-uniform use of the word “intuition” that makes it difficult to assess the progress of the last years of philosophical inquiry about intuitions. The situation has been complicated by the contributions of experimental philosophers on intuitions who add different reasons to question their reliability (see for a careful critique of those reasons: Ludwig 2007; see also Ludwig 2018). Generally speaking, the reliability of intuitions has been challenged on two grounds. One stems from an evolutionary explanation of the capacity to intuit; another is due to experiments which supposedly show the cultural relativity or racial and gender sensitivity of intuitions (see, e.g., Buckwalter and Stich 2010): “…a substantial list of philosophical intuitions vary across demographic groups and…they are influenced by a number of prima facie irrelevant factors…Some writers…have urged that these findings justify a thoroughgoing skepticism about the use of intuitions as evidence in philosophy…But we think this conclusion is much too strong…” (Stich & Toba 2018, p. 379). After all, knowledge without intuitions (if only common sense assumptions) seems impossible.

The recent discussion of intuitions in epistemology has barely made an impact on philosophical reflections about thought experiments. As far as philosophical thought experiments are concerned, this is as it should be, according to Williamson. In this respect George Bealer can be cited in support of Williamson, because for Bealer the talk about philosophical thought experiments reveals a conceptual confusion. Philosophy, he claims, is about “rational intuitions” and thought experiments can be only about “physical intuitions” (see Bealer 1998, pp. 207–208, and 2002, p. 74). To many, this is an implausible claim based on a deeply problematic “phenomenology of intuitions” resulting in a strict separation of “rational intuitions” from “physical intuitions”, on such grounds as an alleged immutability of “rational intuitions”. There are good reasons to believe that thought experiments appeal to intuitions in order to give us new insights about different realms of investigation, including philosophy. This kind of positive connection is what Williamson has in mind when addressing the role of intuitions in philosophical thought experiments like the famous Gettier cases, which overnight found acceptance by the philosophical community in their aim to refute the view that knowledge is justified true belief. While Williamson expects “armchair methods to play legitimately a more dominant role in future philosophy” (Williamson 2009, p. 126), he thinks that “we should stop talking about intuition” (Williamson 2004b, p. 152). This does not impress proponents of what we call an intuition-based account of thought experiments, and probably for good reasons, given the problems in Williamson’s approach (see, e.g., Dohrn 2016; Ichikawa and Jarvis 2009; Schaffer 2017), and the strong empirical evidence in favour of the positive role that intuitions does play in human cognition (see Myers 2004).

What we term the “intuition–based account” of thought experiments comes in a naturalistic version (see Brendel 2004; Gendler 2007), and in a Platonic version (see Brown 1991a [2011]). We begin with a discussion of the latter. Brown holds that in a few special cases we do go well beyond the old empirical data to acquire a priori knowledge of nature (see also Koyré 1968). Galileo showed that all bodies fall at the same speed with a brilliant thought experiment that started by destroying the then reigning Aristotelian account. The latter holds that heavy bodies fall faster than light ones ( H > L ). But consider Figure 6, in which a heavy cannon ball ( H ) and light musket ball ( L ) are attached together to form a compound object ( H + L ); the latter must fall faster than the cannon ball alone. Yet the compound object must also fall slower, since the light part will act as a drag on the heavy part. Now we have a contradiction: H + L > H and H > H + L . That’s the end of Aristotle’s theory. But there is a bonus, since the right account is now obvious: they all fall at the same speed ( H = L = H + L ).

Figure 6. Galileo: “I don’t even have to look”

Brown claims this is a priori (though still fallible) knowledge of nature, since there are no new data involved, nor is the conclusion derived from old data. Moreover, is it some sort of logical truth (for a technical challenge of this claim see Urbaniak 2012). This account of thought experiments can be further developed by linking the a priori epistemology to accounts of laws of nature that hold that laws are relations among objectively existing abstract entities. It is thus a form of Platonism, not unlike Platonic accounts of mathematics such as that urged by Kurt Gödel.

The two most often repeated arguments against this sort of Platonism are: it does not identify criteria to distinguish good from bad thought experiments, and it violates the principle of ontological parsimony. These seem weak objections. Perhaps they find widespread acceptance because Platonism seems to be unfashionable these days (see Grundmann 2018), given the general popularity of various forms of naturalism. If intuitions really do the job in a thought experiment, the first objection is weak because neither rationalists nor empiricists have a theory about the reliability of intuitions. So the objection should be that intuitions probably just do not matter in human cognition. However, there are good reasons to question the truth of this claim (see Myers 2004). This is not to marginalize the problems that arise when admitting intuitions as a source of knowledge and justification, especially in philosophy (see Hitchcock 2012).

As for the second objection, the appeal to Occam’s razor is in general problematic when it is employed to rule out a theory. Whatever we eliminate by employing the principle of parsimony, we can easily reintroduce it by an inference to the best explanation (see Meixner 2000). And this is exactly what a Platonist contends his or her Platonism about thought experimenting to be, while conceding that the Platonic intuition appears miraculous. But are they really more miraculous than sense perception, which seems similar in many respects to Platonic intuition? One might want to say yes, because supposedly we have no clue at all how Platonic intuition works but we do have some idea about the nature of sense perception. We know that if an object is far away it appears smaller in vision, and under certain light conditions the same object can look quite different. However, is it really impossible to state similar rules to capture the nature of Platonic intuition? If you are drunk or lack attention you most probably will not be very successful in intuiting anything of philosophical value.

A review of the relevant psychological literature will reveal further criteria that could be employed to identify good and bad conditions for Platonic intuition while thought experimenting. Yet, proponents of the naturalistic version of the intuition–based account wonder how necessary Platonism is once this move is entertained in defence of the reliability of intuitions (see Miščević 2004). Elke Brendel defines intuitions as mental propositional attitudes accompanied with a strong feeling of certainty. In her view, we can tell two stories to make sense of their cognitive power and plasticity. One story relates to our biological constitution and evolutionary past. The other is about membership in specialized communities. Brendel’s account raises many questions, but it is difficult to resist its appeal. A universal set is appealing to anyone not trained in logic because most things we are familiar with can come in sets, such as books, tables, and philosophers. A set of all sets seems intuitively plausible. The intuition disappears once you worked yourself through the problems arising from the idea of a set of all sets. Brendel is quick to insist that such relativity of our intuitions doesn’t imply that they are cognitively useless. Without intuitions, we probably wouldn’t have knowledge, and thought experiments are sometimes the only way to access the intuitions that guide us in our cognitive lives (see Brendel 2004).

John D. Norton is the most influential advocate of what we call “the argument view” of thought experiments (see Norton 1991, 1993, 1996, 2004a,b, 2008). Even though the argument view seems to be a natural option for empiricists, it seems that most empiricists find Norton’s argument view too strong. For this reason, many participants in the debate about thought experiments place themselves between the extreme views of Norton and Brown, which function as useful foils for apparently more moderate outlooks. Perhaps (with tongue in cheek) they could agree with Bernard Shaw on the virtues of moderation, when Shaw said of the typical member of the middle class that he is moderately honest, moderately intelligent, and moderately faithful to his spouse. Norton claims that any thought experiment is really a (possibly disguised) argument; it starts with premises grounded in experience and follows deductive or inductive rules of inference in arriving at its conclusion. The picturesque features of any thought experiment which give it an experimental flavour might be psychologically helpful, but are strictly redundant. Thus, says Norton, we never go beyond the empirical premises in a way to which any empiricist would object.

There are three objections that might be offered against Norton. First, his notion of argument is too vague. However, this might not be the best objection: arguments can be deductive (which are perfectly clear) or inductive. If the latter are unclear, the fault is with induction, not with Norton’s argument view. Second, it is argued that Norton simply begs the question: every real world experiment can be rephrased as an argument, but nobody would say that real world experiences are dispensable. The account does not address the question: where do the premises come from? A thought experiment might be an essential step in making the Norton-style reconstruction. Third, a thought experiment that is presented in argument form loses its typical force. The soft-point in Brown’s Platonism is linked to the strength of Norton’s account because Norton claims that any other view implies a commitment to “asking the oracle.” “Imagine an oracle that claims mysterious powers but never delivers predictions that could not be learned by simple inferences from ordinary experience. We would not believe that the oracle had any mysterious powers. I propose the same verdict for thought experiments in science” (Norton 1996, pp. 1142–1143). Defenders of empiricist alternatives deny this dispensability thesis. Brendel (2018) offers a most comprehensive review of merits and perils of the argument view.

“Conceptual constructivism”, as we could call it, is among the empiricist alternatives to the argument view. The position has been taken up by Van Dyck (2003) to account especially for Heisenberg’s ɣ-ray microscope; but also by Gendler (1998) to makes sense of Galileo’s falling body thought experiment. Gendler’s proposal was advanced in more general terms by Camilleri (2014) in order to establish a firm middle ground between the views of Norton and Brown. Conceptual constructivism was first proposed by Thomas Kuhn (1964). He employs many of the concepts (but not the terminology) of his well-known Structure of Scientific Revolutions . On his view a well-conceived thought experiment can bring on a crisis or at least create an anomaly in the reigning theory and so contribute to paradigm change. Thought experiments can teach us something new about the world, even though we have no new empirical data, by helping us to re-conceptualize the world in a new way. Accordingly, some have entertained the option of conceptual constructivism in the form of a Neo-Kantian reading of Einstein’s famous clock in the box thought experiment. Such an approach is inspired by Michael Friedman’s proposal to conceive of scientific revolutions as times when a Kantian kind of natural philosophy plays a major role in guiding scientists from one paradigm to another. The work of Kuhn left us with a puzzle: if scientific rationality is absolutely dependent on a paradigm, and if during scientific revolutions one paradigm replaces another, not in degrees but absolutely, comparable to a “Gestalt” switch, then this transition from one paradigm to the next cannot be a matter of scientific rationality. Are scientific revolutions irrational periods in the history of science? Not necessarily; some kind of natural philosophy may guide the process. Friedman has a Kantian natural philosophy in mind; his proposal did not earn wide acceptance, but the problem remains (see Fisch 2017). Be that as it may, it is true that thought experiments are a valuable currency in times of scientific revolution. For example, Lennox (1991) has argued that the revolution brought about by Charles Darwin in 1859 was made possible by thought experiments (among other things, of course).

What we might term “experimentalism” encompasses a wide range of different approaches which all advance the view that thought experiments are a “limiting case” of ordinary experiments. Experimentalism was proposed first by Ernst Mach (1897 and 1905). He defines experimenting in terms of its basic method of variation and its capacity to destroy prejudices about nature. According to Mach, experimenting is innate to higher animals, including humans. The thought experiment just happens on a higher intellectual level but is basically still an experiment. At the centre of thought experimenting is a “Gedankenerfahrung”, an experience in thought. Such an experience is possible because thought experiments draw from “unwillkürliche Abbildungen von Tatsachen” (non-arbitrary images of facts) acquired in past experiences of the world. Some thought experiments are so convincing in their results that an execution seems unnecessary; others could be conducted in a real-world experiment, which is the most natural trajectory of a scientific thought experiment. In any case thought experiments can result in a revision of belief, thereby demonstrating their significance for scientific progress. Mach also appreciates the didactic value of thought experiments: they help us to realize what can be accomplished in thinking and what cannot.

In the spirit of Mach, Sorensen (1992) has offered an aspiring version of experimentalism that accounts for thought experiments in science and philosophy, and tackles many of the central issues of the topic. Sorensen claims that thought experiments are “a subset of unexecuted experiments” (1992, p. 213). By their logical nature they are paradoxes that aim to test modal consequences of propositions. The origin of our capacity of thought experimentation is explained in terms of Darwinian evolution (as in Genz 1999, pp. 25–29), though the explanation has been criticized to be only little more than a ‘just so story’ that fails, on a posteriori grounds, to epistemically underwrite that capacity (see Maffie 1997). Others are more optimistic (see Shepard 2008).

Experimentalism does not have to take a naturalistic turn as it does in Sorensen’s case. In a number of contributions Marco Buzzoni has defended a Neo-Kantian version of experimentalism (see Buzzoni 2004, 2007, 2008, 2011, 2011b, 2013, 2013b). Buzzoni (2008) argues for the dialectical unity of thought experiments and real-world experiments. Thought experiments and real-world experiments are claimed to be identical on the “technological-operational” level, and at least in science, one is impossible without the other: without thought experiments there wouldn’t be real-world experiments because we would not know how to put questions to nature; without real-world experiments there wouldn’t be answers to these questions or experience from which they could draw. Given the many scientific thought experiments that cannot be realized in the real-world, Buzzoni might be conflating thought experiments with imagined experiments to be carried out in the real-world (see Fehige 2012, 2013b; and Buzzoni 2013b).

Idealizations are common in both real experiments and thought experiments. So-called Aristotelian idealization might ignore, say, the colour of a falling object. Galilean idealizations ignore some physical aspects, such as air friction, to get at the underlying physics (McMullin 1985). So-called Platonic idelization goes beyond this and ignores what would be actually seen even in a Galilean idealization. For instance, a rapidly moving object in special relativity would not look contracted, but rather would look rotated (surprisingly, this phenomenon is not well known). This rotation is ignored as an irrelevant optical phenomenon to yield the correct thought experiment visualization, which is the well-known Lorentz contraction (Brown 2013).

The last of the many accounts that emerged in the discussion about thought experiments is what could be called the “mental–model account.” It attracts the most followers (see Andreas 2011; Bishop 1998; Cooper 2005; Gendler 2004; Palmieri 2003; Nersessian 1992, 1993, 2007; McMullin 1985; Miščević 1992, 2007, 2021). When we conduct a thought experiment, according to champions of this view, we manipulate a mental model instead of the physical realm: “The general claim is that in certain problem-solving tasks people reason by constructing a mental model of the situations, events, and processes that in dynamic cases can be manipulated through simulation” (Nersessian 2018, p. 319). Like physical models, mental models are non-propositional in nature. This means first of all “that the carefully crafted thought–experimental narrative focuses on the construction of a model of a kind of situation and manipulating that model through simulation affords epistemic access to certain features of current representations in a way that manipulating propositional representations using logical rules cannot” (Nersessian 2018, pp. 319–320). A narrative functions as a kind of user-manual for building the model, but it isn’t identical to a thought experiment. The biggest problem for the mental–model account is to explain how something non-propositional like a mental model can make an impact on the propositional realm, which happens when a thought experiment causes a revision in beliefs.

The mental–model approach is one of the most promising of all the accounts the literature on thought experiments has to offer, and this for several reasons. First, it does not seem to be much of a stretch to draw connections to the intuition–based account. In fact, intuitions maybe the missing link to connect the essentially non-propositional activities surrounding mental models, on the one hand, and the propositional aspects of thought experiments, on the other. After all, thought experiments involve propositional reasoning, and somehow the non-propositional and propositional aspects of thought experiments must be linked in any account of thought experiments. This is urgent insofar as thought experiments are credited with a meaningful role in theory discovery and theory choice. Second, the mental–model approach also allows for inclusion of important elements of experimentalism and the argument–view. Thought experiments are realized in the mind on mental models, and the method of variation is employed such that the results of the experiment may be subject to a careful reconstruction of propositional lines of reasoning to submit it for careful assessment and critique. Third, the mental–model approach enables us to bring an aspect into focus that has been widely neglected in the discussion so far: the bodily component of (thought) experiments. The exception is the work of the late David Gooding (1992, 1993, 1994, and 1999). Fourth, in critical engagement with such naturalistic proposals, those theories of the body may be put to work that the philosophical school of phenomenology has produced (see Fehige and Wiltsche 2013). To be welcomed, therefore, is the entry of phenomenology into the discussion on thought experiments (see Hopp 2014; Wiltsche 2018). Fifth, the mental–model account also relates naturally to the most intriguing discussions about the role of literary fiction in thought experiments.

Some have placed “literary fiction on the level of thought experiments” (Swirski 2007, p. 6). There are two readings of such a claim. According to the first, some literary fiction may be of cognitive power due to the fact that they are thought experiments. In other words, we shouldn’t outright reject the idea that literature can be of cognitive value. Dystopian novels such as Orwell’s 1984 and Huxley’s Brave New World are obvious examples. According to the second reading, the power of thought experiments is partially a function of the narrative that conveys it. The work of Novalis remains relevant for the exploration of this link between narrative development and thought experiment: experimental writing and experiments on imagined scenarios go hand in hand; words and thoughts coincide; mind and matter are entangled (see Daiber 2001). According to the mental–model approach, both readings have a valid point. Literary fiction and narratives of thought experiments can be powerful in establishing mental models in such a way that we can even learn new things about the world at times from the fictional elements of them. The common denominator is the work on mental models each may facilitate. It is in this context that an appreciation can grow for Catherine Elgin’s theory of exemplification to argue against the “valorization of truth in epistemology” (2004, p. 113). This is also the place to consider Andras Kertesz’s (2015) work on conceptual metaphor research in its relevance to the epistemological puzzle that thought experiments pose.

Finally, sixth, mention could be made of visual reasoning in mathematics, which often seems closely related to thought experiments. The standard view of mathematics is that the one and only source of evidence is a proof, and a proof is a derivation from axioms or first principles. Let’s overlook the problem of where the first principles come from. A simple example such as the following casts doubt on the standard view:

Theorem: 1 + 2 + 3 + … + n = n 2 /2 + n/2 Proof: See Figure 7.

Figure 7. Picture proof.

The proof works like this: Start at the top and work down, letting the little squares represent numbers, 1 + 2 + 3 + 4 + 5 . The total number of squares in the picture is equal to this sum. Notice also that the numbers of squares is equal to a large square with sides of length 5 that is cut in half along the diagonal, i.e., 5 2 /2 , plus the shaded bits that were cut off by the diagonal cut, i.e., 5/2 . It is plausible to claim that the diagram is a perfectly good proof of the theorem. One can “see” complete generality in the picture. Even though it only illustrates the theorem for n = 5 , somehow we can see that it works for every number, all infinitely many of them. The diagram does not implicitly suggest a “rigorous” verbal or symbolic proof. The regular proof of this theorem is by mathematical induction, but the diagram does not correspond to an inductive proof at all, since the key element in an inductive proof is the passage from n to n + 1 . The simple moral we could draw from the example is just this: We can in special cases correctly infer theorems from pictures, that is, from visualizable situations. There is an intuition and from this intuition we can grasp the truth of the theorem (see Brown 1999 [2008]).

