--- title: 3 Thought Experiments to Boggle the Mind description: "Today, we're exploring three lesser-known, yet utterly fascinating thought experiments that will twist your brain in knots. First, we'll tackle The Quantum Suicide, a mind-bending scenario that challenges the very foundations of reality and our understanding of life and death. Next, we delve into Newcomb's Paradox, where free will clashes with a predictive entity. And finally, The Sleeping Beauty Problem, a philosophical puzzle that will make you question how probability and belief intersect.\n\n## The Quantum Suicide\n\nYou've probably heard of the Schrodinger's Cat thought experiment before, but we'll give you a quick refresher. A cat is placed into a box with a vial of poison, an atom of radioactive material, and a Geiger counter. After one half-life of the atom, there is a 50% chance that the atom will decay, triggering the Geiger counter which will then release the poison. At this point, the cat now has a 50% chance of being alive. But thanks to quantum superposition, the entire system can remain in both states until observed.\n\nUnder the Copenhagen interpretation, this is precisely what happens. The cat is simultaneously both alive and dead, and the system doesn't collapse to a singular outcome until the evil scientist performing the experiment opens the box to observe the result. At that point, the cat will only be either alive or dead.\n\nOne of the numerous potential issues with this view is that, because the cat was both dead and alive, it should have a memory of being dead. While this has never been tested experimentally, and with good reason, we have no reason to believe that a cat in this scenario would have memories of its time being dead before the box was opened. There are also other questions regarding whether it's even possible for such a macroscopic system to exist in a quantum superposition, all of which challenges the Copenhagen interpretation.\n\nThe more popular solution is the many worlds interpretation. Under this framework, the system results in two parallel universes: one where the cat is dead and one where the cat is alive. Opening the box doesn't collapse the possible outcomes, it merely reveals which timeline the observer is a part of. There should be two alternate realities with two copies of the same scientist each observing a different result. But those two scientists have no ability to communicate with each other, meaning that the end result observed is no different than the Copenhagen interpretation: there is a single cat that is either dead or alive. So if these wildly different interpretations of quantum superposition both would have the same experimental results, how can we possibly design a test to support one theory over the other?\n\nThat's where the ideas of quantum suicide and quantum immortality come into play. Though several others presented similar ideas in the preceding years, this thought experiment is usually attributed to the Swedish-American physicist Max Tegmark and his 1998 paper. This experiment is a hypothetical means to test the many worlds interpretation, and for once it doesn't involve the senseless murdering of cats. Instead, it is the scientist himself that gets into Schrodinger's box.\n\nRather than a vial of poison, the box will have some sort of murder machine that instantly kills the scientist before they can even feel anything. Once a radioactive atom decays, their death will also happen faster than they can read the Geiger counter or any other measurement tools. These modifications are designed to remove the argument that the scientist would count as an observer of the system, as they would have died before any observation could occur. More importantly, however, instead of a single radioactive atom, the box will contain hundreds.\n\nEach atom has a 50% chance of decaying over the course of one half-life, so according to the many worlds interpretation each of these will result in the creation of parallel universes, one where the scientist dies and one where they don't. But because there are hundreds of atoms, the overall odds of survival for the scientists are the same as flipping heads on a coin hundreds of times in a row; it's essentially zero.\n\nFrom the scientist's point of view, however, the odds of survival under the many worlds interpretation would be 100%. So how can that be possible? The first atom has a chance to decay, at which point it creates two parallel universes. If we ignore the possibility of an afterlife, the scientist's consciousness will never exist in the universe where they die, only continuing in the other universe where they survived.\n\nThat's where the paradoxical nature of this experiment comes into play. Winning all of these coin flips in a row may be a near statistical impossibility, but under the many worlds interpretation it is a necessity that all outcomes exist. As such, the scientist's consciousness will only travel along the singular path of potential outcomes in which they survive the entire ordeal. Despite their death under the conditions of the experiment being all but certain, quantum physics would demand that they survive, making the person functionally immortal. At least immortal in regards to this particular experiment; they will absolutely still die eventually.