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Pratique du shadowing : The Most Controversial Problem in Philosophy

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  1. Do not hit the like button or the dislike button, at least not yet.0:00
  2. I want you to consider a problem that's been one of the most controversial in math and philosophy over the past 20 years.0:04
  3. There is no consensus answer, so I want you to listen to the problem and then vote for the answer you prefer using the like and dislike buttons.0:10
  4. Okay?0:19
  5. Here is the setup.0:20
  6. Sleeping Beauty volunteers to be the subject of an experiment.0:22
  7. And before it starts, she's informed of the procedure.0:25
  8. On Sunday night, she will be put to sleep.0:28
  9. And then, a fair coin will be flipped.0:31
  10. If that coin comes up heads, she'll be awakened on Monday and then put back to sleep.0:34
  11. If the coin comes up tails, she will also be awakened on Monday and put back to sleep.0:39
  12. But then she'll be awakened on Tuesday as well and then put back to sleep.0:44
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  1. Now each time she gets put back to sleep, she will forget that she was ever awakened.0:48
  2. In the brief period, anytime she's awake, she will be told no information.0:52
  3. But she'll be asked one question.0:58
  4. What do you believe is the probability that the coin came up heads?1:01
  5. So how should she answer?1:05
  6. Feel free to pause the video and answer the question for yourself right now.1:07
  7. This was my reaction after hearing the problem for the first time.1:12
  8. I mean, the intuitive answer that pops into my head is clearly one in three.1:16
  9. It could be the Monday when it came up heads, or it could be the Monday when it came up tails, or it could be the Tuesday when it came1:20
  10. up tails.1:29
  11. But you know what's really interesting is you just answered that the probability of a coin coming up heads is one third.1:31
  12. I think a lot of this comes down to what specific question is asked of her.1:35
  13. What is the probability that a fair coin flipped gives heads?1:39
  14. That's 50%.1:43
  15. What is the probability that the coin came up heads?1:44
  16. I would say the answer is a third from her perspective.1:48
  17. It's remarkably the same question.1:54
  18. The simple reason why Sleeping Beauty should say the probability of heads is one half is because she knows the coin is fair.1:56
  19. Nothing changes between when the coin is flipped and when she wakes up, and she knew for a fact that she would be woken up and she receives no new2:03
  20. information when that happens.2:10
  21. Imagine that instead of flipping the coin after she's asleep, the experimenters flip the coin first and ask her immediately.2:13
  22. What's the probability that the coin came up heads?2:21
  23. Well, she would certainly say one half.2:24
  24. So why should anything change after she goes to sleep and wakes up?2:26
  25. This is known as the Haffer position, but there is another way to look at it.2:30
  26. Others would argue that something does change when she's awakened.2:35
  27. I mean, it seems like she gets no new information.2:38
  28. There are no calendars, no entails or anything, and she knew that she would be woken up, but she actually learns something important.2:41
  29. She learns that she's gone from existing in a reality where there are two possible states.2:49
  30. The coin came up either heads or tails, to existing in a reality where there are three possible states.2:53
  31. Monday heads, Monday tails, or Tuesday tails.3:00
  32. And therefore, she should assign equal probability to each of these three outcomes where heads only occurred in one.3:03
  33. So the probability that the coin came up heads is one -third.3:10
  34. This is known as the thirder position.3:14
  35. Now, I know it seems wrong to suggest that a fair coin should have a one -third probability of coming up heads, but that's because the question she's asked is3:18
  36. subtly different.3:25
  37. The implied question is, given you're awake, what's the probability that the coin came up heads?3:26
  38. And that is one -third.3:32
  39. Now, halfers would counter that just because there are three possible outcomes doesn't mean they are each equally likely.3:34
  40. In the Monty Hall problem, for example, the contestant ultimately has to choose between two doors.3:40
  41. But it'd be wrong to assign them 50 -50 odds.3:45
  42. The prize is actually twice as likely to be behind one door than the other.3:48
  43. In the Sleeping Beauty problem, we know a heads outcome and a tails outcome are equally likely, so the chance of waking up on Monday with heads is 50%, and3:52
  44. the chance of waking up on Monday or Tuesday with tails should be 50%.4:01
  45. Therefore, the tails probability gets split across two days, 25 % each.4:05
  46. But if you repeat the experiment over and over, which you can try for yourself by repeatedly flipping a coin, you find she wakes up a third of the time4:11
  47. Monday heads, a third of the time Monday tails, and a third of the time Tuesday tails, not 50, 25, 25, like the previous analysis would suggest.4:19
  48. So if you were Sleeping Beauty and you were awakened and asked, what's the probability that coin came up heads, what would you say?4:30