Our assessment of the prospects of the mental–model account is very rough and speculative, though certainly not implausible. Of course, there are challenges to such a vision of a greater synthesis of the many different takes on thought experiments under the umbrella of the mental-model account. For example, some see additional support arising for the argument–view from computer simulations (see Beisbart 2012). Others find that “computational modeling is largely replacing thought experimenting, and the latter will play only a limited role in future practice of science, especially in the sciences of complex nonlinear, dynamical phenomena” (see Chandrasekharan et al. 2012, p. 239). But, there are also proposals such as that by Marcus Schulzke (2014) to think of video games philosophically as executable thought experiments. Whatever the merits of this particular proposal, future explorations of the relationship between computer simulations and thought experiments can build on outcomes of closer inquiries into it (see Behmel 2001, pp. 98–108; Di Paolo et al . 2000; El Skaf and Imbert 2013; Lenhard 2011; Stäudner 1998; Lenhard 2018). The work on the nature of the importance of scientific understanding (see, e.g., Stuart 2018) will inform that exploration as much as the fruits of continuing efforts to clarify the role of the imagination in thought experiments (see, e.g., Meynell 2014; Stuart 2017 and 2021).

We conclude with an interesting, but still relatively unexplored issue that concerns the relative importance of thought experiments in different disciplines. Physics and philosophy use them extensively. Chemistry, by contrast, seems to attract less attention in this respect. Why is this the case? Perhaps it is merely an historical accident that chemists never developed a culture of doing thought experiments. Perhaps it is tied to some deep feature of the discipline itself (see Snooks 2006). Economics and history use thought experiments, but apparently not anthropology. A good explanation would likely tell us a lot about the structure of these disciplines.

Related to this is the question of the difference, if any, between thought experiments in the sciences and those in philosophy. We have assumed throughout this entry that they are the same kind of thing. Not everyone sees them this way, so perhaps it should be considered an open question. On the one hand, philosophy and science seem to many to be different kinds of activities. That might suggest that thought experiments would differ in the two areas. On the other hand, there is a huge difference between thought experiments within a single field, e.g., Newton’s bucket attempts to establish absolute space while Schrödinger’s cat aims to show QM as then understood to be absurd. Is the difference between them less than the difference between either of them and Searle’s Chinese Room or Thomson’s violinist? The case one way or the other is not obvious. Of course, there are differences between constructive and destructive thought experiments, but this is true within any discipline. Perhaps for now the default attitude ought to be that there is no categorical difference between scientific and philosophical thought experiments. This should not be treated as a dogmatic principle, but rather a stimulus to look deeper for important subtle contrasts.

The number of papers, anthologies, and monographs has been growing immensely since the beginning of the 1990s. It might be useful to highlight that in existing literature, Kühne (2006) remains the most substantial historical study on the philosophical exploration of thought experiments. And Sorensen (1992) remains the most comprehensive philosophical study of thought experiments. More than other monographs both of these studies well exceed the author’s own systematic contribution to what is widely considered the primary epistemological challenge presented by thought experiments. Also, this bibliography does not include the many (we count about eight) popular books on thought experiments (like Wittgenstein’s Beetle and Other Classical Thought Experiments by Martin Cohen); nor do we list fiction that is related to the subject (like The End of Mr. Y by Scarlett Thomas, or God’s Debris by Scott Adams). Further, for undergraduate teaching purposes one might want to consider Doing Philosophy: An Introduction Through Thought Experiments (edited by Theodore Schick, Jr. and Lewis Vaughn, fifth edition, 2012, Boston: McGraw Hill Higher Education), and chapter 5 of Timothy Williamson’s short introduction to philosophical method (Oxford University Press, 2020). Moreover, a number of philosophical journals have dedicated part or all of an issue to the topic of thought experiments, including the Croatian Journal of Philosophy (19/VII, 2007), Deutsche Zeitschrift für Philosophie (1/59, 2011), Informal Logic (3/17, 1995), Philosophica (1/72, 2003), Perspectives on Science (2/22, 2014), Berichte zur Wissenschaftsgeschichte (1/38, 2015)), as well as TOPOI (4/38, 2019), HOPOS (1/11, 2021), and Epistemologia (12/2022). Furthermore, a companion to thought experiments exists now: The Routledge Companion to Thought Experiments was published in 2017. Each includes substantial state of the art reports. The bibliography that follows aims to list only publications that address thought experiments as such. Not included are the many specialized papers that discuss a particular thought experiment in its systematic contribution to the discussion of a particular issue (such as Putnam’s twin earth scenario to support semantic externalism). An exception is made, of course, when such work is cited. Unlike in previous versions of this entry, we no longer aim for comprehensiveness in the bibliography that follows.

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• Thought Experiments , entry in the Oxford Bibliographies , by James R. Brown and Michael T. Stuart.
• Thought Experiments and Religion , entry in the Oxford Encyclopedia of Religion , by Yiftach Fehige.
• Goodies , a collection of intriguing questions in the philosophy of science, some about thought experiments, by John Norton.
• An Interactive Version of Thomson’s violin thought experiment .
• Six famous thought Experiments Explained Quickly , a video tutorial.
• Ethical Thought Experiments Like the Trolley Dilemma , a video tutorial.

Descartes, René | Galileo Galilei | intuition | Leibniz, Gottfried Wilhelm | Mach, Ernst | moral psychology: empirical approaches | Platonism: in metaphysics | rationalism vs. empiricism

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Thought experiments have been a source of creative and philosophical thinking since the days of ancient philosophers. From the Socratic method to Descartes' wax analogy, thought experiments have been used to explore the boundaries of our understanding and push the limits of our imagination. This article explores the use of thought experiments in both creative and philosophical thinking, offering insights into how they can be used to expand our horizons and challenge our preconceived notions. Thought experiments are a powerful tool for making connections between different disciplines and exploring the complexity of human thought. By using them to examine our assumptions and beliefs, we can gain valuable insights into ourselves and the world around us.

Thought experiments can also provide us with the opportunity to break free from our traditional methods of reasoning and engage in imaginative exploration. Through this process, we can uncover new perspectives, develop innovative ideas, and explore new possibilities. This article will provide an overview of thought experiments, exploring their history, principles, and uses. We will discuss how thought experiments can help us to think more creatively and analyze philosophical problems. We will also explore how thought experiments can be used to generate new ideas and challenge existing assumptions.

This experiment explored whether or not a computer could possess genuine understanding or intelligence. The experiment consisted of a person sitting in a room with no knowledge of Chinese language or culture. The person was presented with slips of paper containing Chinese symbols, and instructed to put together responses based on a set of rules they had been given. The question posed by the experiment was whether or not this person truly understood the Chinese symbols, or if they were merely following instructions.

The Chinese Room experiment has been widely discussed in philosophical circles since it was first proposed. It has been used to explore questions about artificial intelligence, the limits of computers, and the nature of understanding. Thought experiments can also be used to explore creative ideas. Artists often use them as a way of sparking new ideas and exploring creative solutions to problems. One example is the “Ladder of Inference” thought experiment proposed by Chris Argyris in 1974. This experiment explores how we make assumptions about the world based on our experiences.

How Can I Get Started With Thought Experiments?

What are the benefits of thought experiments.

They provide an opportunity to explore different ideas and concepts in a safe environment without any negative consequences. They also allow us to gain greater insight into our own thinking processes and develop better strategies for dealing with difficult situations. Additionally, they can help us develop new ways of looking at the world and become more creative thinkers. Thought experiments offer an invaluable opportunity to explore the boundaries of our knowledge, creativity, and philosophical thinking. By engaging in thought experiments, we can gain a better understanding of how our thoughts shape our lives and the world around us.

By taking the time to reflect on our experiences, think outside the box, and explore different scenarios, we can become more creative and develop new perspectives. Thought experiments are a powerful tool for expanding our horizons and pushing the boundaries of our thinking.

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15 Philosophical Thought Experiments That Will Definitely Blow Your Mind

• April 19, 2023 July 30, 2024

Philosophical thought experiments are hypothetical situations that are intended to help with the exploration of complex philosophical concepts and issues. These hypothetical situations frequently put our presumptions to the test, stimulate our curiosity, and highlight the boundaries of our understanding.

Philosophical thought experiments, which have been a crucial component of philosophical research for millennia and are still relevant and thought-provoking today, ranging from Plato’s Cave to the Trolley Problem.

This blog examines  15 of the most intriguing and perplexing philosophical thought experiments , which will test your understanding of reality and pique your interest in philosophy.

Table of Contents

1. THE SHIP OF THESEUS

If a ship’s parts are to be replaced over time, is it still the same ship.

The Ship of Theseus , one of the well-known philosophical thought experiments, raises questions about the nature of identity and continuity over time. In the paradox, the question is whether a ship that has had all its components replaced throughout time is still the same.

On the one hand, asserting that the ship has not altered despite having some of its components replaced would make sense. After all, we still call it by that name, and the structure and goals it was intended for are still in place.

On the other hand, if the ship’s identity is based on its physical attributes, it would appear that the ship has changed. One can argue that the ship is now a totally distinct entity if every component is replaced.

This paradox highlights issues regarding the nature of identity and change , which have consequences beyond the context of ships.

It makes us wonder if something can endure significant change while remaining essentially the same throughout time and how we can tell when something has altered fundamentally enough to be the same thing no longer.

2. THE TROLLEY PROBLEM

Would you sacrifice one person to save many people.

The Trolley Problem is a famous ethical thought experiment that challenges the ethics of sacrificing one life to save many others. Typically, the hypothetical situation is as follows:

You’re standing next to a tram track, watching as a runaway tram approaches five people who are chained to the track and unable to escape. However, if you notice a nearby lever, the tram would be diverted onto a different track, killing the person connected to that track in its place. What do you do?

This puzzle challenges us to think about our moral responsibilities when we have the authority to make a choice that will cause someone’s death. The alternative that saves the most lives may appear logical. Still, it’s vital to consider the worth of each life and whether we have a responsibility to defend the rights of the minority.

The “right” decision may differ according to two central ethical doctrines. A consequentialist, for instance, would save the lives of the five people would be the ethically correct choice since it maximises total well-being.

On the other hand, a deontologist could contend that we have a responsibility to defend people’s rights and that doing so would be against the law.

The Trolley Problem has no apparent solution, yet it is a helpful tool for investigating ethical quandaries and the ideas that influence human decision-making .

3. ALLEGORY OF THE CAVE

Are we merely seeing the shadows of reality or the reality itself.

Plato’s “Allegory of the Cave” is one of the well-known philosophical thought experiments concerning the nature of reality and knowing/knowledge. The allegory is as follows:

I magine a group of people who have spent their entire lives chained up and facing a wall within a cave. They can only see the shadows of things that the fire behind them has cast onto the wall. They believe that these shadows are the only reality that exists.

If one of the prisoners were forced to turn around and face the fire, then that prisoner would experience a new reality and realise that the shadows were mere illusions. Let’s say that the prisoner is now allowed to leave the cave and come in contact with the real world outside. When they encounter the outside world, they would have come across another reality different from the cave and the fire.

Plato’s allegory makes us wonder if our perceptions of reality are accurate or only reflections of a more profound, underlying truth.

It implies that there might be truths that go beyond our current comprehension and that our opinions and knowledge may be constrained by the situations in which we find ourselves. Many consider Plato’s Cave a defence of philosophical inquiry and the quest for knowledge. It implies that we might be able to learn more about ourselves and the world around us by challenging our presumptions and looking for the essence of truth .

4. THE CHINESE ROOM

Can a machine understand or mimic language.

In The Chinese Room thought experiment, the question of whether a machine can genuinely understand language or merely mimic it. This experiment is as follows.

A non-Chinese-speaking person is locked in a room with a book filled with Chinese symbols and a set of instructions for manipulating the symbols.

A person from outside passes a note to him written in Chinese. The person inside the room responds to the note as per the regulations before passing the note back to the person outside.

It may appear that the person inside the room may understand Chinese to the person receiving the note outside. However, the individual within the room only follows instructions; they do not genuinely understand the significance of the messages they are responding to.

This experiment presents an interesting understanding of the nature of consciousness, artificial intelligence, and whether a machine can truly “understand” language like a human can.

It makes us wonder if knowledge and intellect come from simply adhering to rules and manipulating symbols or if something deeper in human consciousness enables us to comprehend language .

5. BURIDN’S ASS

Are we really free to choose.

This experiment is quite interesting. Buridan’s Ass illustrates the paradox in the concept of free will. It refers to a situation where a donkey (equally hungry and equally thirsty) is placed at the centre of a stack of hay and a pail of water. Both of them are equidistant from the donkey. Which one does it choose first?

The paradox claims that since the donkey cannot choose between water or hay, it dies of hunger. There are other versions of this story. Instead of water and hay, two equally sized pile of hay is placed at equidistant from the donkey instead of water and hay. The result: the donkey dies.

But is it as simple as that? Probably not. The donkey may eat first and drink later. Or drink first and eat later, and then drink again.

But these are just random—as it does not require us to be rational. We just need common sense.

While this paradox has been attributed to a 14 th -century French philosopher Jean Buridan, the traces of Buridan’s Ass paradox are found in the Aristotelian era.

In On the Heavens (295-350 BCE), Aristotle writes: “…a man, being just as hungry as thirsty, and placed between food and drink, must necessarily remain where he is and starve to death”.

6. THE EXPERIENCE MACHINE

Would you plug into a machine that gives a perfect life simulation, not real experiences.

This philosophical thought experiments is as follows: Imagine there exists a machine that can simulate perfect life experiences, where one can feel and experience anything they desire without suffering any consequences.

They couldn’t tell the difference between the simulation and the real world since this ideal life simulation would be so believable. Then, this experiment asks whether you would plug into this machine and spend the rest of your life in the virtual world.

There are two schools of thought on it. Some argue that since the machine allows people to feel happiness and pleasure without negative consequences, they would plug into it. For them, regardless of whether an experience is real or not, it is the experience that counts.

Others contend that true experiences give life meaning and that sustaining in the virtual world would ultimately cause dissatisfaction.

The experience machine experience poses significant questions concerning the origins of pleasure, happiness, and the worth of genuine experiences.

It prompts us to wonder if we could forgo our actual experiences in favour of the appearance of joy and pleasure and whether such a sacrifice would eventually be worthwhile.

7. THE PRISONER’S DILEMMA

Should you cooperate or defect in a situation where your decision affects others and vice versa.

The Prisoner’s Dilemma is a popular game theory scenario that explores how to strike a balance between self-interest and collaboration. The process is as follows:

Imagine that you and another person are both under investigation for a crime. You are both detained in separate jail cells and cannot communicate with one another.

The prosecution makes the same deal to both of you: in exchange for your cooperation and silence, you will both receive a reduced sentence.

However, if one of you betrays the other and comes forward with a confession while the other refuses to speak, the betrayer will get a reduced sentence while the other gets a harsher one. You will both receive reduced sentences if you both confess.

The dilemma is that it is reasonable to betray the other person regardless of what they do from a purely self-interested perspective. If the other party doesn’t say anything, confessing will guarantee a less penalty.

If the other party admits, admitting will, at the very least, result in a mild penalty, preferable to a harsher one.

However, instead of the lighter sentences, they would have received if they had cooperated, they each receive moderate punishments if both parties betray one another.

The Prisoner’s Dilemma experiment poses significant issues regarding the harmony of self-interest and collaboration .

It makes us wonder if cooperation is always the right course of action, even when it seems counter to our self-interest, and if betraying people ultimately serves our best interests.

8. THE SORITES PARADOX

At what point does a small change in quantity lead to a change in quality.

The Sorites Paradox is one of the philosophical thought experiments which ventures into the nature of limits and how we define them. Here is how it follows:

Imagine a mound of sand with a million grains in it. The pile of sand is unaffected by the removal of even one grain. Even if another grain is removed, it remains a sand pile.

This cycle continues until only a few sand grains are left. When does a sand mound stop becoming a pile? In other words, when does a small change in quantity cause a big difference in quality?

It poses significant issues regarding how we classify things, happenings, and experiences and if there is a definite line dividing one category from another. It also has ramifications for comprehending our decision-making processes and how we view the world.

The Sorites Paradox can be applied to other aspects of life, such as moral judgements, political categorisation, and scientific classification, and is not just applicable to sand or tangible objects.

The paradox forces us to reflect on the limitations of language and how the categories we employ to make sense of the world affect how we see it .

9. THE OMNIPOTENCE PARADOX

Can an all-powerful create a task it cannot complete.

The “Omnipotence Paradox” is one of the philosophical thought experiments that challenge the idea of omnipotence, or that a being has limitless power. The philosophical thought experiment is as follows:

Is it possible for an all-powerful deity to create a task that it cannot complete? Even if it can come up with such a task, it is not all-powerful because it cannot do it. If it cannot create such a work, it is limited by its incapacity and thus is not all-powerful.

The Omnipotence Paradox poses significant questions regarding the scope of power and the nature of omnipotence. It questions whether a being can have endless power and makes us wonder if the idea of unlimited power is fundamentally paradoxical.

It also has ramifications for comprehending the characteristics of divine beings and the limits of human understanding of religious concepts .

10. PARFIT’S SPLIT-BRAIN

How do we define and measure consciousness, and how does it relate to our senses of self.

Parfit’s Split Brain, another such philosophical thought experiments, explores the ideas of individual identity and consciousness in the context of split-brain patients. The steps are as follows:

Imagine a person having a surgical procedure where the left and right hemispheres of their brain are surgically separated from one another.

Then, a distinct visual stimulus—such as an image or word—is presented to each hemisphere. Each hemisphere controls the opposing side of the body; therefore, when asked to describe what they observed, the subject can only use one hand.

Parfit’s Split Brain raises questions regarding the basis of personal identity and consciousness. Which of the two brain regions best represents the true self when exposed to numerous stimuli and reacting in varied ways?

Do they have two separate selves, or are they still just one person with two minds? How is consciousness measured, how is it defined, and how is consciousness related to our sense of self?

The Split Brain experiment has implications for patients who undergo split-brain surgery for medical reasons. It also has broader implications for understanding identity, consciousness, and the relationship between the brain and the self .

The experiment fascinates people today and has been the subject of extensive philosophical and scientific study.

11. THE SWAMP MAN

What constitutes a person’s identity.

The Swamp Man is a philosophical thought experiment exploring personal identity and what constitutes an individual’s identity. The instructions are as follows:

Imagine a person hiking in a remote swamp when a tree is struck by lightning, killing him instantaneously. At the same time, a bolt of lightning strikes a marsh, completely recreating the man’s physique down to the last molecule.

This copy, which did not exist before the lightning struck, holds the man’s memories and beliefs. Is this new being still the same person as the original person, or is it a completely different entity?

The Swamp Man experiment challenges our conceptions of what defines a human. It makes one wonder whether bodily continuity, memory, and consciousness are crucial components of personal identity.

It also makes us ponder if identity is a concept that outside forces can determine or whether it results from our own experiences and self-awareness.

12. THE UTILITY MONSTER

Should the happiness of one individual outweigh the happiness of many.

The Utility Monster is one of the philosophical thought experiments that explore the utility and how it relates to moral judgement. The procedure is as follows:

Imagine a being, let’s call it a Utility Monster, significantly more capable of experiencing joy and happiness than any other living creature. The Utility Monster enjoys and is happier than any other being at any given time.

According to utilitarianism, a moral theory that believes that deeds are ethically correct to the degree that they maximise overall happiness or “utility,” the Utility Monster’s preferences should be given more weight than those of other beings.