\n\nWhile quantum immortality seems like an elegant way to prove the many worlds interpretation is true, there are still a couple problems. First, it would require creating an absolutely mind blowing number of alternate universes in which the scientist died, and the theory would only be proven true in the one where they survived. And because the odds of survival are effectively zero, their claims of success are likely to be dismissed and chalked up to the death machine not working properly anyway.\n\nAs frustrating as it would be to prove the many worlds interpretation and have nobody believe you, fortunately that should never happen. No scientist would actually be stupid enough to turn this thought experiment into an actual experiment.\n\n## Newcomb's Paradox\n\nWould you like some free money? Then American physicist William Newcomb has the thought experiment for you. Newcomb devised his thought experiment around 1960, and he discussed it frequently with fellow physicists and philosophers. It was first published by American philosopher Robert Nozick in 1969, and people were already extremely divided. Nozick noted in a follow up paper in 1969, \"To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly.\" So what exactly is this confounding problem?\n\nNewcomb's Paradox is a very simple game. You are presented with two boxes, labeled A and B. Box A is clear and you can see that it contains $1,000. Box B is opaque and it will contain either $0 or $1,000,000. You must choose whether you want to only take the mystery box, or if you would rather take both boxes. The twist is that a \"reliable predictor\" has determined beforehand which you would choose.\n\nThere are variations on this where the prediction is 100% perfect, but those get into arguments about freewill and reverse causality and a bunch of other stuff that is really meant to be beside the point. For our purposes, we'll assume that the predictions are correct 90% of the time; they are usually correct, but the predictor is fallible.\n\nAnyway, if it predicted you would only take box B, then that box will have $1,000,000 inside. If it predicted you will take both boxes, then box B will be empty. The prediction was made before you were presented with the boxes, and the contents of box B have already been finalized. So is the correct answer to only take box B, or is it to take both boxes?\n\nWhen presented with this question, most people immediately assume that there is one answer that is very obviously correct. You're probably already sure what the optimal strategy is right now, because the setup for this question is so simple. But as Nozick alluded to back in 1969, half of you reading this right now think the correct answer is obviously to only take box B, and the other half think the obvious answer is to take both boxes.\n\nBy the time you get to choose the box, the contents of box B are already fixed. If the predictor chose you would only take the mystery box and you take both, you will get $1,001,000 instead of just a million. If it predicted you would take both boxes, then by taking both you would get $1,000 instead of nothing. In game theory this is called the strategic dominance principle, because one course of action always has a better result than the other, regardless of what the other player chose. So it's settled then and you should always take both boxes, right?\n\nNot necessarily, because that decision would have been predicted with 90% accuracy. This means that 10% of the time the prediction will have been wrong and you will get $1,001,000, but the other 90% of the time you will only get $1,000. That means that the average value of taking both boxes is only $101,000. However, if you only take box B, 90% of the time you will get the million dollars while only 10% of the time will you get nothing. That makes the average value of choosing only box B $900,000.\n\nIn game theory this is called the expected utility principle, and it is just as valid as strategic dominance. That is the source of the paradox, as two equally flawless forms of analysis result in contradictory answers. And while one of these answers may have initially seemed more obvious to you, neither is particularly more obvious than the other as a general rule. Decades of countless surveys have shown that people are consistently split nearly 50/50 on this question, with the decision to take both boxes usually being a couple percentage points more popular. These numbers remain consistent even when the survey only includes professional philosophers, mathematicians, and game theorists, so it's not like there's some really complicated yet definitive decision matrix that can solve this problem.\n\nIn 2011, a well received paper by physicists David Wolpert and Gregory Benford claimed to unequivocally resolve Newcomb's paradox, and stated that there was only one correct solution. So which answer did Wolpert and Benford choose, do you ask? Rather frustratingly, both.\n\nAccording to their paper, the nature of how the prediction is made is a bit vague, and as such there are two completely different games being played depending on how you assume the probabilistic nature of the predictor's decision works. The two possible choices are each correct in one version of the game but not the other, and everybody just chooses whichever option is correct for the version of the game they believe is being played.