  49. If you would say one third, then hit the like button.4:38
  50. If you would say one half, hit the dislike button.4:41
  51. The answer may seem obvious to you, but you should know that to other people, the other answer seems equally obvious, and that's why hundreds and hundreds of philosophy papers4:45
  52. have been published on this problem over the past 22 years.4:55
  53. There have been many variations of this problem.4:59
  54. Like, what if instead of being woken up twice of the coin lands tails, she's instead woken up a million times?5:02
  55. If the coin comes up heads, she's still woken only once.5:08
  56. Doesn't it seem absurd in this case when Sleeping Beauty wakes up to say that it was just as likely that the coin landed heads as tails?5:12
  57. When we know there are a million more wakeups in the tails case than in the heads case.5:19
  58. I mean, if you reach into a bag of one white marble and a million black marbles, what are the chances that you pull out that one white marble?5:24
  59. I was pretty convinced by this, and I considered myself a thirder, but this same argument is used to convince people that we're living in a simulation.5:32
  60. The thinking goes that our computing technology has improved so dramatically, even over just the last 40 years, that we can imagine a time in the not too distant future5:41
  61. when we can create a completely realistic simulation of our world.5:50
  62. And once that occurs, it should be trivial to make unlimited copies of that simulation.5:54
  63. And then if you were to ask someone if they're living in a simulation, they would have to admit that they probably are because there are many more instances of6:00
  64. that existence than the one true external reality.6:07
  65. But how do we know that this hasn't happened already and that we're living inside a simulation?6:11
  66. I mean, if it can happen, then it probably has happened and we are living in a simulation.6:15
  67. This seems like the logical conclusion of the thirder worldview.6:20
  68. Now, I personally don't buy that I'm living in a simulation, and I think most people don't buy it, but maybe that's just a logical bias.6:25
  69. But there's another thought experiment that makes me seriously reconsider the thirder position.6:32
  70. Let's say there's a soccer game between a really great team like Brazil and a less world -dominating team like Canada.6:37
  71. So the odds are 80 -20 in Brazil's favor.6:44
  72. Now, a researcher is going to put you to sleep before the game starts.6:48
  73. And if Brazil wins, they'll wake you up one time.6:51
  74. But if Canada wins, they'll wake you up 30 times in a row.6:54
  75. And just like Sleeping Beauty, you won't remember if you've been woken before.6:58
  76. Okay, so the game is about to start.7:02
  77. You fall asleep and now you're woken up.7:04
  78. Who do you think won the game?7:09
  79. The thirder would say Canada, but I would almost certainly say Brazil.7:11
  80. I mean, why should I give any weight to what the researcher would have done if Canada had one when I'm fairly confident that they won't?7:16
  81. To extend this, let's say Brazil plays Canada five times, and we do this experiment each time.7:24
  82. Well, then if you say Brazil each time you're woken up, you'll probably be right about four out of five of the games.7:30
  83. But if you said Canada every time, you would be wrong about those four games, but right 30 times in a row when you're repeatedly asked about Canada's one victory.7:36
  84. If you stand to win a bet by correctly answering the question, then by all means, you should bet on Canada.7:46
  85. But if you want to correctly pick the winner of more of the games, well then you should say Brazil.7:51
  86. And this is what's at the heart of the dispute between halfers and thirders in the Sleeping Beauty problem.7:57
  87. If you want to be right about the outcome of the coin tosses, well, you should say the probability of heads is a half.8:02
  88. But if you want to answer more questionings correctly, well then you should say one third.8:08
  89. I want to leave you with one last thought experiment.8:13
  90. Imagine that you know for a fact that before our universe began, there was a coin flip.8:17
  91. And if it came up heads, only a single universe would be created.8:22
  92. But if it came up tails, a quasi -infinite multiverse would be created.8:26
  93. And in each of those multiverse universes, you'd find every possible variation of Earth and the people on it.8:30
  94. In some versions, there would be no Earth.8:36
  95. Now you becoming conscious is just like Sleeping Beauty waking up.8:41
  96. There's no way to tell if you're in that single universe or in one of the multiverse universes, but you know there are a lot more of them.8:45
  97. So would you think that you're for sure in the multiverse?8:54
  98. Or are the chances 50 -50?8:58
  99. The best way to develop intuition about probability is by working through scenarios or running simulations like we did for Sleeping Beauty.9:05
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  114. I will put that down in the description.10:11
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Mesuré dans ce clip

Débit
207 mots par minute — plus rapide que 66% du catalogue
Niveau CECRL
B2
Mots à connaître
worldview, org, multiverse, tosses, subtly, entails
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