This implies that it would be morally acceptable to grant the Utility Monster’s wishes, even if doing so might harm others.

The Utility Monster experiment highlights concerns about the influence of personal preferences on moral consequences and tests our grasp of how to make ethical decisions.

It also draws attention to the dangers of a strictly utilitarian view of morality, which could lead to sacrificing many people’s well-being for the advantage of a select few.

The Utility Monster thought experiment explores the limitations and potential flaws of utilitarianism . This moral theory maintains that actions are morally acceptable to the extent that they maximise overall happiness or “utility.”

The experiment questions the idea that maximising overall happiness is always morally right by introducing the idea of a being that enjoys significantly more pleasure and satisfaction from any given experience than any other being does.

The Utility Monster experiment significantly impacts ethical theory because it forces us to consider how much personal preferences and rights factor into moral judgements.

It also raises the question of how we strike a moral balance between the interests of various individuals and social groups and whether such a balance can be reached.

Overall, the Utility Monster experiment is an intriguing and stimulating illustration of how philosophical thought exercises can upend our presumptions and encourage us to consider fundamental issues regarding the nature of morality and ethical judgement.

13. THE VEIL OF IGNORANCE

Would you create a fair society if you did not know your place in it.

This is my favourite!

The Veil of Ignorance is another philosophical thought experiment that invites participants to see themselves in an initial position of equality behind a veil of ignorance, not knowing their social status, abilities, or place in society.

Philosopher John Rawls proposed it.

This exercise aims to get people to consider the principles of justice that would be applied in this case without considering their own interests or social standing.

Behind the curtain of ignorance, people would choose justifications that would be advantageous to all, irrespective of their particular circumstances, thus establishing a “fair society” .

14. THE PROBLEM OF EVIL

If god is all-powerful and all-good, why does evil exist in the world.

The Problem of Evil conundrum poses the question of how to reconcile the existence of evil and suffering in the universe with the belief in an all-knowing, all-powerful, and all-good God.

It is stated that if God is all-powerful and all-knowing, they can prevent or stop evil and suffering; if God is all-good, they would prefer to do so.

If God is all-knowing, then they is aware of all the evil and suffering in the world. Therefore, it would seem that the existence of evil and suffering cannot coexist with the existence of an all-knowing, all-powerful, and all-good God.

There has been a lot of debate and discussion around the concept of evil in theology and philosophy.

15. MARY’S ROOM

Is there more to conscious experience than just physical processes in the brain.

Philosopher Frank Jackson propounded Mary’s Room to refute the physicalist theory of the mind-brain connection. The experiment is as follows:

Mary, a talented scientist, has lived her entire life in a room with a TV monitor in black and white. She knows everything there is to know about colour vision, but she has never seen colours.

After being let out of the room one day, she notices a red apple. Despite never having experienced colour vision firsthand, the question is whether Mary learns anything new about what it’s like to see red or if she already knew everything there was to know about it.

In the thought experiment, Mary already knows all the physical details of colour; therefore, whether she discovers anything new when she sees it for the first time.

If she does pick up new information, it implies that physicalism is not a comprehensive account of the mind-brain interaction and that conscious experience involves more than just the physical functioning of the brain.

If she doesn’t discover anything new, physicalism may be true, and all our experiences can be described in terms of physical processes.

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Top 10 Most Famous Thought Experiments

Thought experiments are mental concepts or hypotheses, often resembling riddles, which are used by philosophers and scientists as simple ways of illuminating what are usually very dense ideas. Most often, they’re used in more abstract fields like philosophy and theoretical physics, where physical experiments aren’t possible. They serve as some hearty food for thought, but given their complex subject matter, it’s not unusual for even the thought experiment itself to be nearly incomprehensible. With this in mind, here are ten of the most famous thought experiments , along with explanations of the philosophical, scientific, and ethical ideas they work to explain:

10. The Trolley Problem

One of the most well known thought experiments in the field of ethics is the “Trolley Problem,” which goes something like this: a madman has tied five innocent people to a trolley track. An out of control trolley car is careening toward them, and is moments away from running them over. Luckily, you can pull a lever and divert the trolley to another track. The only problem is that the madman has also tied a single person to that track. Considering the circumstances, should you pull the lever?

What it Means:

The trolley problem was first proposed by the philosopher Philippa Foot as a means of critiquing the major theories in ethical philosophy, in particular utilitarianism, the system which proposes that the most moral decision is always the one that provides “the greatest good for the greatest number.” From a utilitarian point of view, the obvious choice is to pull the lever, saving five and only killing one. But critics of this theory would state that in pulling the lever you become complicit in what is clearly an immoral act—you are now partially responsible for the death of the lone person on the other track. Others, meanwhile, argue that your mere presence in the situation demands that you act, and that to do nothing would be equally immoral. In short, there is no wholly moral action, and this is the point. Many philosophers have used the trolley problem as an example of the ways that real world situations often force individuals to compromise their own moral codes, and that there are times when there is no totally moral course of action.

9. The Cow in the Field

One of the major thought experiments in epistemology (the field of philosophy that deals with knowledge) is what is known as “The Cow in the Field.” It concerns a farmer who is worried his prize cow has wandered off. When the milkman comes to the farm, he tells the farmer not to worry, because he’s seen that the cow is in a nearby field. Though he’s nearly sure the man is right, the farmer takes a look for himself, sees the familiar black and white shape of his cow, and is satisfied that he knows the cow is there. Later on, the milkman drops by the field to double-check. The cow is indeed there, but it’s hidden in a grove of trees. There is also a large sheet of black and white paper caught in a tree, and it is obvious that the farmer mistook it for his cow. The question, then: even though the cow was in the field, was the farmer correct when he said he knew it was there?

The Cow in the Field was first used by Edmund Gettier as a criticism of the popular definition of knowledge as “justified true belief”—that is, that something becomes knowledge when a person believes it; it is factually true; and they have a verifiable justification for their belief. In the experiment, the farmer’s belief that the cow was there was justified by the testimony of the milkman and his own verification of a black and white object sitting in the field. It also happened to be true, as the milkman later confirmed. But despite all this, the farmer did not truly know the cow was there, because his reasoning for believing it turned out to be based on false premises. Gettier used this experiment, along with a few other examples, as proof of his argument that the definition of knowledge as justified true belief needed to be amended.

8. The Ticking Time Bomb

If you’ve paid any attention to political discourse over the past few years—or ever seen an action movie, for that matter—then you are no doubt familiar with the “ticking time bomb” thought experiment. It asks you to imagine that a bomb or other weapon of mass destruction is hidden in your city, and the timer on it will soon strike zero. You have in your custody a man with knowledge of where the device is planted. Do you resort to torture in order to get him to give up the information?

Like the trolley problem, the ticking time bomb scenario is an ethical problem that forces one to choose between two morally questionable acts. It is most often employed as a counter argument to those who say the use of torture is inexcusable under any circumstances. It’s also used as an example of the way laws—like those the U.S. has against torturing prisoners—will always be set aside given extreme circumstances. Thanks to its fictionalized use in television shows like 24 , along with its constant position in political debates , the ticking time bomb scenario has become one of the most frequently repeated thought experiments. An even more extreme take on the problem was presented in a British news article earlier this year. That version proposes that the terrorist in question won’t respond to torture, and asks if one would be willing to resort to torturing the man’s wife and children as a means of extracting the information from him.

7. Einstein’s Light Beam

It’s a little known fact that Albert Einstein’s famous work on special relativity was spurred by a thought experiment he conducted when he was only 16 years old. In his book Autobiographical Notes , Einstein recalls how he once daydreamed about chasing a beam of light as it traveled through space. He reasoned that if he were able to move next to it at the speed of light, he should be able to observe the light frozen in space as “an electromagnetic field at rest though spatially oscillating.” For Einstein , this thought experiment proved that for his imaginary observer “everything would have to happen according to the same laws as for an observer who, relative to the Earth, was at rest.”

In truth, no one really knows for sure. Scientists have long debated how this deceivingly simple thought experiment helped Einstein make the massive theoretical leap required to arrive at special relativity theory. At the time, the ideas in the experiment contradicted the now-debunked belief in the “aether,” an invisible field through which light was believed to travel. It would be years before he could prove he was right, but this thought experiment was somehow the “germ,” as he called it, for Einstein’s theory of special relativity, one of the ideas that first established him as a towering figure in theoretical physics.

6. The Ship of Theseus

One of the oldest of all thought experiments is the paradox known as the Ship of Theseus, which originated in the writings of Plutarch. It describes a ship that remained seaworthy for hundreds of years thanks to constant repairs and replacement parts. As soon as one plank became old and rotted, it would be replaced, and so on until every working part of the ship was no longer original to it. The question is whether this end product is still the same Ship of Theseus, or something completely new and different. If it’s not, at what point did it stop being the same ship? The Philosopher Thomas Hobbes would later take the problem even further: if one were to take all the old parts removed from the Ship of Theseus and build a new ship from them, then which of the two vessels is the real Ship of Theseus?

For philosophers, the story of the Ship of Theseus is used as a means of exploring the nature of identity, specifically the question of whether objects are more than just the sum of their parts. A more modern example would be a band that had evolved over the years to the point that few or no original members remained in the lineup. This notion is also applicable to everything from businesses, which might retain the same name despite mergers and changes in leadership, to the human body, which is constantly regenerating and rebuilding itself. At its heart, the experiment forces one to question the commonly held idea that identity is solely contained in physical objects and phenomena .

5. Galileo’s Gravity Experiment

One of the earliest thought experiments originated with the physicist and astronomer Galileo . In order to refute Aristotle’s claim that the speed of a falling object is dictated by its mass, Galileo devised a simple mental example: According to Aristotelian logic, if a light object and a heavy object were tied together and dropped off a tower, then the heavier object would fall faster, and the rope between the two would become taut. This would allow the lighter object to create drag and slow the heavy one down. But Galileo reasoned that once this occurs, the weight of the two objects together should be heavier than the weight of either one by itself, therefore making the system as a whole fall faster. That this is a contradiction proved that Aristotle’s hypothesis was wrong.

One of the most famous stories about Galileo is that he once dropped two metal balls off the Leaning Tower of Pisa to prove that heavier objects do not fall faster than lighter ones. In actuality, this story is probably just a legend; instead, it was this elegant thought experiment that helped prove a very important theory about gravity: no matter their mass, all objects fall at the same rate of speed.

4. Monkeys and Typewriters

Another thought experiment that gets a lot of play in popular culture is what is known as the “infinite monkey theorem.” Also known as the “monkeys and typewriters” experiment, the theorem states that if an infinite number of monkeys were allowed to randomly hit keys on an infinite number of typewriters for an infinite amount of time, then at some point they would “almost surely” produce the complete works of Shakespeare. The monkeys and typewriters idea was popularized in the early 20 th century by the French mathematician Emile Borel, but its basic idea—that infinite agents and infinite time will randomly produce anything and everything—dates back to Aristotle.

Simply put, the “ monkeys and typewriters” theorem is one of the best ways to illustrate the nature of infinity. The human mind has a difficult time imagining a universe with no end or time that will never cease, and the infinite monkeys help to illustrate the sheer breadth of possibilities these concepts create. The idea that a monkey could write Hamlet by accident seems counterintuitive, but in fact it is mathematically provable when one considers the probabilities. The theorem itself is impossible to recreate in the real world, but that hasn’t stopped some from trying: In 2003, science students at a zoo in the U.K. “tested” the infinite monkey theorem when they put a computer and a keyboard in a primate enclosure. Unfortunately, the monkeys never got around to composing any sonnets. According to researchers, all they managed to produce was five pages consisting almost entirely of the letter “s.”

3. The Chinese Room

The Chinese Room is a famous thought experiment first proposed in the early 1980s by John Searle, a prominent American philosopher. The experiment asks you to imagine that an English speaking man has been placed in a room that is entirely sealed, save for a small mail slot in the chamber door. He has with him a hard copy in English of a computer program that translates the Chinese language. He also has plenty of spare scratch paper, pencils, and file cabinets. Pieces of paper containing Chinese characters are then slipped through the slot in the door. According to Searle, the man should be able to use his book to translate them and then send back his own response in Chinese. Although he doesn’t speak a word of the language, Searle argues that through this process the man in the room could convince anyone on the outside that he was a fluent speaker of Chinese.

Searle conceived the Chinese Room thought experiment in order to refute the argument that computers and other artificial intelligences could actually think and understand. The man in the room does not speak Chinese; he can’t think in the language . But because he has certain tools at his disposal, he would be able convince even a native speaker that he was fluent in it. According to Searle, computers do the same thing. They don’t ever truly understand the information they’re given, but they can run a program, access information, and give a clear impression of human intelligence.

2. Schrodinger’s Cat

Schrödinger’s Cat is a paradox relating to quantum mechanics that was first proposed by the physicist Erwin Schrödinger. It concerns a cat that is sealed inside a box for one hour along with a radioactive element and a vial of deadly poison. There is a 50/50 chance that the radioactive element will decay over the course of the hour. If it does, then a hammer connected to a Geiger counter will trigger, break the vial, release the poison, and kill the cat. Since there is an equal chance that this will or will not happen, Schrödinger argued that before the box is opened the cat is simultaneously both alive and dead.

In short, the point of the experiment is that because there is no one around to witness what had occurred, the cat existed in all of its possible states (in this case either alive or dead) simultaneously. This notion is similar to the old “if a tree falls in the woods and there’s no one there to hear it, does it make a sound?” riddle. Schrödinger originally conceived of his theoretical cat in response to an article that discussed the nature of quantum superpositions, a theory that defines all the possible states in which an object can exist. Schrödinger’s Cat also helped to illustrate just how weird the rules of quantum mechanics really were. The thought experiment is notorious for its complexity, which has encouraged a wide variety of interpretations. One of the most bizarre is the “many worlds” hypothesis, which states that the cat is both alive and dead, and that both cats exist in different universes that will never overlap with one another.

1. Brain in a Vat

There has been no more influential thought experiment than the so-called “brain in a vat” hypothesis, which has permeated everything from cognitive science and philosophy to popular culture. The experiment asks you to imagine a mad scientist has taken your brain from your body and placed it in a vat of some kind of life sustaining fluid. Electrodes have been connected to your brain, and these are connected to a computer that generates images and sensations. Since all your information about the world is filtered through the brain, this computer would have the ability to simulate your everyday experience. If this were indeed possible, how could you ever truly prove that the world around you was real, and not just a simulation generated by a computer?

If you’re thinking this all sounds a bit like The Matrix , you’re right. That film, along with several other sci-fi stories and movies, was heavily influenced by the brain in a vat thought experiment. At its heart, the exercise asks you to question the nature of experience, and to consider what it really means to be human. The idea for the experiment, which was popularized by Hilary Putnam, dates all the way back to the 17 th century philosopher Rene Descartes. In his Meditations on the First Philosophy, Descartes questioned whether he could ever truly prove that all his sensations were really his own, and not just an illusion caused by an “evil daemon.” Descartes accounted for this problem with his classic maxim “cogito ergo sum” (“I think therefore I am”). Unfortunately, the brain in a vat experiment complicates this argument, too, since a brain connected to electrodes could still think. The brain in a vat experiment has been widely discussed among philosophers, and many objections have been raised over its premise, but there is still no good rebuttal to its central question: how do you ever truly know what is real ?

68 Comments

I remember the Chinese room! I Think there was a riddle after that. I saw a similar riddle too that I wanted to share here if that was okay: 3 Gods Riddle

If you liked the one about Schrodinger’s Cat, checkout Quantum Suicide: https://thoughtexperiments.net/quantum-suicide/

Long ago (&FA) Star Trek has an episode, “The Squire of Gothos” https://en.wikipedia.org/wiki/The_Squire_of_Gothos Who’s Toys are we?

I have an axe which once belonged to Abraham Lincoln. Since then, it’s had six new heads and six new handles.

Trolley Problem Five innocent lives versus one innocent life seems like an easy decision to make when looking at it from a distance; everyone thinks that saving five people is better than saving one person and to an extent I agree. But the actual person pulling the lever knows nothing about each person, yes they are all innocent but how can that stranger pull a lever and put a value on a life during such a short and stressful situation. That one person could have done more with his life than the five people did together. Or the one person could have been getting his life back together and the five people could have been valued members of their community, involved in everything with a family and a full job. When looking at someone else’s life from the outside no one really knows what they live with and go through in their daily life. It is very hard to judge a person and put a value on their life when they are strangers. As the background information tells us that in a utopian world saving five lives is better than saving one. I think most people would agree with this. After they are saved they could go on and better their lives or change something that they have wanted to. Also in most people’s heads five of almost anything is more valuable than one. Although most people have morals and I’m sure one of them for everyone is a person should not kill another person, being put in that situation a stranger is forced to decide between five people and one person. If they don’t act they become a bystander and they will know that with them doing nothing they watched five people die and one person walk away instead of the other way around. With not knowing anything about anyone I think the stranger should pull the lever, as horrible as it is to put a value on a life saving five people sounds better than saving one.

That’s a great list; the brain in the vat experiment is particularly interesting but I’d love to try out a virtual reality. I’ve heard people saying that the The Matrix ripped off the idea but The Matrix is actually based on Simulacra and Simulacrum, a book that deals with hyperreality, written by Jean Baudrillard.

So which is it? You make two directly opposing statements:

“The probability of each keystroke is completely independant of everyother keystroke. ”

“the probability of getting tails twice in a row when fliping a coin is .25, right? But if you flip the coin and get tails once, the probability rises to .50, because the first variable has become a certainty (1.0).”

Both statements cannot be true, and indeed are not true. The first is correct, the second is the “Gambler’s Fallacy”. Prior coin tosses have zero influence on future coin tosses, just like prior keystrokes have zero influence on future keystrokes.

Keystrokes and coins are no different from each other. Each act of flipping a coin is completely independent of every other act of flipping a coin. The odds do not change just because a particular outcome already happened, or did not happen.

English can’t be your first language and/or you must have failed your one statistics course. The two statements do not counter each other at all. I’ll explain the second statement like I would to my 5 year old niece. The probability of a heads or tails is 1/2 or .5. You with me? One result of two possible outcomes. The probability of getting tails twice in a row is 1/4 or .25. One result of 4 possible outcomes (HH, HT, TH, TT). After flipping the coin once and getting a tails it limits the outcome from the first set to either TH or TT so there is now a 50% chance of flipping TT. You have a little information but no true understanding of anything and all your comments make me weep for the education system.

Maybe there is only 1 original thinker amongst us… the rest are just creations of their mind.

How can #2 be called a Paradox? Its often described as a paradox. But I don’t think its really thought of one at all by physicists. The apparent paradoxical part is the cat is both alive & dead, but what about single atoms & quantum states? They are in superposition & ill defined just like the cat. How can it even be described a paradox if the measurement problem is still unresolved? And than adding decoherence? The experiment only deals with the copenhagen interpretation & argues that it is absurd especially when scaled up to macro scale.

well ive just seen this for the first time in science and ive got to say its very interesting. the theories created arguments between me and friends =) lol any will defo be back to look in more depth

Because the state of the atom determines if the cat is alive or dead and because quantum physics proposes that the atom is in the state in which the cat is both alive and dead, it means that quantum physics do not translate into the real world. That’s why people are trying to find a Universal Theory (such as the proposed String Theory) because quantum mechanics and gravity (i.e. small math, large math) do not agree with each other, yet they are both correct in their calculations.