\n\nUnfortunately, Wolpert and Benford did not weigh in on what they believed was the correct interpretation, leaving us no closer to a definitive answer. However, they did make some interesting word choices that you are free to interpret however you like. They defined taking both boxes as the realist position and taking only box B as the fearful position, arguing that the latter position was seemingly based on the participant believing that they lacked free will in this scenario.\n\n## Sleeping Beauty Problem\n\nThe Sleeping Beauty Problem was first published in 2000 by philosopher Adam Elga, expanding on ideas first introduced in 1990 by philosopher Arnold Zuboff. The setup for this thought experiment is very simple, but agreeing on a solution has proven to be much harder.\n\nOur test subject for this experiment is Sleeping Beauty, who has been made fully aware of the details of the experiment beforehand. On Sunday, Sleeping Beauty will be put to sleep. While she is asleep, one of the researchers will flip a fair coin. If the coin lands on tails, she will be woken up on Monday and asked a single question as laid out by Elga: \"What is your credence now for the proposition that the coin landed heads?\" In this context, \"credence\" means what does she believe is the probability that the coin landed heads.\n\nAfter answering the question, Sleeping Beauty will be given a drug that will make her fall back asleep and forget that the interview ever happened. She will then be woken up again on Tuesday, asked the same question, and put back to sleep. If the coin landed on heads, she will only be interviewed on Monday and will sleep through all of Tuesday. So how should Sleeping Beauty answer the question when she is interviewed?\n\nThere are two conflicted schools of thought, both of which have proofs that are accepted as being mathematically valid. The first answer is the thirder position, which states that Sleeping Beauty should believe that there is a 1/3 chance that the coin landed on heads. This seems counterintuitive since, by definition, a fair coin has a 50% chance of landing on head, but the math behind this argument is sound.\n\nFirst, let's assume that today is Monday. When Sleeping Beauty is woken up, the probability of it being Monday and tails is equal to the probability of it being Monday and heads. Next, let's instead assume that the coin landed tails. Since a tails result always results in her being woken up twice, when she is woken up the probability of it being Monday and tails is equal to the probability of it being Tuesday and tails. Since the probability of Monday tails is equal to both Monday heads and Tuesday tails, all three outcomes have the same probability.\n\nSome of you may be screaming at your screens that this sounds like some sort of trick, but we promise you that these two equalities can be combined like this even though they were derived from different assumptions. You can even test it yourself by flipping a coin 100 times and keeping track of when Sleeping Beauty will be woken up. Assuming fair coin flips, you will find that she is woken up at each of the three possible timings about 50 times each.\n\nBecause all three of these events have an equal probability of happening, thirders argue that Sleeping Beauty should say she believes there is a 1/3 probability that the coin landed heads. After all, 2/3 of the time that she is interviewed it is because the coin landed tails. This was the position that Elga took, and while there is no general consensus it is definitely the more popular of the two answers among philosophers. However, it happens to be the rather vehement opinion of the writer of this episode that the thirder position is an utter abomination, and all those who support it should be ashamed of themselves.\n\nThe halfer position argued that Sleeping Beauty should believe that there was a 1/2 chance that the coin landed heads, because there was. By the very definition of it being a fair coin flip, the odds were 50%. Sleeping Beauty went to sleep knowing this, and when the researcher wakes her up she has no new information. She has no idea what day of the week it is or if she has already been interviewed. Since she knew that it was a fair coin flip, why should she suddenly believe that there is anything other than a 50% chance of the coin landing on heads?\n\nInstead of flipping the coin while Sleeping Beauty was asleep, the researchers could flip it on Sunday while she was still awake and ask her what she believed the probability was that the coin landed on heads. And of course she would say it was 1/2. Likewise, when the experiment ended on Wednesday, if she was asked the question again, now knowing that the experiment had ended, she would always answer that it was a 1/2 probability that the coin landed on tails at the beginning of the experiment.\n\nThirders try to make the answer seem more persuasive by extending the length of the experiment to better illustrate their point, such as making tails result in Sleeping Beauty being woken up and mind-wiped 999 times. By extending the equalities we did earlier, this could prove there is only a 1 in 1,000 chance that the fair coin landed on heads. However, these events aren't independent of each other. Either all 999 tails events happen or 0 of them do, and that is a 50% chance.\n\nOf course, the real issue may be that the question itself is ambiguous and that thirders are answering a question that wasn't asked. The question posed by Elga in the original paper, and the question that is always asked of Sleeping Beauty, is \"what do you believe is the probability that the coin landed on heads.