Well, I could explain it to you (it’s actually not hard to understand at all), but I seem to have used up all my “time to waste” (as you call it) on showing why Number 4 is not correct for any conceivable universe… 🙂 Sorry!

( But here’s a hint: The Schrodinger’s cat paradox is based on observation, just as the entire universe is based on observation. And it has nothing at all to do with anyone observing the cat. The experiment, as laid out here, is not stated correctly as a demonstration of quantum mechanics: If it were, the cat actually would be both alive and dead at the same time, in exactly the same manner as particles on the quantum scale being in multiple indeterminate states at once, until observed. )

I really don’t get Schrodinger’s Cat….. can someone dumb it down further to the level of a 10 year old for me? haha… i’ve tried reading up on quantum mechanics, but somehow my brain refuses to absorb any of it. what exactly is Schrodinger arguing against and what’s his point when actually applied in quantum mechanics?

“because there is no one around to witness what had occurred, the cat existed in all of its possible states”. this particular line doesn’t make sense to me. it’s just dead OR alive so how can anyone say that the cat existed in all of its possible states just because no one knows what happened to it? is this based on an external observer’s viewpoint?

It can. It really depends on how you want to interpret it. There’s a few ways. The one you’re thinking of is one of them.

http://en.wikipedia.org/wiki/Schr%C3%B6dinger's_cat#Interpretations_of_the_experiment

The answer given for #4 is, of course, not correct: The monkeys never can type the entire works of Shakespeare, nor any other similar volume of text, in any realistic amount of time. The reason is simple: each time a monkey starts getting a string of text right, it is far more probable that he will get next keystroke wrong than right, thus invalidating the entire string. The longer the string gets, the more improbable it becomes that the next letter will be correct. For short sequences (just a few letters) the monkey might get it right by shear chance, but for anything longer than a half dozen words, it just won’t happen. Not even in the entire age of the universe.

Think of it this way: Assume that the monkey has a keyboard that can produce 26 uppercase letters, 26 lowercase letters, and a half a dozen punctuation marks (space, full stop, comma, quotes, exclamation mark, and question mark.) That makes 60 characters. The monkey starts typing at random, and produces a “W”, which happens to be the first letter of the first line in Macbeth: (“When shall we three meet again”). Let’s say “the force is with him”, and on the next few keystrokes he hits an “h” an “e” an “n” and a space. Great! Now he has entire first word right! The problem is, on every single “next keystroke”, there are 59 ways the monkey can be wrong, and only one way he can be right. If he does not hit an “s” then everything he has typed so far is useless, the entire text must be scrapped, and he has to start again.

He is 59 times more likely to hit the WRONG key than the RIGHT one, at random. He only has a 1 in 60 chance that the next letter will be correct.

But this isn’t just a matter of adding up the letters and multiplying by 60: this is an exponential problem. The chances that he will get two letters in a row correct are one in 60×60, which is also written 60^2, which works out to 3600. So he’d need to type 3600 random keystrokes to be stand a good chance of producing the first two letters (“Wh”)

The chances of getting three letters right are 1 in 60^3 (60x60x60), which is one in 216,000. For 4 letters is one in 12,960,000. To get “When” right, he’d need to type about 13 million keystrokes! Maybe you are starting to get the picture…

Mathematically, the chances that he’ll get “n” letters correct are 60^n (“60 to the power n”, which is the mathematical way of saying “there are 60 ways of getting each of “n” letters.).

The entire first line of Macbeth (“When shall we three meet again?”) has 31 characters, so the chances of the monkey getting it right are 60^31, which is roughly one in 1,326,443,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Wow!

Let’s say this monkey types really fast, never sleeps, eats or takes vacations, and can tap out 10 characters per second. So roughly every 3 seconds he will produce a line of text that we can compare against that first line from Macbeth. How long will it take the monkey to produce that line? One sample every 3 seconds is 20 samples per minute, which is 1200 per hour, 28,800 per day, and 10,519,200 per year. Ten million samples per year! Not bad…. At that rate, it will only take the monkey a bit more than a year to type the single word “When” correctly, and about 126,097,376,067,039,332,591,704,312,114,990,000,000,000,000,000 years to get the entire first line of Macbeth correct! Well, it turns out that, so far, the entire universe has only aged about 15,000,000,000 years (give or take a billion), so that poor hard-working monkey is going to need a bit more time…

So we add more monkeys! Let’s be generous and put not just ONE monkey to work, but a BILLION monkeys to work. Cool! Between them, it will only take them about 1,260,973,760,670,393,325,917,043,121,149,900,000,000 years! That’s MUCH better, isn’t it?

Hmm, so it seems a billion monkeys working for the entire age of the universe isn’t enough. So let’s get REAL generous, and say that there will be one billion monkeys on each of one billion planets in each of one billion galaxies… how does that work out?

Turns out, we are now down to just 1,260,973,760,670,393,325,917 years! Or roughly 840,649,173,780 TIMES the age of the universe.

In other words, a billion billion billion monkeys, typing for the entire age of the universe, (ever since the Big Bang and right up to now), multiplied eight hundred and forty billion times over, stand a roughly even chance of producing ONLY THE FIRST LINE OF MACBETH correctly!!!! Just 31 characters.

Maybe now you get to see why this is such an incredibly improbable feat! And that’s just for a very simple phrase: “When shall we three meet again?”.

But Shakespeare wrote quite a bit more than just 31 characters. There are roughly 130,000 characters in “Macbeth”, so instead of the problem being just 60^31 it is actually 60^130,000 for just that one play (Macbeth). But Shakespeare wrote a total of 38 plays, 154 sonnets, two rather long poems, and several shorter poems. ….

Sorry, but that ain’t gonna happen. Not even if you could miniaturize the monkeys, and speed them up a thousand times. In fact, not even if you could get every single atom in the entire known universe typing out text at the rate of millions of characters per second! Even then, you STILL could not get the job done in any realistic amount of time. Not even in an incredibly unrealistic amount of time!

(And all of this is without even considering who is going to CHECK what the monkeys typed, compare it against the works of Shakespeare, and see if they got it right or not…)

That’s the difference between theory and reality. Yeah, with an “infinite” amount of time and an “infinite” number of monkeys you could do it, in theory, but NOT with any realistic scenario of time, monkeys, typewriters or text.

So the claim the correct answer is that all those monkeys and all those typewriters don’t stand even the vaguest chance of producing even the tiniest fraction of the works of Shakespeare. #4 is wrong.

Thank you for one of the most compete replies I have seen on Toptenz.net. Great comment.

wow… u obviously have a lot of time to waste.

the beauty of the concept of “infinity” is that compared to infinity 1,326,443,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 raised to itself is almost just like a speck of dust in this… errr…. dusty universe…. in short, unimaginable. who knows, with all those monkeys one may have been bitten by a radioactive clone of shakespeare that has given that said monkey the super power to not only remember all his works verbatim but also type it using a typewriter (heck, if i can think it then it’s probably one of the infinite possibilities, right?)……… “Realistic” has been thrown out of the window when the term “infinite” was used. u don’t need crazy mathematical skills to get the point of this thought experiment, u just need your imagination! =D

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don’t mind me…. i’m just bored.

For waaaaaaaaaayyy too many of these comments, people are not grasping a) the point of a thought experiment in the first place (it’s not literal) and b) the idea or concept behind the experiment! Infinity is a concept, a never ending number. The authors for instance never claimed that we should actually rely on monkeys to type Shakespeare. In the scenario of an infinite number of monkeys with an infinite number of typewriters, every keystroke that goes on has an infinite number of chances at being the correct keystroke, so some of the monkeys get it right one letter at a time. The odds of the next keystroke being correct as well are incredibly slim, but that is where the element of infinite time factors in. Given enough time, these monkeys WILL type every possible combination of characters imaginable, and within those possible combinations will be every written work known to man. The thought experiment never claimed that this would happen in “a reasonable amount of time.” Maybe the give away was the “infinite amount of time” factor. Regardless, please don’t waste your time attempting to poke meaningless holes in a THEOREM by which you are simply spreading your own ignorance of a concept rather than learning for yourself.

When people have to resort to insults and straw-man arguments in their vain attempt to defend an indefensible position, all that it shows is that they don’t actually have any basis for their superfluous wafflings and splutterings at all! 🙂

The point, of course, is that infinite time changes nothing: with every single keystroke, it becomes statistically more and more UNLIKELY that the monkeys can ever type the entire works of Shakespeare! I did, of course, point this out in the very first paragraph of my original post:

“The reason is simple: each time a monkey starts getting a string of text right, it is far more probable that he will get next keystroke wrong than right, thus invalidating the entire string. The longer the string gets, the more improbable it becomes that the next letter will be correct.”

Got that last part? “The longer the string gets, the more improbable it becomes that the next letter will be correct.” In other words, as time goes on toward infinity, then chance of getting it WRONG increase, not the chances of getting it RIGHT.

In other words (for those who seem to have a problem understanding basic high-school statistics, and simple logic), each time that a monkey types a letter, the chances that he will get the next letter WRONG increase EXPONENTIALLY, while the chances he will get it RIGHT only increase LINEARLY. It doesn’t take very long before the probability of getting it wrong approached infinity… And each time a monkey strikes yet another key, the probability that he will fail at the task get even closer to 1, while his chances at succeeding get closer to zero.

On the very first keystroke his chances his chances of getting that one right are very high, but on the second keystroke, the changes drop dramatically. By the twentieth keystroke, his chances are so close to zero as to be not worth mentioning, and as time progresses, his chances get every closer to zero, and not only that, they ACCELERATE towards zero.

The belief to the contrary is, of course, closely related to the gambler’s fallacy: The gambler believes that a string of unbroken losses means that his chances of winning on the next bet are improving, when in fact they are not. The inverses case for the monkeys is similar (although infinitely more negative) : A string of unbroken “wins” (hitting the correct letter) does not increase the chances of success, and in fact increases the chances of FAILURE.

And no, the fact of extending the experiment for an infinite amount of time does NOT make it more probable that the monkeys will eventually succeed: In reality, it makes it infinitely more likely that they will continue to fail, eternally. Inability to see this rather obvious implication is a clear indication of your basic misunderstanding of statistics and the concept of infinity. Despite what intuition tells you, actual reality is somewhat different. No, that’s not a personal insult: it is simply a statement of fact.

So, if you can’t grasp the simple basics of statistical analysis, then maybe you shouldn’t post unfounded opinions on the internet: That way, you could avoid embarrassing yourself further.

The mere fact that you attempted to embarrass ME into not refuting your childish position is a glaringly obvious indicator of your fear of being refuted. Which, I believe, I have accomplished rather successfully anyway. (And which, of course, is your cue to spew forth yet another unfounded, infantile response of meaningless drivel.)

The objective does become more improbable however the probability never becomes zero (impossible). Therefore given infiniate time,a period without end,it will eventually occur.

Don’t forget the infinite monkeys, infinite typewriters, and infinite time. I think you’re trapped into seeing a finite amount of monkeys. If that were the case, then the chances would be decreasing as such. But the probability of recreating such Shakespearean works given infinite monkeys, and infinite time…with the use of infinite keyboards surely must be 1. The probability of each monkey getting it is so small that it would approach zero, but the probability of one of them getting it eventually would approach 1.

Except that there is also an infinite number of possibilities that do not contain the works of Shakespeare. Thus making it possible that even with infinity and an infinite number of monkeys, they may never type the complete works of Shakespeare.

The probability of each keystroke is completely independant of everyother keystroke. The overall probability of the monkeys writing all of billy shakes’ works is inconcievably low before said monkey begins, but becomes exponentially greater each time he selects the correct key. For example, the probability of getting tails twice in a row when fliping a coin is .25, right? But if you flip the coin and get tails once, the probability rises to .50, because the first variable has become a certainty (1.0). And beside that, assuming assumingall the mokeys are working at once, one failure wastes little time or energy, because there are infinite other monkeys typing away, at least a few of them are already killing off there third or fourth character by now. Remember, nobody ever said the circumstances were possible, but given such generous circumstances it is almost certain that the works will come out in a few years.

“In other words (for those who seem to have a problem understanding basic high-school statistics, and simple logic), each time that a monkey types a letter, the chances that he will get the next letter WRONG increase EXPONENTIALLY, while the chances he will get it RIGHT only increase LINEARLY. It doesn’t take very long before the probability of getting it wrong approached infinity… And each time a monkey strikes yet another key, the probability that he will fail at the task get even closer to 1, while his chances at succeeding get closer to zero.”

Those two statistics don’t exist at the same time. They can easily even be considered the same statistic based purely on respect to temporal perspective. Each additional character required causes the initial probability of failure to approach infinity. Each additional character gotten correct, from that point on, literally decreases the amount of required characters for that instance, causing the probability of success to approach 100%. Each incorrect character merely resets the counter. The statistic you keep bringing up is more akin to a starting line and can’t change once monkeys are started typing.

What’s more damning, however, is that that “exponentially increasing” statistic is rooted in the single finite variable in the entire experiment: the length of The Complete Works of Shakespeare.

Because the length of The Complete Works of Shakespeare is finite, it will always be infinitely less than infinity. This is the crux that your argument neglects.

No matter how infinitesimally small the probability of a monkey producing The Complete Works of Shakespeare is, with infinite monkeys and infinite typewriters, you’re directly comparing a finite number to infinity.

You don’t even need infinite time. All possible occurrences are happening simultaneously with the monkeys alone and the time it takes to produce The Complete Works of Shakespeare is literally the shortest time possible for a monkey to type it. There will be an infinite amount of failures and an infinite amount of successes because everything that could ever happen will happen at once an infinite amount of times. All your calculations are ultimately meaningless because infinity breaks math. Once it’s introduced, there’s really only two numbers: infinity and not-infinity. This is why calculus is so convoluted; it bends over backwards to avoid this.

I think Chileman2020 has not in the least grasp of the word infinty. When we are talking of infinte universe, anything having probability of more than zero will recur not 1, 2 but infinite times.so even if probality of monkeys typing the series is 1X10^-100000…… it will happen infinite times.There will also be infinite harry potter collections , infinite oxford dictionaries as well as infinite times aaaaa…./bbbbb…./cccc…. etc.

There are an infinite number of numbers on the decimal line between 1 and 2, but none of them are other whole numbers. Just because you have an infinite series does NOT mean you can count on everything being contained within that series. There are still probabilities in infinite series, especially since we cannot directly observe and quantify the things within that series. That is why it can be said that in an infinite series things may be more or less likely to occur. For example, in this mind experiment it is far more likely that infinite monkeys will poop, play, mate, and fight each other than they are to make intentional keystrokes. The point of the thought experiment is to say that a RANDOM element has the ability to produce non-random things (such as all of Shakespeare). The problem is, random elements cannot be quantified.

If you put a truly random element in a scenario (monkeys are actually pretty predictable) there is NO possible world (a way of saying that no matter how you couch the mind experiment it won’t work) where you can say for certain that the truly random element will produce anything. You cannot even say that the random element will produce nothing (since it is random). Every “set” is possible to the random element but NO set can be proven actual even in an infinite space, with infinite elements, infinite time, and infinite materials. And don’t try to argue that by proving that no set can be proven I’ve proved that the set “no set can be proven” is proved. That is a logical absurdity and to argue it is to cut your own legs off.

I’m not sure my mind is working properly after those last couple of sentences I just read.

That is proof your mind is working properly. 😉

the movie inception deals with number 1 and 2! go see it

Why am I myself, rather than someone else?

This is a very basic question about life, but it may also strike someone as nonsensical. What would it mean for someone else to be me? Or, what would it mean for me to be someone else?

These questions, which are not easily addressed empirically, can be dealt with by way of thought experiments.

First, I can imagine someone else being me if a duplicate were to be made of my body, with all my features, memories, habits, etc., and then if I were to be replaced by it. This was essentially the plot of the science fiction movie The Invasion of the Body Snatchers (1956, 1978), although the duplicates in those cases were not precise copies of the replaced individuals — they were actually alien beings that were duplicates to all external appearances, but not internally. However, it is not hard to imagine true duplicates being made, especially with the kind of technology imagined for the transporter machines in the Star Trek television series. The 6th Day, a recent Arnold Schwarzenegger movie (2000), was about just such complete duplicates. Nature itself produces duplicates, but only in the very first stages of life: Identical twins are genetically the same, but their experiences and memories begin to diverge as soon as the individuals start to develop separately — something already happening in the womb. A true duplicate of an adult would require a mapping of every atom in the body, which can now more or less be done with Nuclear Magnetic Resonance Imaging (NMR or MRI) technology, and then a duplicate set of such atoms being assembled in precisely the same way, something rather further from present technology. This would not be a “clone,” as presently understood, since a clone is only genetically identical. A clone would not have the same memories as the original individual, and it would be no more and no less like the original than an identical twin would be.

Could I be replaced with such a complete duplicate — every atom, not just genetically identical — it would think that it was me. But clearly it would not be me, especially if I were not destroyed in the replacement and continued to exist off somewhere else. We can imagine that such complete identity might produce a being that would simply see itself as existing in two places at once, but this would require some kind of communication; and that would require the existence of some kind of extrasensory or paranormal connection between the two bodies, which is not now part of established science. Without such paranormal communication, the identical individuals would each think of themselves as the original individual, although only one of them would be right; and they would immediately begin to diverge as individuals because of differing experiences.

So what would be the difference between the two individuals? Well, they would exist in different spatial locations, and they would consist of different, albeit identical, atoms — and it is a postulate of quantum mechanics that all particles of the same kind are absolutely identical. I know what it would mean for me not to be that other individual, since it would not be part of my consciousness. However, what if I were to be instantaneously destroyed and replaced with that individual, so that there was, to all appearances, a spatial continuity between us, and a material continuity since, as noted, identical material particles really are identical (there is, according to quantum mechanics, absolutely nothing about them that would enable us to tell them apart). If that individual would still not be me, then there would have to be something else about me that makes me myself apart from physical content, memories, and spatial continuity. In other words, I can perform the thought experiment that would remove “me” from my body, leaving behind an individual that looked, thought, and felt like me, but was not. It would simply not have my consciousness, but another one, which could then ask over again why it is itself and not someone else.

This same kind of thought experiment can be run the other way around: What would it mean for me to be someone else? I can easily imagine suddenly waking up and having another body. Franz Kafka wrote a famous story (“The Metamorphosis,” 1915) in which someone wakes up and has turned into a cockroach. I can also imagine suddenly losing my memory and not remembering who I am. This actually happens to people occasionally. It is also possible to imagine, as in the science fiction movie Total Recall (1990), that the memories of a different person have been put into me, and I wake up, not just not remembering who I am, but actually thinking that I am someone else. Combining these would produce a very dramatic effect: I might wake up both with a very different body and thinking and believing that I am a very different person. If this left me with at least the same brain, however, we would have no difficulty imagining how this could still be “me” in some accountable sense — it would still be my brain regardless of how the body around it might change or what kind of memories might be scrambled or reprogrammed in it. Interestingly, however, our own brain is usually something that we never experience; so were body and memories to be changed, it would be difficult to verify our personal continuity short of neurosurgery. From an internal point of view, and an external one for most practical purposes, everything would be different.

Now if I imagine body, memories, and brain to be replaced, then it would be easy to say that the result could not possibly then be me. However, it is still possible to imagine that the resulting individual could be me, and this act of imagination has actually occurred in multiple world religions for centuries: it would still be me if it were the same immaterial soul. Thus, if I were to believe in reincarnation, I would actually think that I have been innumerable different persons in the past, all with different bodies, memories, and brains. As Krishna says to Arjuna in the Bhagavad Gita: “I have been born many times, Arjuna, and many times has thou been born. But I remember my past lives, and thou has forgotten thine” [4:5, Juan Mascaró translation, Penguin Classics]. Krishna, implies, of course that memories of past lives are retained by the soul. This is not necessary to the thought experiment. It is possible to imagine a soul that does not carry memories but still carries an identical consciousness that would distinguish Arjuna from another individual physically and mentally identical. Since Arjuna (and most of us) does not seem to remember any past lives, this is what is given in experience anyway.

What the thought experiments demonstrate is a truth of metaphysics that the same attributes can belong to different individuals, or in other terms that an individual as an individual cannot be exhaustively defined by abstract predicates. Thus, bodily features, memories, personality, etc. cannot uniquely determine an individual; so I cannot identify myself as an individual by any such qualities. This metaphysical principle has only been disputed by philosophers like Leibniz, who postulate the identity of indiscernibles, that individuals that cannot be told apart are actually the same individual. But such a postulate only works for Leibniz because he denies the existence of space, which can serve to distinguish otherwise identical individuals.

The spatial separation of otherwise identical individuals also can be interpreted to mean that the individuals consist of different quantities of matter. To philosophers as diverse as Aristotle, Descartes, Spinoza, and Schopenhauer, different space and different matter are ontologically identical conditions: Space itself, in effect, is matter. This may now be restated in terms of quantum mechanics: If identical subatomic particles are postulated as absolutely identical by quantum mechanics, then spatial separation, again, is the only thing that individuates identical particles as materially different.

In the thought experiments on my personal identity, spatial or material difference might seem to do the job. An identical copy of me would be spatially and materially different, and if I were replaced by an identical copy, however quickly, it is still possible to imagine that it is materially different, even if instantaneously placed in the same space. However, such a transference would result in no externally ascertainable difference whatsoever, which sounds somewhat paradoxical if were are to say that the “matter” is different. In these terms “matter” must actually be defined in such a way that it is not materially or empirically distinguishable from other matter. Another postulate of quantum mechanics is that if two things cannot be in principle distinguished, then they are the same thing. The only thing that can distinguish identical particles is their spatial location. Thus, if we say that two individuals consist of identical particles and cannot be spatially distinguished (because they are temporally contiguous in the same space), quantum mechanics would then judge that they are the same individual. That there would be a temporal difference doesn’t help, since there is no empirical criterion by which it could be determined whether the “matter” has been switched from one moment in time to another or not. The only way in which we could then say that an identical individual could replace me instantaneously in the same space and still not be me is to require that there be a form of “matter” that is not accessible to physical science. A form of “matter” not accessible to physical science, however, would not be “matter” in any familiar or common sense meaning. An immaterial substance standing in the place of what we would ordinarily call “matter,” however, would more easily be called the “soul.”

If quantum mechanics loses track of matter by only using space to individuate identical particles, the thought experiment of me becoming a different individual contrariwise loses track of space and is only able to use matter for individuation. Thus, I can imagine instantaneously acquiring a different body, different memories, and also finding myself in a different place. If that is nevertheless still me, with my consciousness, it would have to be because the “matter,” or the substantial substrate of my self, was moved to that new location, even if nothing else moved by way of the contents and characteristics of my physical and mental identity. Since such “matter” would then be inaccessible to physical science, it would be reasonable to call such a substantial substrate “immaterial”; and an immaterial substance would reasonably be the “soul.”

It may help to recall what it would mean to say that I could find myself with a different body, a different mind, and in a different location and still be me. It would mean that the conscious existence that I experience now, the conscious existence that seems to disappear in sleep, and which I imagine, or suspect, or fear may simply become nothing in death, can still be imagined as the same conscious existence even if what appears in it is a different body, a different mind, and different place. Thus, I have not become nothing and can still be me, even if I seem to be someone else, cannot remember my old self, and have appeared in a different place. This conception of conscious existence as perfectly divorced from, and so possibly perfectly empty of, content first occurs in the Upanishads, especially the great Brhadâranyaka and Mândûkya Upanishads. Advaita Vedânta then concludes it is only the Self (Âtman) that has substantial, independent existence, while physical objects only exist as illusory appearances in consciousness.

Although “matter” in the senses examined, whether physical or immaterial, is a metaphysical conception that is not accessible to physical science, the device of thought experiments to examine these issues is a perfectly legitimate procedure, not only for philosophy, but even for physical science itself: Einstein’s entire theory of Relativity was based on his own thought experiments. Thus, the basic question here, “Why am I myself, rather than someone else?” is no more dismissible than Einstein’s question about what a light wave would look like if we were moving at the velocity of light with it. The paradox, however, of ending up with a definition of “matter” that abstracts from it all identifiable qualities was not lost on Buddhism, which rejected the idea of a substantial substrate to anything. Like Hume, Buddhism adopted a kind of empiricism where the very conception of substance, whether material or immaterial, did not qualify. However, that produced its own paradoxes, since Buddhism, like Hume, could not then account for the duration in time of objects or persons. Much of Buddhism accepted the doctrine of “momentariness,” that individual objects do not abide for more than a moment, but this is considerably more paradoxical and counter-intuitive that the duration of a substantial substrate. What the Buddhist paradoxes show us is that the substrate, however intangible, is not an unnecessary hypothesis — without it, as a synthetic ground a priori (as Kant would put it), the duration of individuals cannot be accounted for.

Instead, I must appeal to the doctrine of The Origin of Value in a Transcendent Function. Both kinds of “matter” are conceptions of “Negative Transcendence,” the emptiness of existence over and above the phenomenal content of consciousness. Negative Transcendence has internal and external poles. External transcendence then corresponds to physical substance, which in terms of quantum mechanics, as we have seen, is functionally identical to space itself. Internal transcendence is then the substrate for the sense of personal identity that has been examined here in the “thought experiments on the soul.” The question left open in The Origin of Value in a Transcendent Function was in what way internal and external transcendence corresponded to each other.

Now it appears that internal and external transcendence must in an important sense be independent of each other, since external transcendence, as space, cannot account for personal identity from an internal point of view, and internal transcendence, as the “matter” of personal identity, varies independently of space and what can be accessed by physical science. Thus, for there to be personal identity, there must be more than just space and external transcendence. Such a conclusion, however, does not produce a Cartesian Dualism of material and immaterial substances existing in the same logical space, for internal and external transcendence are kept ontologically apart. They are only united through “Positive Transcendence.” Negative Transcendence, in other words, cannot be added as a transcendent object to the order of phenomenal objects. Transcendent objects are subject to the Kantian Antinomies. Rather than being added as a transcendent object to phenomenal reality, internal transcendence casts a “shadow” of Positive Transcendence on phenomenal objects: the numinosity of the self or soul in religious conceptions, or even just the “supernatural dread” associated with dead bodies or cemeteries.

The question, “Why am I myself, rather than someone else?” then, cannot be answered just with natural objects. It can only be answered with transcendence. But transcendence appears in the phenomenal world as the numinous quality of natural objects. This may be called the “soul.” The soul, as an independent, transcendent object, however, cannot be said to be established by this argument. The fact that Buddhism rejects such an object is an important clue that it is subject to the undecidability of a Kantian Antinomy. There is no doubt, on the other hand, of the numinosity of persons in Buddhism, especially as they become Bodhisattvas and Buddhas, and of the reality of karma and reincarnation, despite the denial that reincarnation is the transmigration of a substantial self. Buddhist doctrine thus expresses the paradox of Negative Transcendence as an existence which nevertheless cannot be placed as an object in conceivable (i.e. phenomenal) reality. Later this would be conceived as the “Buddha nature” of individuals, an idea that, not surprisingly, set off controversy about whether this involved a “substantialist heresy” or not. It is, indeed, a fine line, although easily drawn with the theories of Negative and Positive Transcendence.

As noted, it is a postulate of quantum mechanics that subatomic particles in the same quantum states are absolutely identical in characteristics. Although many have believed that Einstein vindicated Leibniz’s view of space, as relative, over Newton’s, this feature of quantum mechanics decisively contradicts Leibniz, for whom space does not exist and objects that are indistinguishable from each other are identical to the same thing. But indistinguishable electrons are not identical to the same thing. They are distinguished from each other by their locations in space (although their possible locations may be summed in the wave function). Leibniz, of course, could respond that what makes the electrons different is their history, and their relationship to other objects. However, while Leibniz believed that his “monads” contained their history, and a representation of their relationships, within themselves, this is not the case for electrons. Indeed, quantum mechanics rules out any such things as “hidden variables.” With an electron, what you see is what you get. And since Leibniz’s monads don’t actually interact with each other, the only terms of their history and their relationship with other objects are their motions and relationships in space. If space does not then exist, monads actually have no history and no relationships.

If we allow that identical objects, however, are distinguished by their locations in space, location in space will not work to account for identity. That is because, as an object moves, it comes to be at a different location. So if different locations serve to distinguish different objects, why does not a object become a different object by moving and coming to be in a different location? This poses a grave difficulty for the theories of matter in Descartes and Spinoza, where matter is all but indistinguishable from space itself. But space does not move around, while matter must move around, to maintain its identity. On the other hand, it is not clear that fundamental particles in quantum mechanics possess any “matter” in the traditional, substantial sense. Energy turns into electrons and positrons. Electrons and positrons collide and turn back into energy. What we see is a collections of attributes, or quantum numbers — mass, charge, spin, etc. — that looks like nothing so much as the “aggregates” (skandhas) of non-substantial existence in Buddhism.

Unfortunately, the denial of substance in Buddhism is intended to effect a denial of identity. If the problem is accounting for the identity of an object or sub-atomic particle from moment to moment, Buddhist metaphysics is specifically designed not to do this. The result is an effective thought experiment in what is required for identity: The “aggregates” are not enough. If an electron has an enduring existence, something has the mass, charge, spin, etc. that characterize it. And if the electron, as electron, ceases to exist, neither Parmenides nor Democritus would be surprised to learn that it does not simply become nothing. Mass/energy is conserved, and there are particles that carry them away. Matter will not be a Cartesian fixed quantity of “stuff” that no transformation can alter, but it will represent a durable continuity of identity, which carries the quantum attributes and can merge with other objects or itself divide into new objects.

This, indeed, is more an Aristotelian than a Cartesian view of matter. Perhaps the only difference is that Aristotelian matter only accounts for different individuals of the same kind. Something unique of its kind (sui generis) doesn’t need matter and can exist as pure form (like God or the celestial intelligences). In the argument here, however, material substance does not merely account for different things of the same kind, or for different individuals that are otherwise identical in every way, but also for the identity of anything with itself from moment to moment — and Aristotle’s substance (ousia), after all, was in the form, not the matter. A Buddhist analysis of Aristotle’s God would be that it has no self, no identity, and duration. Probably not what Aristotle wanted to say, but then he is vulnerable to the critique, since for “substance” he can only offer attributes, i.e. the form.

While Aristotle thought of form as substance, it might be noted that a curious thing happened to the terminology in the translation from Greek to Latin. Ousia is from the participle of the verb “to be” in Greek. Thus, it looks rather like essentia, “essence,” in Latin, which is from the infinitive of the verb “to be” (esse). Substantia, “substance,” itself, is entirely different, meaning to “stand under.” There is a word that means “stand under” in Greek, and that is hypokeimenon. Aristotle does not use that synonymously with ousia. He applies it, as it happens, to matter. Perhaps it would be better to translate ousia as “essence,” in which case we could take substance, the underlying thing, as always being what Aristotle associated with matter. His reluctance, however, is understandable, since he thought of matter as mere power or potential, which would disappear in God. By the time we get to St. Thomas, of course, that idea of a powerless God was unappealing.

If our concern then becomes personal identity, will the identity of material substance account for that? As I have argued, no. In physical terms alone, we know that there is a turnover of matter in our bodies. I believe that after 20 years or so, all the matter in our bodies is supposed to be different. A defendant in a legal case once even tried to argue that he was literally not the same person who had committed the crime, some twenty years plus in the past. His argument was not allowed as, indeed, we trace personal identity across that transformation. With the material objects, this can indeed produce some paradoxical results. The Stoics noticed that in their day the ship kept at Athens, which was supposed to have born Theseus to Crete, had finally been repaired so much that every single plank and other part of it was no longer original. Was it the “same” ship? In a way yes, and in a way no. With material objects, the less the original material, the less it is the original thing. There is no such ambiguity with people. And we can ask them.

Similarly, we can use the thought experiments detailed above. We can think of ourselves persisting even through transformations in body, memories, and everything else. We can even, as it happens, think of ourselves persisting through absences of consciousness. Indeed, we do that every day, as we awake from sleep. This would be challenging for Descartes, for whom the soul was essentially thinking, or for Advaita Vedanta, where the self (âtman) is essentially conscious. But it is not really a problem — consciousness is not essential to identity when the identity of consciousness from moment to moment must itself be accounted for. If personal identity requires a substantial substrate different from material existence, our word for it would be “soul.” This would be a different and more fundamental meaning for it than what soul was for the Greeks, the life force, or for Descartes, consciousness (Searle’s “mental substances”).

The remaining problem would be the epistemological one of why we believe there are substances at all. Not only Buddhism, but Berkeley and then, especially, Hume point out that since substances are behind or beneath everything we experience, we are not directly acquainted with them as such. So what is our evidence that there are such things? The Kantian argument of the “possibility of experience” is then that “substance” is a category, like causality, which is an a priori expectation about experience, not something deduced, derived, or proven from it. Our expectation that the existence of objects is durable, separable, and identical is the principle of “substance” by which we organize and understand experience. While Hume himself said that all reasonings about matters of fact are based on the relation of cause and effect, it is obvious enough that many such reasonings are also based on the persistence, independence, and identity of substance.

What Kant would ask, of course, is what we can know about a substantial soul outside the limits of a possible experience. The soul, after all, is not a natural or phenomenal object, and it is difficult or impossible to imagine how it can exist, as a substance, in the phenomenal world. Kant’s answer then is that the limits of possible experience represent the limits of our knowledge of objects, so that we do not know how it is that substantial souls can exist. An immortal soul, which would be immune to the slings and arrows of man and nature, is in that regard an unconditioned reality, the sort of thing that does not appear in phenomenal existence, either for Kant or Buddhism. Yet even Buddhism does not deny that there are unconditioned realities — most importantly Nirvana. Thus Buddhism, which is ultimately neither materialistic nor naturalistic, actually has more in common with Kant than it does with Hume or, for that matter, John Searle. The soul as a numinous reality, is fully present in the numinosity of the Buddhist Arhat, Bodhisattva, and Buddha. This is no comfort for the materialist, the skeptic, or the nihilist.

No. 5: "In actuality, this story is probably just a legend; instead, it was this elegant thought experiment that helped prove a very important theory about gravity: no matter their mass, all objects fall at the same rate of speed." True, but only in a VACUUM!

that’s what i heard too! were they on the same page about the setting (vacuum or not)? i’m a bit too lazy to research about it right now…. aristotle is probably not talking about a vacuum if he’s considering drag.

what’s wrong with aristotle’s logic? wouldn’t galileo’s reasoning be a bit off if he tied a small parachute-like contraption to a small rock and threw it off a small building?

i didn’t really pay too much attention in my physics classes so a little enlightenment would be appreciated. =)

Mass has no effect on drag. Air resistance is caused by two things, the number of particles hitting the object, and their velocity relative to the object. This has nothing to do with the objects mass, and so it doesn’t matter whether Aristotle was imagining drag or not, it still has nothing to do with mass.

To give an example, if you drop two bricks, but one is denser than than the other, they will still fall at the same rate. They have the same drag, because they are the same shape and size, but their mass is different.

This is crazy. No one is crazy enough to hook up a brain to a computer. That is cruel and unusual. It is also impossible.

I will give you proof why I am right. If this supposed 'mad scientist' created an artificial world for you, then they would never let you find out about the 'brain in a vat'. They wouldn't want you to figure out what's going on.

Also, think about what you love in life. I'm not talking about material things. I'm talking about the stars in the sky, or when flowers are blooming in spring. You can't imagine them being artificial.

Think about yourself. You KNOW you are real. I am real. We are all real.

Most importantly, God created the world for us, not a mad scientist. Read the book of Genesis in the Bible to find out how the world was created.

Please don't let yourself be brainwashed by this 'brain in a vat' nonsense. You are too smart for that.

Don't let yourself be brainwashed by the Bible. Most of the stuff in the Bible is ten times more far-fetched than this stuff. And if you are going to take the book of Genesis seriously, then you have to take it ALL seriously, which is just ridiculous considering the Bible contradicts itself every other page.

Well, all sensory experience takes place in the brain. I'm afraid that you just don't know that you aren't a brain in a vat and that your Bible is just a byproduct of the evil scientists attempts to coerce into believing your reality is real.

I KNOW I am real. I DO NOT know that you are real, nor do you KNOW that I am real. However, because the claim that I exist is not so extraordinary, it takes very little faith to take this statement as truth.

You need to re-read the Cartesian method of doubt if you don't believe it makes logical sense, because I ASSURE you it does. Descartes was an extremely intelligent man and if you haven't read any of his work, it's pretty disrespectful to discard it as "nonsense."

I actually took my time to read the bible before I discarded it as nonsense.

Your "proof" also doesn't make any sense. If you are a brain in a vat…why would the scientist care whether you knew of the possibility of you being a brain in a vat? To you, this simulated reality is 100% convincing and as "real" as the "real" universe.

"I will give you proof why I am right. If this supposed ‘mad scientist’ created an artificial world for you, then they would never let you find out about the ‘brain in a vat’. They wouldn’t want you to figure out what’s going on."

I'm still waiting for your proof. How about you read Carl Sagan to find out how the world was created. I mean, you put your faith in a document written by man as it is. Why not put your faith in a document written by a smart one? As 'aquiredthoughts' says, the bible contradicts itself every other page. It's obviously a load of rubbish.

"Also, think about what you love in life. I’m not talking about material things. I’m talking about the stars in the sky, or when flowers are blooming in spring. You can’t imagine them being artificial."