\" She knew it was 1/2 when she went to sleep and had no new information when she woke up, so of course the answer to that question should remain unchanged. However, if the question being asked was \"what do you believe is the probability that I woke you up because the coin landed on heads\", well that is a completely different situation.\n\nIf the coin landed heads she will be woken up once and if it landed tails then she would be woken up twice, so of course tails is the more likely option under this phrasing. If the experiment was repeatedly performed and Sleeping Beauty was going to be given $100 every time she correctly guessed whether the coin landed on heads or tails, she would make twice as much money by always guessing tails. Not because tails was a more likely result, just because she was asked more times when it was the correct answer.\n\nTo many people that may sound like an endorsement of the thirder position, as this sort of wager argument is often used to illustrate their point. However, here's one final variation on this thought experiment that may help show the difference between the question being asked and the question that thirders seem to be answering.\n\nLet's stop injecting Sleeping Beauty with drugs, and instead we'll use a simple ball pit. Whenever a fair coin lands on heads one green ball will be put in the pit, and whenever it lands on tails two red balls will be put in the pit. We could flip the coin a million times and ask you what the probability is that a green ball was put in the pit, and every time you would correctly say that it was 1/2. However, if we were to then pull one ball at random out of the pit and ask you what the probability is that a green ball was removed? The answer may now be 1/3, but it is a very different question.\n\n## Key Takeaways\n\n- The Quantum Suicide thought experiment explores the many worlds interpretation of quantum mechanics.\n- Newcomb's Paradox presents a scenario where strategic dominance and expected utility principles conflict.\n- The Sleeping Beauty Problem challenges understanding of probability and belief through a coin flip experiment.\n- The Copenhagen interpretation suggests a cat in a box is both alive and dead until observed.\n- The thirder and halfer positions offer differing solutions to the Sleeping Beauty Problem.\n\n## Frequently Asked Questions\n\n### What is the Quantum Suicide thought experiment?\n\nThe Quantum Suicide thought experiment is a hypothetical scenario where a scientist enters a box with a murder machine triggered by radioactive decay to test the many-worlds interpretation of quantum mechanics.\n\n### What is the many-worlds interpretation in the context of the Quantum Suicide experiment?\n\nThe many-worlds interpretation suggests that each possible outcome of a quantum event occurs in a separate, parallel universe. In the Quantum Suicide experiment, this means the scientist's consciousness would only exist in the universe where they survive.\n\n### What is Newcomb's Paradox?\n\nNewcomb's Paradox is a thought experiment where you choose between taking one opaque box or two boxes, one of which is clear and contains $1,000. The opaque box contains either $0 or $1,000,000, determined by a reliable predictor.\n\n### What are the two main strategies in Newcomb's Paradox?\n\nThe two main strategies are taking both boxes, which follows the strategic dominance principle, and taking only the opaque box, which follows the expected utility principle.\n\n### What is the Sleeping Beauty Problem?\n\nThe Sleeping Beauty Problem is a thought experiment where Sleeping Beauty is put to sleep and woken up depending on the outcome of a coin flip. She is asked to determine the probability that the coin landed heads.\n\n### What are the two main positions in the Sleeping Beauty Problem?\n\nThe two main positions are the thirder position, which argues that Sleeping Beauty should believe there is a 1/3 chance the coin landed heads, and the halfer position, which argues that she should believe there is a 1/2 chance.\n\n### What is the thirder position in the Sleeping Beauty Problem?\n\nThe thirder position argues that Sleeping Beauty should believe there is a 1/3 chance the coin landed heads because, out of the three possible waking scenarios (Monday heads, Monday tails, Tuesday tails), two involve the coin landing tails.\n\n### What is the halfer position in the Sleeping Beauty Problem?\n\nThe halfer position argues that Sleeping Beauty should believe there is a 1/2 chance the coin landed heads because the coin flip is fair, and she has no new information upon waking.\n\n### What is the Copenhagen interpretation of quantum mechanics?\n\nThe Copenhagen interpretation suggests that a quantum system exists in all possible states simultaneously until it is observed, at which point it collapses into one definite state.\n\n### What is the strategic dominance principle in game theory?\n\nThe strategic dominance principle in game theory states that one course of action always has a better result than the other, regardless of what the other player chose.\n\n## Sources\n\n- [Original Side Projects video: 3 Thought Experiments to Boggle the Mind](https://www.youtube.com/watch?v=894vqDKd5RM)\n\n## Related Coverage" url: https://sideprojects.pub/article/3-thought-experiments-to-boggle-the-mind.md canonical: https://sideprojects.pub/article/3-thought-experiments-to-boggle-the-mind datePublished: 2026-06-25 dateModified: 2026-06-25 author: - name: Simon Whistler url: https://sideprojects.pub/author/simon-whistler publisher: Side Projects image: "https://media.sideprojects.pub/cdn-cgi/image/width=1600,height=900,fit=cover,quality=80,format=auto/articles/894vqDKd5RM/hero.jpg" type: NewsArticle contentHash: 16a1fcccca9108b12ae52f0362c862b82a26a53ad23c9a5b502ca9773df408d8 tokens: 5416 summaryUrl: https://sideprojects.pub/article/3-thought-experiments-to-boggle-the-mind.md.summary.md --- Today, we're exploring three lesser-known, yet utterly fascinating thought experiments that will twist your brain in knots. First, we'll tackle The Quantum Suicide, a mind-bending scenario that challenges the very foundations of reality and our understanding of life and death. Next, we delve into Newcomb's Paradox, where free will clashes with a predictive entity. And finally, The Sleeping Beauty Problem, a philosophical puzzle that will make you question how probability and belief intersect. ## The Quantum Suicide You've probably heard of the Schrodinger's Cat thought experiment before, but we'll give you a quick refresher. A cat is placed into a box with a vial of poison, an atom of radioactive material, and a Geiger counter. After one half-life of the atom, there is a 50% chance that the atom will decay, triggering the Geiger counter which will then release the poison. At this point, the cat now has a 50% chance of being alive. But thanks to quantum superposition, the entire system can remain in both states until observed. Under the Copenhagen interpretation, this is precisely what happens. The cat is simultaneously both alive and dead, and the system doesn't collapse to a singular outcome until the evil scientist performing the experiment opens the box to observe the result. At that point, the cat will only be either alive or dead. One of the numerous potential issues with this view is that, because the cat was both dead and alive, it should have a memory of being dead. While this has never been tested experimentally, and with good reason, we have no reason to believe that a cat in this scenario would have memories of its time being dead before the box was opened. There are also other questions regarding whether it's even possible for such a macroscopic system to exist in a quantum superposition, all of which challenges the Copenhagen interpretation. The more popular solution is the many worlds interpretation. Under this framework, the system results in two parallel universes: one where the cat is dead and one where the cat is alive. Opening the box doesn't collapse the possible outcomes, it merely reveals which timeline the observer is a part of. There should be two alternate realities with two copies of the same scientist each observing a different result. But those two scientists have no ability to communicate with each other, meaning that the end result observed is no different than the Copenhagen interpretation: there is a single cat that is either dead or alive. So if these wildly different interpretations of quantum superposition both would have the same experimental results, how can we possibly design a test to support one theory over the other? That's where the ideas of quantum suicide and quantum immortality come into play. Though several others presented similar ideas in the preceding years, this thought experiment is usually attributed to the Swedish-American physicist Max Tegmark and his 1998 paper. This experiment is a hypothetical means to test the many worlds interpretation, and for once it doesn't involve the senseless murdering of cats. Instead, it is the scientist himself that gets into Schrodinger's box. Rather than a vial of poison, the box will have some sort of murder machine that instantly kills the scientist before they can even feel anything. Once a radioactive atom decays, their death will also happen faster than they can read the Geiger counter or any other measurement tools. These modifications are designed to remove the argument that the scientist would count as an observer of the system, as they would have died before any observation could occur. More importantly, however, instead of a single radioactive atom, the box will contain hundreds. Each atom has a 50% chance of decaying over the course of one half-life, so according to the many worlds interpretation each of these will result in the creation of parallel universes, one where the scientist dies and one where they don't. But because there are hundreds of atoms, the overall odds of survival for the scientists are the same as flipping heads on a coin hundreds of times in a row; it's essentially zero. From the scientist's point of view, however, the odds of survival under the many worlds interpretation would be 100%. So how can that be possible? The first atom has a chance to decay, at which point it creates two parallel universes. If we ignore the possibility of an afterlife, the scientist's consciousness will never exist in the universe where they die, only continuing in the other universe where they survived. That's where the paradoxical nature of this experiment comes into play. Winning all of these coin flips in a row may be a near statistical impossibility, but under the many worlds interpretation it is a necessity that all outcomes exist. As such, the scientist's consciousness will only travel along the singular path of potential outcomes in which they survive the entire ordeal. Despite their death under the