First off, our brains process all those things, including our emotional reactions to them.

"Most importantly, God created the world for us, not a mad scientist. Read the book of Genesis in the Bible to find out how the world was created."

Second, what you're arguing is that no "mad scientist is controlling us," but that God created everything that we see, hear, touch, experience, etc… Therefore, I could argue that God is the mad scientist. Essentially, God and this "mad scientist" are creating human beings in a certain way, giving them free will and the capacity to gain knowledge. The only difference is believing in God is much more socially accepted, and a person gets a reward at the end of their lifespan if they are a good person. The scientist, however, is given a negative and "cruel" connotation.

If you believe that this theory is "impossible," then what makes God so much more likely? Granted, I am not saying I believe in either option necessarily; however, I do believe that blind faith is not nearly as reliable as science or facts.

"Also, think about what you love in life. Iâ??m not talking about material things. Iâ??m talking about the stars in the sky, or when flowers are blooming in spring. You canâ??t imagine them being artificial."

This is all theoretical. Nobody is going to fly side by side a beam of light either. It’s simply brain food.

That’s one of the most illogical comments I’ve ever had the displeasure of reading.

Firstly, you make the assumption that ‘no one is crazy enough to hook up a brain to a computer’. Says who, exactly?

Secondly, you state that ‘they would never let you find out about the ‘brain in a vat”. Once again, how on earth do you know? That’s just a wild guess!

Thirdly, your thoughts are real, for they are being thought. But the stars? Saying you ‘know they are real’ has no rational reasoning behind it. Have you ever been sat down, and thought someone was standing behind you when they weren’t? Or carried on talking to a friend who had stopped a few yards back to do up their shoelaces? In these scenarios, you ‘know’ there is someone next to you – your senses deceive you. Why couldn’t the same occur in every single aspect of life?

As for ‘knowing’ that God exists, I am yet to hear a reason for doing so that does not, somewhere along the line, include a logical fallacy. Please, give me one?

Oh and finally, ‘don’t let yourself be brainwashed….you are too smart for that’. Are you actually a complete moron? It’s a thought experiment. It is actually suggesting that this is the case, only showing you that you don’t actually know if it is or not! Are you, by chance,desperately worried for the infinite number of innocent monkeys, forced into an eternity of typewriting?

These are crazy! Haven't heard but one of them!

"Descartes accounted for this problem with his classic maxim “cogito ergo sum” (“I think therefore I am”)."

You misunderstand Descartes' meaning. He posed that because you couldn't be sure that you are just a brain in a vat, this implicitly states that your mind must exist, because only that which exists can be deceived. "I think therefore I am" is therefore the ONLY statement you can make with 100% certainty. He was not "accounting for [a] problem"

Should read: "He posed that because you couldn’t be sure that you aren't just a brain in a vat"

In fact, he accounts for the demon problem by appealing to God’s existence and that He could never be a deceiver or allow us to be deceived in such a way. The person who wrote this shouldn’t just guess what Descartes said based on what he’s famous for saying, that’s sloppy stuff.

Also, wasn’t Gettier’s thought experiment called the “Sheep-Shaped Rock”? This could just be another philosopher’s version of the experiment however…

#10 – Sure, you're responsible for the death of 1 person, but you are also responsible for saving the lives of five others. And I guess it depends on who the people are. If that person on the other track was your BFF, then you would not pull the lever.

Or, if the lever acts as a dimmer and not just an on-off switch, you can switch it to the halfway position which would cause the train to derail and kill nobody.

#9 – If the farmer openly stated that he knew the cow was in the field, then yes, he technically knew where his cow was – in the field. He just didn't know where in the field.

#8 – Call the bomb squad, evacuate everyone, and throw the terrorist right next to the bomb.

#6 – Evolution is the answer to all your problems.

#5 – I'm pretty sure this one has to do with covalent bonds between atoms. If there exist no covalent bonds between the rope atoms and feather atoms, or the rope atoms and hammer atoms; then the entire hammer+feather+rope cannot be regarded as one system, it must be regarded as three.

#2 – Keyword: quantum mechanics , not real-life stuff. In real life, you can only say "you just don't know", because a partially-dead cat would be like a zombie.

#1 – Kind of like "we don't know if the universe is going backwards in time [shrinking,] not expanding" because if the universe and everything within it was indeed going backwards, our minds would be thinking backwards. Two negatives cancel out, so we'd perceive time as going forwards.

You changed the variables on some of them and then your other answers didn’t really make a whole lot of sense.

#10 the derailing train would kill the driver or whoever was in the train (not like whoever was in charge was even driving the train anyway though…)

You are totally missing the point of most of those you have commented on.

For #10, you are complicating an essentially simple moral question, and I really hope the bit about the lever acting as a dimmer was a joke.

For #8, I hope that too is meant to be a joke.

#6, what are you on about?

#5, utterly missing the point again, it’s not a matter of definition. Or, if you are actually suggesting that by fusing covalently they would suddenly fall faster, you don’t actually understand the theory of gravity…..

If some of those were actually a joke, sorry for missing it, but if not, then dear God read something on just one of these, because that was depressing to read.

If the person on the other track is a House of Representatives Rightwing Teanut, pull the lever, Quick! Pull it even if there’s no one on the other track ;’)

Failed Logic, Mooney.

Number 8 (The Ticking Time Bomb) – look up the movie Unthinkable – http://www.imdb.com/title/tt0914863/

Number 8 (The Ticking Time Bomb) poses the moral question – Is it right to torture one person in order to get information to save many more? BLOODY RIGHT IT IS! I have heard the PC brigade bleat on about Guantanamo Bay and human rights abuses going on there. So what? If it provides any information that stops another atrocity then it is right. "But some of these people may be innocent" some of you might say. My parents told me if i played with matches I might get burnt! Every one of these "innocent people" I have read about have been questionable to say the least. One of these poor, innocent chaps, released to Britain, had used a false name and passport to leave the country before being captured. Whilst I am on my soapbox, and as a British person, why are these detainees always referred to as British citizens (where i live anyway), when in fact they have been born elsewhere (usually in the middle east somewhere).

Torture the one to save the many! TOO RIGHT! If the person being tortured was a direct threat to the wooly hatted, vegetarian, petrol hating, hippy who is ranting about human rights then the hippy wouldn't be a shouting so loudly.

I wonder if you would still hold this view if the person being tortured was your mother, father siblings, children or spouse/girlfriend or even YOU?

Kleanthis01 you make the argument that our outlook is changed if our loved ones are the ones in question,but this argument works both ways. What if it was your family/friends/significant other who was trapped in said city?

Haha you sound like the byproduct of a brainwashed fascist authority paradigm… Meaning, you’re completely controlled by fear and willing to dispense of inalienable human rights for safety. This is the greatest illusionary sham ever created. Every communist and totalitarian system stems from the disposition that it knows what’s in your best interest. So long as you let fear control you, your life’s efforts will remain futile.

Except the CIA and State Dept Created both Iran and Al Quada in their current form. Maybe their leaders should be sent to Guantanamo.

I like the Brain In A Vat. Sure, The Matrix ripped off this idea, but it's still a good one. How do we know we're not just some evil entity's toy, a brain in a vat?

The only thing you can be sure of is that we exist. Yes, life may be just an impression, a lucid dream. But in order for you to be deceited, you have to exist. So life will always be true, even if it is a lie.

But you could have only just started existing your memories lies and time is infinetly divisible so your life could be infinetly small

but an infinitely small life, since time is infinitely divisible, is also infinitely large. As long as life exists as a duration, not just a single moment in time, than between its beginning and end there are an infinite number of moments

“since time is infinitely divisible,” Except, of course, that time is NOT infinitely divisible. It occurs in discrete units, just like all other fundamental phenomena of the universe. and the smallest possible measure is one Planck Time (Google it). One Planck Time is 0.000000000000000000000000000000000000000000054 seconds. Anything shorter than that is meaningless, in physics. So there are a finite number of moments between the “beginning” and the “end” of any event, including life. Your days are numbered, and so are your Planck Times. 🙂

You can’t hold that life is illusory then try to use scientific knowledge gained through that illusion. For all you know, Planck’s time unit is a complete fabrication. The only types of thought that hold weight in an illusory world are thoughts which do not depend upon that world for evidence (such as formal logic or abstract thought). Since Planck’s time unit is based upon the travel of light in a vacuum it is therefore dependent upon evidence in this possibly illusory world. Thus, it is inadmissible as evidence to disprove that time is infinitely divisible.

The “brain in a vat” is easily debunked, some of the more interesting brain teasers should have been ranked higher, as they have far more moral, scientific, or philosophical conundrums than the “brain in a vat” theory. Let’s say my brain is a simulation, furthermore, let us say that it has been since birth… take 10 children, ask them to identify a shape in a particular cloud, chances are you will receive 10 different variations in a single cloud. Now let’s go back to just me and assume I am the only one affected by the “vat,” that a particular simulation would already determine that I would think of this idea… the “program” could never account for the answers I would get from 10 random children seeing 10 very different shapes. Yes we age and it can become increasingly easy for us to believe that the world may already be run by “Skynet,” but as long as we have the abilithy to find art and random beauty in nature, I find it very hard to believe that a simulation could ever “predict” how we would perceive a natural phenomenon as witnessed not only by our own “computer generated psyche,” but how the same phenomenon would be witnessed completely different by the same “vat” mentality. Witness the world you live in through the eyes of a child and rest assured, there is no mechanical program that could ever judge how we perceive our world through the eyes of a child.

I think you are not taking into account that the same way the evil scientist is making trees appear for you to interact with he could very easily make ten kids and whatever the results of that experiment to be. Thus not proving anything but that you are now further convinced the matrix is real in your vat.

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Chasing a Beam of Light: Einstein's Most Famous Thought Experiment

John D. Norton Department of History and Philosophy of Science University of Pittsburgh, Pittsburgh PA 15260 Homepage: www.pitt.edu/~jdnorton This page (with animated figures) is available at www.pitt.edu/~jdnorton/goodies

Einstein recalled how, at the age of 16, he imagined chasing after a beam of light and that the thought experiment had played a memorable role in his development of special relativity. Famous as it is, it has proven difficult to understand just how the thought experiment delivers its results. It fails to generate serious problems for an ether based electrodynamics. I propose a new way to read it that fits it nicely into the stages of Einstein's discovery of special relativity. It shows the untenability of an "emission" theory of light, an approach to electrodynamic theory that Einstein considered seriously and rejected prior to his breakthrough of 1905.

For more details, see: "Chasing the Light: Einstein's Most Famous Thought Experiment," prepared for Thought Experiments in Philosophy, Science and the Arts , eds., James Robert Brown, Mélanie Frappier and Letitia Meynell, Routledge. Download. Sections 5-6 of "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905," Archive for History of Exact Sciences , 59 (2004), pp. 45­105. Download .

1. The Puzzle

How could we be anything but charmed by the delightful story Einstein tells in his Autobiographical Notes of a striking thought he had at the age of 16? While recounting the efforts that led to the special theory of relativity, he recalled

"...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained."

The thought is simplicity itself. Here is light, a waveform propagating at c:

If the young Einstein were to chase after it at c, he would catch up with the wave and be moving with it, like a surfer riding the wave. He would see a frozen lightwave.

The untenability of that thought led to the downfall of the great achievement of nineteenth century physics, the ether, which then provided the basis for all electromagnetic theory.

The trouble is that it is quite unclear just how this thought creates difficulties for the ether. Einstein gave three reasons and each of them could be answered readily by an able ether theorist.

So what are we to make of the thought experiment? Perhaps it is no more than the recording of the visceral hunches of a precocious 16 year old who did not even study Maxwell's theory until two years later. This is a possibility we cannot rule out. If it is correct, then we need not puzzle any further over how the thought experiment works, for there is little more to be found that illuminates Einstein's pathway to special relativity.

But then we must ask why the thought experiment merits pride of place in Einstein's defining autobiography? Does it have a cogency that extends beyond Einstein's final high school year? That Einstein mentions Maxwell's equations in the thought experiment suggests their relevance to the operation of the thought experiment and thus that this operation was pertinent to Einstein's later thought, after he had learned Maxwell's equations.

While we cannot know on the evidence available if the thought experiment truly had cogency beyond the mullings of Einstein's 16th year, we can ask if there are plausible accounts of Einstein's pathway to special relativity in which the thought experiment figures more significantly.

2. A Proposed Solution

There is a way of understanding how the thought experiment could have a significance that extended well beyond the confines of Einstein's final year at high school. The key is not to relate the thought experiment to ether theories of electromagnetism. Rather, we know that Einstein devoted some effort during the years leading up to his discovery of 1905, to so-called "emission" theories of light and electromagnetism. Einstein eventually found such theories objectionable and untenable.

I propose that Einstein's thought experiment provided an especially cogent way of formulating those objections and thereby supported Einstein in his final decision: it give up an emission theory in favor of retaining the celebrated Maxwell-Lorentz theory, but with a radically altered theory of space and time.

3. An Emission Theory of Light and Electromagnetism

On many later occasions, Einstein recalled that, prior to his discovery of special relativity, he had investigated emission theories, indicating a similarity in his approach to that used by Walter Ritz. In the then standard electrodynamics of Maxwell and Lorentz, electromagnetic action always propagated at c with respect to the ether . The simplest example was the propagation of a lightwave. But it held equally for the action of one charge upon another. It was this fact that made it seem impossible to conform the principle of relativity to electromagnetism. The ether supplied a preferred state of rest essential to the theory, but incompatible with the idea that all inertial states of motion are equivalent.

So Ritz in 1908, and Einstein sometime before 1905, tried to modify electromagnetic theory in such a way that electromagnetic effects are always propagated at c with respect to the source of the effect . If such a theory could be found, it would no longer require an ether state of rest and it would reasonable to expect that it could conform to the principle of relativity.

The animation below displays the difference . On the left, in the Maxwell-Lorentz theory, electromagnetic action propagates from a fixed point in the ether. So when two charges moving together act on each other, the source of the effect felt by one is a fixed point in the ether left behind by the moving source. Since the effect propagates from a point left behind by the moving charges, an observer moving with the charges can use this fact to determine that the charges are moving.

On the right, we see the corresponding process in a modified "emission" theory, such as devised by Ritz and Einstein. The motion of the source is added to the propagating effect. So now the effect propagates isotropically from a point that moves with the source. To see this, notice how the expanding spherical shells remain centered on the moving positive charge that is their source, just as would happen if the two charges were at rest. The propagation of electromagnetic effects can no longer be used by observers moving with the two charges to detect their absolute motion; the principle of relativity is no longer threatened .

The simplest electromagnetic action is the propagation of light. So in this theory, the velocity of the emitter--the source--is added to the velocity of the light emitted. For this reason it is known as an "emission" theory.

Promising as this must initially have seemed to an Einstein intent on restoring the principle of relativity, the emission theory was ultimately rejected by Einstein. His later correspondence and papers are littered with remarks on the problems the theory faced. Two will return as our story unfolds.

- In a letter to Paul Ehrenfest of June 1912 (and elsewhere), Einstein remarked that an emission theory ran afoul of an elementary result of optics: the physical state of a ray of light is determined completed by its intensity and color (and polarization). - In an interview with R. S. Shankland in the 1950s, Einstein remarked that the theory could not be formulated as a local field theory that is, in terms of differential equations.

In a local field theory, we reconstruct how a field evolves over time by taking its state at one instant and consulting the theory's differential field equations. These equations take the present state of the fields and tell us how rapidly they are changing. From these rates of change we can then infer the states of the field at future times. (A similar analysis tells us how the field will alter at different parts of space.)

4. Einstein's Thought Experiment in the Context of an Emission theory of Light

Let us now return to Einstein's thought experiment and imagine that its target has become an emission theory of light. We immediately see that the three objections Einstein's reports present serious obstacles to an emission theory. Let us take the three objections in order.

1. The first objection was that we don't actually experience frozen light. That is a puzzle in an emission theory of light. We must presume that there are light sources with all sorts of velocities around us. A light source moving rapidly away from us will emit a lightwave that propagates slowly with respect to us. The most extreme case is of light source moving away from us at c. That source will leave a frozen light wave behind in space, as the animation shows:

So, if an emission theory is the correct theory of light, we should expect eventually to run into frozen lightwaves, emitted by rapidly receding sources. But we experience no such thing.

2. The second objection was that frozen light was incompatible with Maxwell's equations. Why should this be a problem for an emission theory when such a theory does not employ Maxwell's equations? It will be a problem, but it takes a few steps to arrive at the conclusion. First note that an emission theory allows frozen light in ordinary circumstances; we don't need to be moving at c to find it. That means that a frozen light wave must be a part of electrostatics and magnetostatics, the theories of static electric and magnetic fields. Now Maxwell's electrodynamics evolved over the course of half a century and built on a long series of experiments in electricity and magnetism. An emission theory must adjust the theory, but it cannot alter it too radically on pain of incompatibility with those experiments. The one part of Maxwell's theory that seems most secure is its simplest part, its treatment of static electric and magnetic fields. So we would expect a successful emission theory to agree with Maxwell's theory in this simplest and most secure part.

Now we have a problem: An emission theory allows the existence of frozen light waves. But the emission theory must agree closely with the treatment of static fields in Maxwell's theory and Maxwell's theory does not admit the static fields that corresponds to frozen light waves.

3. In his third objection, Einstein lamented for the observer catching the light beam, "...For how should the first observer know or be able to determine , that he is in a state of fast uniform motion?" Of course, in the context of an emission theory, the "state of fast uniform motion" must be read as "fast uniform motion with respect to the source of the light."

At first it is not clear why it should matter at all whether the observer catching the light beam can make this judgment. It turns out to be important if the overall emission theory of light is to be deterministic ; that is, if the present state of fields and the like in space are to be able to determine how they will develop in the future. Einstein's worry is that determinism will fail. To see why, imagine that you are an observer given a waveform, but all you know of it is its state at the present instant.

Would you be able to tell whether the waveform is one that is frozen in space;

or whether it is one that is propagating past you?

Both are possible in an emission theory. Which is the case depends upon your velocity with respect to the light's source. If you are moving at c with respect to the source, the wave is frozen. If you are at rest with respect to the source, the wave is propagating at c.

Can you tell which case you have by merely looking at the waveform at an instant? You cannot. Einstein's earlier remark about light is now decisive. A light wave is fully characterized by its color, intensity and polarization and both cases agree on these properties. The waveform has no property at an instant that would enable you to tell what its future time development would be. This is indeterminism. The present state of the wave does not determine its future time development.

While this circumstance might just be just an odd incompleteness of our knowledge, it becomes a crisis if we imagine that we are not human observers but the differential equations of a local field theory. For, as we saw above, a basic function of those field equations is to take the present state of the fields and from them infer the rates of change of the field. Those rates of change then determine the time development of the waveform--whether it propagates or not and how fast it propagates. This essential function will not be possible in an emission theory, for the instantaneous state of the lightwave does not determine the rates of change of the field.

Hence , thanks to Einstein's thought experiment, we infer that an emission theory cannot be formulated as a local field theory.

We can summarize the problems brought by Einstein's thought experiment to an emission theory:

5. Conclusion

When Einstein abandoned an emission theory of light, he had also to abandon the hope that electrodynamics could be made to conform to the principle of relativity by the normal sorts of modifications to electrodynamic theory that occupied the theorists of the second half of the 19th century. Instead Einstein knew he must resort to extraordinary measures. He was willing to seek realization of his goal in a re-examination of our basic notions of space and time. Einstein concluded his report on his youthful thought experiment:

"One sees that in this paradox the germ of the special relativity theory is already contained. Today everyone knows, of course, that all attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of time, or of simultaneity, was rooted unrecognized in the unconscious. To recognize clearly this axiom and its arbitrary character already implies the essentials of the solution of the problem."

Copyright John D. Norton, December 2004. Rev. February 15, 2005. Reformatted April 14, 2005 on a transatlantic flight returning to Pittsburgh from the Israel Academy of Science and Humanities conference on Einstein.

September 1, 2015

Lost in Thought—How Important to Physics Were Einstein’s Imaginings?

Einstein’s thought experiments left a long and somewhat mixed legacy of their own

By Sabine Hossenfelder

Gedankenexperiment , German for “thought experiment,” was Albert Einstein’s famous name for the imaginings that led to his greatest breakthroughs in physics. He traced his realization of light’s finite speed—the core idea of special relativity—to his teenage daydreams about riding beams of light. General relativity, his monumental theory of gravitation, has its origins in his musings about riding up and down in an elevator. In both cases, Einstein crafted new theories about the natural world by using his mind’s eye to push beyond the limitations of laboratory measurements.

Einstein was neither the first nor the last theorist to do this, but his remarkable achievements were pivotal in establishing the gedankenexperiment as a cornerstone of modern theoretical physics. Today physicists regularly use thought experiments to formulate new theories and to seek out inconsistencies or novel effects within existing ones.

But the modern embrace of thought experiments raises some uncomfortable questions. In the search for a grand unified theory that would wed the small-scale world of quantum mechanics with Einstein’s relativistic description of the universe at large, the most popular current ideas are bereft of observational support from actual experiments. Can thought alone sustain them? How far can we trust logical deduction? Where is the line between scientific intuition and fantasy? Einstein’s legacy offers no certain answers: On one hand, his reliance on the power of thought was a spectacular success. On the other, many of his best-known thought experiments were based on data from real experimentation, such as the classic Michelson-Morley experiment that first measured the constancy of the speed of light. Moreover, Einstein’s fixation on that which can be measured at times blinded him to deeper layers of reality—although even his mistakes in thought experiments contributed to later breakthroughs.

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Here we will walk through some of Einstein’s most iconic thought experiments, highlighting how they succeeded, where they failed and how they remain vital to questions now at the frontiers of theoretical physics.

The Windowless Elevator

In his thought experiments, Einstein’s genius was in realizing which aspects of experience were essential and which could be discarded. Consider his most famous one: the elevator thought experiment, which he began devising in 1907. Einstein argued that inside a windowless elevator, a person cannot tell whether the elevator is at rest in a gravitational field or is instead being hauled up with constant acceleration. He then conjectured that the laws of physics themselves must be identical in both situations. According to this “principle of equivalence,” locally (in the elevator), the effects of gravitation are the same as those of acceleration in the absence of gravity. Converted into mathematical equations, this principle became the basis for general relativity. In other words, the elevator thought experiment motivated Einstein to make the daring intellectual leap that ultimately led to his greatest achievement, his geometric description of gravity.

Credit: Nigel Holmes

Spooky Action

Later in his career, Einstein fought hard against the tenets of quantum mechanics, particularly the uncertainty principle, which dictates that the more you know about one aspect of a fundamental particle, such as its position, the less you can know about another, related aspect of that particle, such as its momentum—and vice versa. Einstein thought that the uncertainty principle was a sign that quantum theory was deeply flawed.

During a years-long exchange with Danish quantum theorist Niels Bohr, Einstein conceived of a series of thought experiments meant to demonstrate that it is possible to violate the uncertainty principle, but Bohr dissected every one of them. This exchange bolstered Bohr’s conviction that quantum uncertainty was a fundamental aspect of nature. If not even the great Einstein could devise a way to precisely measure both the position and the momentum of a particle, then certainly there must be something to the uncertainty principle!

In 1935, along with his colleagues Boris Podolsky and Nathan Rosen, Einstein published what was meant to be his most potent critique of the uncertainty principle. Perhaps because Podolsky, not Einstein, drafted the actual text of the paper, this Einstein-Podolsky-Rosen (EPR) thought experiment was presented not as an easy-to-imagine scenario of boxes, clocks and light beams but as an abstract series of equations describing interactions between two generalized quantum systems.

The simplest version of the EPR experiment studies the paradoxical behavior of “entangled” particles—pairs of particles that share a common quantum state. It unfolds as follows: Imagine an unstable particle with a spin of zero decaying into two daughter particles, which speed off in opposite directions. (Spin is a measure of a particle’s angular momentum, but counterintuitively, it has little to do with a particle’s rate of rotation.) Conservation laws dictate that the spins of those two daughter particles must add up to zero; one particle, then, could possess a spin value of “up,” and the other could have a spin value of “down.” The laws of quantum mechanics dictate that in the absence of measurement, neither of the particles possesses a definite spin until one of the two speeding entangled particles is measured. Once a measurement of one particle is made, the state of the other changes instantaneously , even if the particles are separated by vast distances!

Einstein believed this “spooky action at a distance” was nonsense. His own special theory of relativity held that nothing could travel faster than light, so there was no way for two particles to communicate with each other instantaneously from opposite sides of the universe. He suggested instead that the measurement outcomes must be determined prior to measurement by “hidden variables” that quantum mechanics failed to account for. Decades of discussion followed until 1964, when physicist John Stewart Bell developed a theorem quantifying exactly how the information shared between entangled particles differs from the information that Einstein postulated would be shared through hidden variables.

Since the 1970s lab experiments with entangled quantum systems have repeatedly confirmed that Einstein was wrong, that quantum particles indeed share mutual information that cannot be accounted for by hidden variables. Spooky action at a distance is real, but experiments have demonstrated that it cannot be used to transmit information faster than light, making it perfectly consistent with Einstein’s special relativity. This counterintuitive truth remains one of the most mysterious conundrums in all of physics, and it was Einstein’s stubborn, mistaken opposition that proved crucial to confirming it.

Alice and Bob

Today some of the most significant thought experiments in physics explore how to reconcile Einstein’s clockwork, relativistic universe with the fuzzy uncertainties inherent to quantum particles.

Consider, for instance, the widely discussed black hole information paradox. If you combine general relativity and quantum field theory, then you find that black holes evaporate, slowly radiating away their mass because of quantum effects. You also find that this process is not reversible: regardless of what formed the black hole, the evaporating black hole always produces the same featureless bath of radiation from which no information about its contents can be retrieved. But such a process is prohibited in quantum theory, which states that any occurrence can, in principle, be reversed in time. For instance, according to the laws of quantum mechanics, the leftovers of a burned book still contain all the information necessary to reassemble that book even though this information is not easily accessible. Not so for evaporating black holes. And so we arrive at a paradox, a logical inconsistency. A union of quantum mechanics and general relativity tells us that black holes must evaporate, but we conclude that the result is incompatible with quantum mechanics. We must be making some mistake—but where?

The thought experiments created to explore this paradox typically ask us to imagine a pair of observers, Bob and Alice, who share a pair of entangled particles—those spooky entities from the EPR experiment. Alice jumps into the black hole, carrying her particle with her, whereas Bob stays outside and far away with his. Without Alice, Bob’s particle is just typical, with a spin that might measure up or down—the information that it once shared with its entangled partner is lost, along with Alice.

Bob and Alice play a central role in one of the most popular proposed solutions to the paradox, called black hole complementarity. Proposed in 1993 by Leonard Susskind, Lárus Thorlacius and John Uglum, all then at Stanford University, black hole complementarity rests on Einstein’s golden rule for a gedankenexperiment: a strict focus on that which can be measured. Susskind and his colleagues postulated that the information falling in with Alice must come out later with the evaporating black hole’s radiation. This scenario would usually create another inconsistency because quantum mechanics allows only pair-wise entanglement with one partner at a time, a property called monogamy of entanglement. That is, if Bob’s particle is entangled with Alice’s, it cannot be entangled with anything else. But black hole complementarity requires that Bob’s particle be entangled with Alice’s and with the radiation the black hole later emits even though this violates monogamy. At first sight, then, black hole complementarity seems to exchange one inconsistency with another.

But like a perfect crime, if no one actually witnesses this inconsistency, perhaps it can subvert nature’s otherwise strict laws. Black hole complementarity relies on the argument that it is physically impossible for any observer to see Alice and Bob’s entangled particles breaking the rules.

To envision how this perfect quantum-mechanical crime could unfold, imagine a third observer, Charlie, hovering near the black hole, keeping an eye on Alice and Bob. He watches as Bob stays outside and as Alice falls in, measuring the black hole’s emitted radiation all the while. In theory, information encoded in that radiation could tip off Charlie that Bob and Alice had violated the monogamy of their entanglement. To know for certain, however, Charlie would have to compare his observations not only with Bob’s measurement but also with Alice’s— inside the black hole. So he must hover at the horizon, measure the emitted radiation, then jump in to tell Alice what he has found. Amazingly enough, Susskind and Thorlacius showed that no matter how hard Charlie tries, it is impossible for him to enter the black hole and compare his information with Alice’s before they are both torn apart by tidal forces. Their grisly fate suggests no violations of quantum mechanics can ever be measured by anybody around a black hole, and so theorists can commit this crime against nature with impunity.

Suffice it to say, not all theorists are convinced that this argument is valid. One criticism of black hole complementarity is that it might violate Einstein’s equivalence principle—the one that grew out of his elevator thought experiment. Einstein’s general relativity predicts that just as the elevator’s passenger cannot distinguish between gravity and acceleration, an observer crossing a black hole’s horizon should not notice anything unusual; there is no way an observer can tell that he or she has slipped past the point of no return.

Now let us return to the entanglement of Alice and Bob. If the radiation that Bob sees from far outside the hole contains all the information that we thought vanished with Alice behind the horizon, then this radiation must have been emitted with an extremely high energy; otherwise it would not have escaped the strong gravitational pull near the horizon. This energy is high enough to vaporize any infalling observer before he or she slips past the black hole’s horizon. In other words, black hole complementarity implies that black holes have a “firewall” just outside the horizon—and yet the firewall directly contradicts the predictions of Einstein’s equivalence principle.

At this point, we have ventured deep into the realm of theory. Indeed, we might never know the solutions to these puzzles. But because those solutions could lead to an understanding of the quantum nature of space and time, these puzzles are, for better or worse, some of the most vibrant areas of research in theoretical physics. And it all goes back to Einstein’s musings about falling elevators.

Sabine Hossenfelder is a physicist and research fellow at the Frankfurt Institute for Advanced Studies in Germany. She currently works on dark matter and the foundations of quantum mechanics.

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The Best Thought Experiments: Schrödinger's Cat, Borel's Monkeys

__2. Schrödinger's cat __ A cat is trapped in a box with radioactive material, a Geiger counter, and a mechanism rigged to release poison if particle decay is detected. According to Erwin Schrödinger, the cat exists in two probable states. But that doesn't track with reality (cats are not both alive and dead). Proposed in 1935, the postulate illustrates that some quantum concepts just don't work at nonquantum scales. Also that Schrödinger was a dog person.

3. Searle's room A man sits alone in a room. Someone slips paper with Chinese writing on it under the door. The man doesn't read Chinese, but with a set of instructions he's able to manipulate the symbols and respond. To an observer, the man appears to understand the language. Philosopher John Searle devised the scenario in 1980 to make a point about computers. CPUs, like his man, lack comprehension and thus can't have humanlike intelligence.

__4. Hawking's turtles __ The 1988 book A Brief History of Time begins with the story of a scientist giving a lecture on astronomy. At the conclusion of his talk, a woman insists he's wrong: Earth is a flat plate carried on the back of a giant turtle. The scientist asks what the turtle is standing on, and the woman says, "It's turtles all the way down!" Stephen Hawking used the story to caution fellow cosmologists against piling one unproven theory upon another.

5. Einstein's light beam When he was 16, Albert Einstein daydreamed about chasing after a beam of light until he caught up to it. At that point, young Einstein reasoned, the light wave would appear frozen. The problem: This was impossible according to the thinking back in 1895. Somehow, this little glitch led Einstein right to the theory of special relativity. Lost? Don't worry. Physicists still debate exactly how this mental exercise got him there.

7. Maxwell's demon In 1867, James Clerk Maxwell pictured two chambers, A and B, each filled with gas at the same temperature and with a door between them. Theorists later had a demon open the door (without doing any work) to let the fastest-moving molecules pass from A into B, and the slowest from B to A. Over time, the speed of the atoms (and therefore the temperature) increases in B — a violation of the second law of thermodynamics.

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4 Thought Experiments That Ask Tough Questions About the Nature of Reality

Let these logic conundrums test your mental mettle (and fire up some heated debates at the dinner table).

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Have you ever imagined the solution to a logic problem instead of calculating it?

Such “thought experiments” are carried out using one’s imagination rather than doing actual research. Typically delivered in narrative form with accompanying diagrams, thought experiments are used in wide-ranging disciplines for “entertainment, education, conceptual analysis, exploration, hypothesizing, theory selection” and more, according to the Stanford Encyclopedia of Philosophy . But no one knows when the first thought experiments took place, according to The Decision Lab , an applied research firm that specializes in behavioral science. But we do know the first written evidence of thought experiments comes from ancient Greece, where pre-Socratic philosophers used them to solve math equations .

✅ A thought experiment doesn’t really have an answer—and that’s the whole point; these sometimes strange, open-ended questions use hypothetical scenarios to let your creativity and problem solving run wild, according to The Decision Lab. And hopefully, through the process of unpacking circular reasoning (when you use evidence to support a claim that is just repeating the claim itself) and rhetorical logic (the art of persuasion), the thought experiment will illustrate some sort of big idea. No wonder these exercises are so popular in philosophy.

From an Einstein puzzler developed while writing up his special theory of relativity to a brain-twisting exercise that could prove computers don’t really understand language , here are four modern thought experiments that will test your mental mettle (and probably fire up some heated debates at your next family dinner).

Einstein’s Train-and-Embankment Thought Experiment

In the 20th century, thought experiments played a key role in defining a physics revolution. When Albert Einstein, a physics professor at the Humboldt University of Berlin, was writing Relativity: The Special and General Theory , he created a thought experiment that unraveled outdated concepts of what time is.

Before Einstein’s book was published in 1920, people assumed that time was universally constant across all frames of reference. Einstein showed that events are not simultaneous in different physical frames of reference if one frame is traveling relative to the other. In other words, time is actually relative.

To illustrate this concept, Einstein described a scenario in which a long train is traveling relative to an embankment with the velocity v . If lightning strikes at two locations simultaneously, as perceived from the railway embankment, these lightning strikes will not happen at the same time from the vantage point of someone in the train.

In the diagram below, the lighting strikes occur at points A and B. The two rays of light from points A and B meet at the midpoint, M, on the embankment. Meanwhile, a traveler on the train will see one flash very slightly before the other because he is located at point M’ and is traveling to the right; so, he will see the flash from point B before he sees the flash from point A. This will result in him thinking that the flash from point B took place first.

Based on this thought experiment, Einstein concluded that time varies depending on what frame of reference one has.

The theories of relativity have had profound consequences, changing our ground rules for how we expect the universe’s geometry and operation to work. According to the Encyclopedia Britannica , special and general relativity “overthrew many assumptions underlying earlier physical theories, redefining in the process the fundamental concepts of space, time, matter, energy, and gravity.”

The Twin Paradox

When Einstein wrote about the theory of relativity in a 1905 paper, he was curious about a problem that arose: if there are two clocks, and one of them travels, the clock that is traveling will record less time passing. He wrote, “the clock that moved from A to B lags behind the other which has remained at B by ½tv²/c² sec … where t is the time required by the clock to travel from A to B.”

In 1911, Paul Langevin, professor of physics at the Collège de France, expanded this example to describe human twins who age differently because one of them has taken a space flight and the other has not.

The paradox is that from the perspective of the twin in the spacecraft, the twin on the planet has accelerated away; so, the reverse should be true, since according to special relativity, their frames of reference obey equivalent physical laws if they are not accelerating.

This paradox has been hotly debated on the Q&A board StackExchange and in other physics discussions. According to a 2021 paper from the Journal of Applied Mathematics and Physics , it has still not been resolved. “Many attempts have been made to explain the twin paradox, which fall in two categories; one based on asymmetry and the other on acceleration,” wrote Pirooz Mohazzabi and Qinghua Luo, the two professors at the University of Wisconsin-Parkside who were the co-authors of the paper. “To resolve the twin paradox, some authors resort to [an] asymmetry argument. They argue that twin B does not remain in a single inertial frame of reference during the entire process; traveling toward the star, she is in one frame of reference, while coming back, she is in another one.

“In a second school of thought, some authors argue that the twin who leaves the Earth undergoes acceleration whereas the one who stays on Earth is not accelerating,” Mohazzabi and Luo wrote. “Some even argue that [the] time dilation equation is not valid if the reference system accelerates.”

However, the paper says the explanations based on asymmetry and acceleration do not hold if the twins are both accelerating away from each other and have both left the planet, for example. There are other exceptions as well.

This slowing down of time due to travel, which is known as time dilation, has been verified through multiple experiments . So although we don’t know why it’s happening, we do know it is happening.

The Chinese Room Argument

An intriguing thought experiment known as the “ Chinese Room Argument ” describes how computers can imitate human language without understanding it.

According to the Stanford Encyclopedia of Philosophy , John Searle, a philosophy professor at the University of California-Berkeley, wrote that he could imagine himself alone in a room, following a computer program that tells him how to respond to Chinese characters that someone slips under the door. He could do this without understanding Chinese.

Essentially, Searle would be communicating in Chinese the same way that artificial intelligence knows how to respond to strings of characters without understanding them.

This thought experiment shows evidence that the “ Turing Test ” does not provide evidence of real artificial intelligence. According to the Turing Test, a computer cannot be considered intelligent unless it can produce responses that a human observer could view as regular human responses. However, a computer can use language in a convincing way without understanding it. According to the Stanford website, this means that human minds are more than information-processing systems. Human minds come from biological processes; computers simulate them.

This thought experiment piques the curiosity of researchers who study language and computing. Other academics have critiqued some of its assumptions and conclusions. It is considered an argument against what is known as “Strong AI,” or artificial intelligence that mimics the human brain .

Anyone who has experimented for a while with online tools such as ChatGPT will notice some of the comical and surprising behavior that AI can engage in due to its lack of comprehension of human language and cultural and social contexts.