conditions of the experiment being all but certain, quantum physics would demand that they survive, making the person functionally immortal. At least immortal in regards to this particular experiment; they will absolutely still die eventually. While quantum immortality seems like an elegant way to prove the many worlds interpretation is true, there are still a couple problems. First, it would require creating an absolutely mind blowing number of alternate universes in which the scientist died, and the theory would only be proven true in the one where they survived. And because the odds of survival are effectively zero, their claims of success are likely to be dismissed and chalked up to the death machine not working properly anyway. As frustrating as it would be to prove the many worlds interpretation and have nobody believe you, fortunately that should never happen. No scientist would actually be stupid enough to turn this thought experiment into an actual experiment. ## Newcomb's Paradox Would you like some free money? Then American physicist William Newcomb has the thought experiment for you. Newcomb devised his thought experiment around 1960, and he discussed it frequently with fellow physicists and philosophers. It was first published by American philosopher Robert Nozick in 1969, and people were already extremely divided. Nozick noted in a follow up paper in 1969, "To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly." So what exactly is this confounding problem? Newcomb's Paradox is a very simple game. You are presented with two boxes, labeled A and B. Box A is clear and you can see that it contains $1,000. Box B is opaque and it will contain either $0 or $1,000,000. You must choose whether you want to only take the mystery box, or if you would rather take both boxes. The twist is that a "reliable predictor" has determined beforehand which you would choose. There are variations on this where the prediction is 100% perfect, but those get into arguments about freewill and reverse causality and a bunch of other stuff that is really meant to be beside the point. For our purposes, we'll assume that the predictions are correct 90% of the time; they are usually correct, but the predictor is fallible. Anyway, if it predicted you would only take box B, then that box will have $1,000,000 inside. If it predicted you will take both boxes, then box B will be empty. The prediction was made before you were presented with the boxes, and the contents of box B have already been finalized. So is the correct answer to only take box B, or is it to take both boxes? When presented with this question, most people immediately assume that there is one answer that is very obviously correct. You're probably already sure what the optimal strategy is right now, because the setup for this question is so simple. But as Nozick alluded to back in 1969, half of you reading this right now think the correct answer is obviously to only take box B, and the other half think the obvious answer is to take both boxes. By the time you get to choose the box, the contents of box B are already fixed. If the predictor chose you would only take the mystery box and you take both, you will get $1,001,000 instead of just a million. If it predicted you would take both boxes, then by taking both you would get $1,000 instead of nothing. In game theory this is called the strategic dominance principle, because one course of action always has a better result than the other, regardless of what the other player chose. So it's settled then and you should always take both boxes, right? Not necessarily, because that decision would have been predicted with 90% accuracy. This means that 10% of the time the prediction will have been wrong and you will get $1,001,000, but the other 90% of the time you will only get $1,000. That means that the average value of taking both boxes is only $101,000. However, if you only take box B, 90% of the time you will get the million dollars while only 10% of the time will you get nothing. That makes the average value of choosing only box B $900,000. In game theory this is called the expected utility principle, and it is just as valid as strategic dominance. That is the source of the paradox, as two equally flawless forms of analysis result in contradictory answers. And while one of these answers may have initially seemed more obvious to you, neither is particularly more obvious than the other as a general rule. Decades of countless surveys have shown that people are consistently split nearly 50/50 on this question, with the decision to take both boxes usually being a couple percentage points more popular. These numbers remain consistent even when the survey only includes professional philosophers, mathematicians, and game theorists, so it's not like there's some really complicated yet definitive decision matrix that can solve this problem. In 2011, a well received paper by physicists David Wolpert and Gregory Benford claimed to unequivocally resolve Newcomb's paradox, and stated that there was only one correct solution. So which answer did Wolpert and Benford choose, do you ask? Rather frustratingly, both. According to their paper, the nature of how the prediction is made is a bit vague, and as such there are two completely different games being played depending on how you assume the probabilistic nature of the predictor's decision works. The two possible choices are each correct in one version of the game but not the other, and everybody just chooses whichever option is correct for the version of the game they believe is being played. Unfortunately, Wolpert and Benford did not weigh in on what they believed was the correct interpretation, leaving us no closer to a definitive answer. However, they did make some interesting word choices that you are free to interpret however you like. They defined taking both boxes as the realist position and taking only box B as the fearful position, arguing that the latter position was seemingly based on the participant believing that they lacked free will in this scenario. ## Sleeping Beauty Problem The Sleeping Beauty Problem was first published in 2000 by philosopher Adam Elga, expanding on ideas first introduced in 1990 by philosopher Arnold Zuboff. The setup for this thought experiment is very simple, but agreeing on a solution has proven to be much harder. Our test subject for this experiment is Sleeping Beauty, who has been made fully aware of the details of the experiment beforehand. On Sunday, Sleeping Beauty will be put to sleep. While she is asleep, one of the researchers will flip a fair coin. If the coin lands on tails, she will be woken up on Monday and asked a single question as laid out by Elga: "What is your credence now for the proposition that the coin landed heads?" In this context, "credence" means what does she believe is the probability that the coin landed heads. After answering the question, Sleeping Beauty will be given a drug that will make her fall back asleep and forget that the interview ever happened. She will then be woken up again on Tuesday, asked the same question, and put back to sleep. If the coin landed on heads, she will only be interviewed on Monday and will sleep through all of Tuesday. So how should Sleeping Beauty answer the question when she is interviewed? There are two conflicted schools of thought, both of which have proofs that are accepted as being mathematically valid. The first answer is the thirder position, which states that Sleeping Beauty should believe that there is a 1/3 chance that the coin landed on heads. This seems counterintuitive since, by definition, a fair coin has a 50% chance of landing on head, but the math behind this argument is sound. First, let's assume that today is Monday. When Sleeping Beauty is woken up, the probability of it being Monday and tails is equal to the probability of it being Monday and heads. Next, let's instead assume that the coin landed tails. Since a tails result always results in her being woken up twice, when she is woken up the probability of it being Monday and tails is equal to the probability of it being Tuesday and tails. Since the probability of Monday tails is equal to both Monday heads and Tuesday tails, all three outcomes have the same probability. Some of you may be screaming at your screens that this sounds like some sort of trick, but we promise you that these two equalities can be combined like this even though they were derived from different assumptions. You can even test it yourself by flipping a coin 100 times and keeping track of when Sleeping Beauty will be woken up. Assuming fair coin flips, you will find that she is woken up at each of the three possible timings about 50 times each. Because all three of these events have an equal probability of happening, thirders argue that Sleeping Beauty should say she believes there is a 1/3 probability that the coin landed heads. After all, 2/3 of the time that she is interviewed it is because the coin landed tails. This was the position that Elga took, and while there is no general consensus it is definitely the more popular of the two answers among philosophers. However, it happens to be the rather vehement opinion of the writer of this episode that the thirder position is an utter abomination, and all those who support it should be ashamed of themselves. The halfer position argued that Sleeping Beauty should believe that there was a 1/2 chance that the coin landed heads, because there was. By the very definition of it being a fair coin flip, the odds were 50%. Sleeping Beauty went to sleep knowing this, and when the researcher wakes her up she has no new information. She has no idea what day of the week it is or if she has already been interviewed. Since she knew that it was a fair coin flip, why should she suddenly believe that there is anything other than a 50% chance of the coin landing on heads? Instead of flipping the coin while Sleeping Beauty was asleep, the researchers could flip it on Sunday while she was still awake and ask her what she believed the probability was that the coin landed on heads. And of course she would say it was 1/2. Likewise, when the experiment ended on Wednesday, if she was asked the question again, now knowing that the experiment had ended, she would always answer that it was a 1/2 probability that the coin landed on tails at the beginning of the experiment. Thirders try to make the answer seem more persuasive by extending the length of the experiment to better illustrate their point, such as making tails result in Sleeping Beauty being woken up and mind-wiped 999 times. By extending the equalities we did earlier, this could prove there is only a 1 in 1,000 chance that the fair coin landed on heads. However, these events aren't independent of each other. Either all 999 tails events happen or 0 of them do, and that is a 50% chance. Of course, the