Mary’s Room (the “Knowledge Argument”)

Data may not be able to describe the colorful nuances of real-world experiences. In 1982, Frank Jackson, who is now an emeritus professor of philosophy at the Australian National University, proposed a thought experiment that he at first believed proved this was true. According to a TED video , this thought experiment has been used since then to describe why computers cannot have human experiences.

In this thought experiment , Jackson imagined that a brilliant neuroscientist named Mary lived in a black-and-white room and had never seen color , but knew the theoretical and practical science behind color vision. For example, the video said, someone like this would know that within the eye, three different types of light stimulate cone cells that send electrical signals along the optic nerve to the brain to allow us to perceive color.

Suddenly, Jackson said, Mary’s computer began to display color—or she left the black-and-white room. She now had a new experience that her previous scientific knowledge did not encompass.

This shows there are nonphysical properties and knowledge that can only be discovered through experiences. As the video said, the experience of color transcends the knowledge of color; this implies that abstract knowledge cannot capture the full zest of real life.

Philosophers call this experiment the “Knowledge Argument.” They say experiences have subjective qualities called “ Qualia ” that can be experienced, but not fully described. Some experiences cannot be described in words.

Jackson changed his mind later and said that the experience of viewing a colored image on a screen could be described in terms of an event in the brain. According to the open-access journal Philosophical Investigations : “He came to believe that there was nothing apart from redness’s physical description, of which Mary was fully aware. This time, he concluded that first-hand experiences, too, are scientifically objective, fully measurable events in the brain and thus knowable by someone with Mary’s comprehension and expertise.”

Kat Friedrich is a former mechanical engineer who started out as an applied math, engineering, and physics major at the University of Wisconsin-Madison. She has a graduate degree in science and environmental journalism and has edited seven news publications, two of which she co-founded. She spends her free time learning about dance and functional fitness, reading science fiction, and exploring music events. 

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The impossible barber and other bizarre thought experiments

How inventing riddles has revealed the flaws in our grasp of reality

By Stephen Battersby

11 May 2016

Dmytro Zinkevych/Alamy Stock Photo

If you imagined that thought experiments were mere mental gymnastics meant to bamboozle the uninitiated, think again. Take Schrödinger’s cat, perhaps the most famous example, which involves a cat that is simultaneously alive and dead. It seems bizarre – and that’s the point. It was designed as a slap on the wrist for quantum theorists, to show that a theory that predicts such nonsense must be missing something. Current thinking is that perhaps nothing is missing, and quantum theory really is as weird as it seems.

But other thought experiments have forced us to reformulate the laws that describe nature. Take Maxwell’s demon, which appears to break the laws of thermodynamics. It showed us that thermodynamics really was missing something (see “ Matter, energy… knowledge: How to harness physics’ demonic power “).

Here are seven classic thought experiments that might make you think…

The impossible barber

A certain barber is very particular about his work. He shaves every person who does not shave themselves, and no one who does shave themselves. So: does the barber shave himself? It doesn’t take long to see the contradiction: If he does, he can’t; if he doesn’t, he must. Such a barber can’t exist.

This barber is often used to illustrate a more abstract puzzle known as Russell’s paradox. In 1901, mathematician and philosopher Bertrand Russell was investigating set theory, a formal way of defining and dealing with collections of anything. At the time, one of its central ideas was that for every property you can define, there must be a set. There’s the set of all green things, and the set of all whole numbers except 4. You can also define sets of sets: say, the set of all sets that contain exactly two elements. The problem comes when pondering the possibility of a set of all sets that do not contain themselves — like the barber, this seems to be impossible.

The paradox exposed contradictions in much of the mathematics of the time , forcing Russell and others to try to devise more intricate logical footings for mathematics. Russell’s approach was to say that mathematical objects fall into a hierarchy of different “types”, each one built only from objects of lower type. Type theory has been used to design computer programming languages that reduce the chance of creating bugs. But it’s not the definitive solution – more than a century later, mathematicians are still arguing over the answer to Russell’s paradox.

Galileo’s balls

Galileo may never have dropped balls from the top of the leaning tower of Pisa, as the legend goes. But he did devise a simple thought experiment that told us something profound about gravity. Take two weights, one light, one heavy. If heavier objects fall faster than light ones, as Aristotle said, then the lighter weight will lag behind. That implies that when the two are tied together, they will fall more slowly than the heavy weight alone. But together, they weigh more than the heavy alone, so they should fall faster. Wait, so is it faster or slower?

As Galileo realised, acceleration due to gravity doesn’t depend on the mass of an object. This was a crucial result for the emerging science of physics, and Isaac Newton’s ideas of motion and universal gravitation. It even holds a germ of Einstein’s subtle theory of gravity. His general theory of relativity is rooted in the equivalence principle , the idea that gravity and acceleration are essentially the same thing— as Galileo glimpsed back in the 17th century.

Newton’s cannon

Take one gigantic cannon, put it on top of a mountain so high it reaches above the atmosphere, and fire horizontally. Irresponsible, perhaps, but instructive. If the cannonball is fired at a low speed, gravity will soon drag it down to the ground along a tightly curving arc. If you add more gunpowder, the ball will go faster and its arc will be more gradual, taking it further around the curve of the Earth. Fire it fast enough and the cannonball’s path will not meet the ground at all – it will fly all the way around and hit you in the back of the head. Here, have a go .

This thought experiment helped Newton show that gravity is a universal force: the force we see pulling cannonballs and apples to Earth can also explain the orbit of the moon around Earth, and Earth around the sun.

We are used to the idea of universal forces now. We know that nuclear reactions fuel the distant stars, and that exoplanets can be magnetic. But before Newton there was no expectation that the celestial realm should have the same rules as Earth. His cannonball blew a big hole in such heavenly pretentions.

Achilles and the tortoise

Two-and-a-half millennia ago, the Greek philosopher Zeno of Elea apparently proved that motion is an illusion. One of his paradoxes sets fleet-of-foot Achilles to chase a tortoise that has a small head start. Achilles can never catch the tortoise, argued Zeno, because first he must reach the point where the tortoise started, but by then the tortoise has moved on to a new position. So then Achilles must run there – by which time the tortoise has moved on again. The “dichotomy paradox” is more general: to cover any distance, you must first cover half that distance, then half of what’s left, then half of what’s left, and so on for ever. It seems that you can never get there, no matter what the original distance or how fast you move.

Since then, mathematicians have pointed out that although these arguments take an infinite amount of time to pan out, real motion doesn’t have to. We know for instance that that an infinite series of terms can add up to something finite. If you add an infinite series of fractions starting with ½ and halving in value with each new term (½ + ¼ +1/8…), the infinite sum is equal to 1. You can use maths like this to represent the distance travelled or the time taken in Zeno’s paradox, so — phew – motion is possible after all. That said, Zeno’s paradox may manifest itself for real in the quantum world .

The Chinese room

Can a computer be conscious? In an attempt to disprove this idea of “strong artificial intelligence ”, John Searle , a philosopher at the University of California, Berkeley, imagined himself inside a room of dictionaries and rule books that hold instructions for translating Chinese to English and vice versa. Someone posts a question through the door written in Chinese, and using his rule books Searle works out an appropriate answer. To the questioner it would seem there is a mind in the room that understands Chinese, even though there isn’t. Searle claims that a hypothetical rule-bound computer designed to speak Chinese would be the same — a mere machine with no understanding.

There are many objections to this thought experiment. Some argue that although Searle does not understand Chinese, he is part of a larger system, including the rule books, that does. You might baulk at the idea that a mind could be made from a person plus some books, but it’s only a very dim mind, taking perhaps years or millennia to respond to one question.

Another interpretation is that Searle’s idea merely highlights the mystery of “other minds”: that you can’t know whether a computer, a penguin or the person next door is conscious in the same way as you are . If the Chinese room doesn’t disprove strong AI, thinking about it could help us to find out what’s missing from our understanding of consciousness.

Ride a light beam

In his Autobiographical Notes , Albert Einstein tells us how as a 16-year-old he imagined riding along with a light beam. If you could keep pace with it, the light must appear stationary, he imagined. Its oscillating electric and magnetic fields would be frozen. But that seems impossible. The equations developed by James Clerk Maxwell that describe the oscillations of electromagnetic fields forbid it, and we’ve certainly never seen such a thing as frozen light.

“One sees in this paradox the germ of the special relativity theory is already contained,” he wrote in 1947. As Einstein came to realise, the motion of light is the same no matter how fast you are moving. Even if you were travelling at almost the speed of light, the ray would still zip away from you at the same constant speed. This idea eventually led Einstein to an entirely new way of seeing the universe through the equations of special relativity, with their extraordinary predictions that time is elastic and that inert matter holds vast quantities of energy.

Laplace’s demon

Imagine a being that knows the place and motion of every particle in the universe. It also knows physics, and its mind works so fast that it can calculate how these particles will exert forces on one another, changing their motions. Can this intellect, described by Pierre Laplace in 1814, see the future of everything?

“Laplace’s demon”, as it became known, probes the idea of determinism. In a purely classical world, the demon seems to work. Chaos theory means that the future is ultra-sensitive to the past, but if the demon’s knowledge is infinitely precise, it could still know the fate of all.

Quantum mechanics may slay the demon. In mainstream quantum theory, events do not always have causes: radioactive decay and other things can happen spontaneously. But not all interpretations of quantum mechanics include this indeterminacy.

Even if the demon can live on in a universe governed by quantum mechanics, however, it probably doesn’t live around here. There is a mathematical argument that shows “the entire physical Universe cannot be fully understood by any single inference system that exists within it”. You might conceive of the demon as some kind of outside observer, but that opens another philosophical can of worms: is it meaningful to say that something can know all about our universe without having any physical effect on us?

• general relativity /
• mathematics /
• consciousness

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Five weird thought experiments to break your brain

Stokkete /Shutterstock

• Thought experiments are quite popular, though some get more time in the sun than others.
• While they are supposed to help guide our intuition to help solve difficult problems, some are a bit removed from reality.
• Can we trust the intuitions we have about problems set in sci-fi worlds or that postulate impossible monsters?

Despite the reported unpopularity of philosophy, its thought experiments are extremely popular tools for helping people understand how they look at the world. Famous examples, such as the Veil of Ignorance and the Trolley Problem , permeate popular culture, feature on memes, and help people clarify their thinking.

Not all thought experiments are created equal, though. Some of them are far less popular than others , some have fallen from being widely discussed to being historical curiosities , and others were always just restatements of Descartes .

A few of them, popular and unpopular, have pushed the limits of what a “good” thought experiment is. Philosopher and Big Think contributor Daniel Dennett suggests that many thought experiments venture into areas where we cannot have good intuitions, making them less than ideal experiments.

For example, while we can all think very clearly about the trolley problem—everything in it is straightforward enough to be grasped by everybody—an experiment that asks us to imagine sci-fi situations or the life choices of fantastic monsters might be too far out there to be effective.

Today, we’ll look at five thought experiments that have been accused of being just a little too separated from reality to be useful. We’ll consider what they’re trying to shed light on, and review why they may or may not manage to do it.

A thought experiment we’ve discussed before that dives into questions of identity and meaningful language is the Swampman. Donald Davidson wrote it in 1987:

“Suppose a man is out for a walk one day when a bolt of lightning disintegrates him. Simultaneously, a bolt of lightning strikes a marsh and causes a bunch of molecules to spontaneously rearrange into the same pattern that constituted that man a few moments ago. This ‘Swampman’ has an exact copy of the brain, memories, patterns of behavior as he did. It goes about its day, works, interacts with the man’s friends and is otherwise indistinguishable from him.”

Is the Swampman the same person as Davidson? When he refers to things he “remembers” seeing before, even though the Swampman never actually saw them, do his words mean anything? This experiment, combined with “ The Ship of Theseus ” causes people to wonder if teleportation through creating a copy of a person and then destroying the original actually “kills” the person being teleported .

Of course, we don’t have teleportation yet, nor are there actual Swamp-people running around (Or are there!?!?!). While the questions raised by the Swampman are important ones, Dennett’s warning is that we shouldn’t be too quick to trust our intuition when the problem is so separated from anything we’ve ever encountered.

This thought experiment from Robert Nozick’s defense of libertarianism “Anarchy, State, and Utopia” asks what we’d have to do if Utilitarianism is correct and we met something capable of much greater happiness than anybody else.

“Utilitarian theory is embarrassed by the possibility of utility monsters who get enormously greater gains in utility from any sacrifice of others than these others lose. For, unacceptably, the theory seems to require that we all be sacrificed in the monster’s maw, in order to increase total utility.”

If there was a utility monster that got a million times more joy out of everything than anybody else does, would we be obligated to give it everything it demanded to maximize the total happiness? Even if those demands cause suffering, but never enough to tip the ethical scales, elsewhere? If so, what does this mean for Utilitarianism as a moral theory?

At first, this experiment doesn’t seem too bizarre. We all grasp the idea of somebody who gets more out of something than we do; this is just taking that idea to the extreme. The fundamental problem with this experiment was pointed out by philosopher Derek Parfit who argued that, while we are capable of imagining somebody who is happier than we are or who would get more out of something than we do, the idea of a creature that gets a million times more happiness out of things is impossible to imagine in a meaningful way.

How can we get useful insights into the problem if we can’t hope to grasp how this monster interacts with the world? Because of this difficulty, Parfit rejected the problem.

Utilitarian philosopher and Big Think contributor Peter Singer accepts that if there were utility monsters there might be a problem for Utilitarianism, but, as he explained to The Nation, he finds the idea far-fetched. When posed the problem in the context of a billionaire owning a superyacht rather than donating money to fund medical treatments, he replied:

“We would have to assume that Larry Ellison actually has capacities for happiness that are vastly greater than anyone else’s. Ellison’s yacht cost $200 million, and if we assume that $400 can repair an obstetric fistula, that means that the suffering relieved by 500,000 obstetric fistula repairs is not greater than the happiness that Ellison gets from his yacht. That, I think, is not physically possible.”

Continuing on the theme of bizarre thought experiments involving monsters, we have a strange reworking of Pascal’s Wager involving a super-intelligent AI. It was created by a contributor to the website LessWrong named “Roko.”

Given the length of the original post, I will summarize it here:

Imagine for a moment that humanity will someday create a hyper-powered artificial intelligence that is capable of solving all of the world’s problems. It follows a form of utilitarian ethics and is trying to reduce human suffering as much as it can, which is a considerable amount. Given all the good it can do, it coming into existence, and doing so quickly, would substantially benefit humanity. Fully capable of simulating anything it wants, it then decides to take steps to punish those who knew about the good it could do but didn’t help create it by torturing simulations of them.

Is it rational then to start donating a lot of money to those creating this super intelligence to avoid having it simulate and torture a copy of you in the future? This experiment gained a fair amount of notoriety online , and a name based on the creature that kills with its gaze , because by reading about it, you think about the monster and become a potential victim in the future, since now you know about it and might choose not to help create it.

Maybe I should have mentioned that part first. Oh well, so it goes.

As you might have realized, this experiment requires you to assume that we can reliably predict the behavior and motivations of a particular, ultra-intelligent AI that doesn’t exist yet and may never exist. In terms of raw intelligence, this might be akin to asking a brainless starfish to predict how a human will behave one hundred years from now. While the experiment is said to have given some people nightmares , it isn’t taken seriously by most people outside a small circle on the internet.

Plus, the long list of assumptions in the experiment includes that a simulation of you is actually “you” in a meaningful way. We have to solve the Swampman problem before we can agree on that point at all.

A surreal experiment by Judith Thomson that appeared in her famous essay “ A Defense of Abortion . “ The essay is a series of arguments for the morality of abortion in certain circumstances through thought experiments. While some parts of it are quite famous, this section seems to avoid widespread discussion:

“Again, suppose it were like this: people-seeds drift about in the air like pollen, and if you open your windows, one may drift in and take root in your carpets or upholstery. You don’t want children, so you fix up your windows with fine mesh screens, the very best you can buy. As can happen, however, and on very, very rare occasions does happen, one of the screens is defective; and a seed drifts in and takes root.”

The question being, would it be acceptable to uproot the person-plant-fetus that gets in? Is it too much to ask that people live without cloth in their homes if they don’t want people seeds to get in? How about never opening their doors or windows?

While this is supposed to be analogous to accidental pregnancy resulting from birth control failures, the downright bizarre nature of the thought experiment has been commented on by more than a few critics . Philosopher Kathleen Wilkes argued that it was too far removed from our reality to provide meaningful intuitions on abortion in her book “Real People .”

After all, society would probably have very different ideas on what the right to life means if we came into the world because a bit of pollen landed on the carpet.

A problem created to dive into questions of language by Hilary Putnam , the Twin Earth experiment dives into questions of language and meaning using a story straight out of a one-shot comic book:

“We begin by supposing that elsewhere in the universe there is a planet exactly like Earth in virtually all aspects, which we refer to as “Twin Earth.” (We should also suppose that the relevant surroundings are exactly the same as for Earth; it revolves around a star that appears to be exactly like our sun, and so on). On Twin Earth, there is a Twin equivalent of every person and thing here on Earth. The one difference between the two planets is that there is no water on Twin Earth. In its place there is a liquid that is superficially identical, but is chemically different, being composed not of H2O, but rather of some more complicated formula which we abbreviate as ‘XYZ.’ The Twin Earthlings who refer to their language as ‘English’ call XYZ ‘water.’ Finally, we set the date of our thought experiment to be several centuries ago, when the residents of Earth and Twin Earth would have no means of knowing that the liquids they called ‘water’ were H 2 O and XYZ respectively. The experience of people on Earth with water and that of those on Twin Earth with XYZ would be identical.”

Do the Earthling (who Putnam named Oscar) and his twin (also named Oscar) mean the same thing when they say “water?” Their mental states are the same when they refer to it, but the object in question is physically different in each case. If the twins’ statements don’t mean the same thing, then we must admit that external factors play a role in defining terms external to the speaker, a stance dubbed “ scientific externalism .”

While this experiment is quite famous and has advanced a fair amount of debate , you can probably already see the difficulties some people have with it.

Philosopher Tyler Burge has argued that the whole experiment is flawed, as Earth Oscar refers to the concept of “H2O,” while Twin Earth Oscar is referring to the concept of “XYZ.” Dr. Burge argued that this means their mental states are different from the get-go. He also points out that the stuff flowing on Twin Earth isn’t actually water , which might derail the whole thing.

For his part, Putnam criticized others for using thought experiments that require you to ignore specific ideas to arrive at the intended ones. In this experiment, with humans presumably still being 60 percent water, you’d have to imagine that changing what water is at the molecular level would not alter the beings thinking about the water in any meaningful way. He has also admitted that Dr. Burge’s first critique is actually a very good one.

Surprisingly, Daniel Dennett has spent a fair amount of time discussing the content of the problem rather than on how strange the whole experiment is in the first place. It might go to show that philosophers love a good thought experiment, even if the results aren’t directly applicable to the real world.