real issue may be that the question itself is ambiguous and that thirders are answering a question that wasn't asked. The question posed by Elga in the original paper, and the question that is always asked of Sleeping Beauty, is "what do you believe is the probability that the coin landed on heads." She knew it was 1/2 when she went to sleep and had no new information when she woke up, so of course the answer to that question should remain unchanged. However, if the question being asked was "what do you believe is the probability that I woke you up because the coin landed on heads", well that is a completely different situation. If the coin landed heads she will be woken up once and if it landed tails then she would be woken up twice, so of course tails is the more likely option under this phrasing. If the experiment was repeatedly performed and Sleeping Beauty was going to be given $100 every time she correctly guessed whether the coin landed on heads or tails, she would make twice as much money by always guessing tails. Not because tails was a more likely result, just because she was asked more times when it was the correct answer. To many people that may sound like an endorsement of the thirder position, as this sort of wager argument is often used to illustrate their point. However, here's one final variation on this thought experiment that may help show the difference between the question being asked and the question that thirders seem to be answering. Let's stop injecting Sleeping Beauty with drugs, and instead we'll use a simple ball pit. Whenever a fair coin lands on heads one green ball will be put in the pit, and whenever it lands on tails two red balls will be put in the pit. We could flip the coin a million times and ask you what the probability is that a green ball was put in the pit, and every time you would correctly say that it was 1/2. However, if we were to then pull one ball at random out of the pit and ask you what the probability is that a green ball was removed? The answer may now be 1/3, but it is a very different question. ## Key Takeaways - The Quantum Suicide thought experiment explores the many worlds interpretation of quantum mechanics. - Newcomb's Paradox presents a scenario where strategic dominance and expected utility principles conflict. - The Sleeping Beauty Problem challenges understanding of probability and belief through a coin flip experiment. - The Copenhagen interpretation suggests a cat in a box is both alive and dead until observed. - The thirder and halfer positions offer differing solutions to the Sleeping Beauty Problem. ## Frequently Asked Questions ### What is the Quantum Suicide thought experiment? The Quantum Suicide thought experiment is a hypothetical scenario where a scientist enters a box with a murder machine triggered by radioactive decay to test the many-worlds interpretation of quantum mechanics. ### What is the many-worlds interpretation in the context of the Quantum Suicide experiment? The many-worlds interpretation suggests that each possible outcome of a quantum event occurs in a separate, parallel universe. In the Quantum Suicide experiment, this means the scientist's consciousness would only exist in the universe where they survive. ### What is Newcomb's Paradox? Newcomb's Paradox is a thought experiment where you choose between taking one opaque box or two boxes, one of which is clear and contains $1,000. The opaque box contains either $0 or $1,000,000, determined by a reliable predictor. ### What are the two main strategies in Newcomb's Paradox? The two main strategies are taking both boxes, which follows the strategic dominance principle, and taking only the opaque box, which follows the expected utility principle. ### What is the Sleeping Beauty Problem? The Sleeping Beauty Problem is a thought experiment where Sleeping Beauty is put to sleep and woken up depending on the outcome of a coin flip. She is asked to determine the probability that the coin landed heads. ### What are the two main positions in the Sleeping Beauty Problem? The two main positions are the thirder position, which argues that Sleeping Beauty should believe there is a 1/3 chance the coin landed heads, and the halfer position, which argues that she should believe there is a 1/2 chance. ### What is the thirder position in the Sleeping Beauty Problem? The thirder position argues that Sleeping Beauty should believe there is a 1/3 chance the coin landed heads because, out of the three possible waking scenarios (Monday heads, Monday tails, Tuesday tails), two involve the coin landing tails. ### What is the halfer position in the Sleeping Beauty Problem? The halfer position argues that Sleeping Beauty should believe there is a 1/2 chance the coin landed heads because the coin flip is fair, and she has no new information upon waking. ### What is the Copenhagen interpretation of quantum mechanics? The Copenhagen interpretation suggests that a quantum system exists in all possible states simultaneously until it is observed, at which point it collapses into one definite state. ### What is the strategic dominance principle in game theory? The strategic dominance principle in game theory states that one course of action always has a better result than the other, regardless of what the other player chose. ## Sources - [Original Side Projects video: 3 Thought Experiments to Boggle the Mind](https://www.youtube.com/watch?v=894vqDKd5RM) ## Related Coverage