space and games

January 9, 2008

Infinite Certainty

Filed under: General — Peter de Blanc @ 9:26 pm

On Overcoming Bias, Eli says:

I don’t think you could get up to 99.99% confidence for assertions like “53 is a prime number”. Yes, it seems likely, but by the time you tried to set up protocols that would let you assert 10,000 independent statements of this sort – that is, not just a set of statements about prime numbers, but a new protocol each time – you would fail more than once. Peter de Blanc has an amusing anecdote on this point, which he is welcome to retell in the comments.

Here’s the anecdote:

Conversation with squallmage at 2006-07-28 23:46:54 on OneTrueCalculus (aim)
(23:47:19) OneTrueCalculus: oi
(23:47:23) SquallMage: oi
(23:47:33) OneTrueCalculus: how likely would you rate it that 81,241 is prime?
(23:47:59) SquallMage: very
(23:48:03) OneTrueCalculus: you can go ahead and calculate it if you want, or just give me a probability
(23:49:03) OneTrueCalculus: obviously this would be the subjective sort of probability
(23:49:11) SquallMage: yes.
(23:50:30) OneTrueCalculus: well?
(23:50:35) OneTrueCalculus: or are you busy calculating?
(23:50:38) SquallMage: I said ‘very’.
(23:50:42) OneTrueCalculus: ah
(23:50:46) SquallMage: Quantify that if you must, I’m too tired to.
(23:50:55) OneTrueCalculus: ok
(23:51:10) OneTrueCalculus: I won’t quantify it for you, since I don’t know how you are calibrated
(23:51:22) OneTrueCalculus: okay, how about 7?
(23:51:46) SquallMage: the probability of it’s primacy, or as a quantification of ‘very’?
(23:51:55) OneTrueCalculus: the probability of 7 being prime
(23:52:02) SquallMage: 7 is prime.
(23:52:08) OneTrueCalculus: with probability 1?
(23:52:18) SquallMage: Yes.
(23:52:41) OneTrueCalculus: so will you accept this deal? If you ever find out that 7 is not prime, you will give me $100.
(23:53:10) SquallMage: Only if you explain to me in detail what brought you to propose that deal to me.
(23:53:37) OneTrueCalculus: I am trying to swindle you out of your cash and/or teach you a valuable lesson
(23:54:09) OneTrueCalculus: also, I am trying to figure out how overconfident people are
(23:55:42) SquallMage: Well. I would make a deal with you that I would give you $100 if it were ever proven to me that it was possible in base-ten to generate the quantity 7 by multiplying together any two integers other than 1 and 7.
(23:55:55) OneTrueCalculus: okay
(23:56:05) OneTrueCalculus: I am only talking about the standard natural numbers. No weird groups or anything
(23:56:20) OneTrueCalculus: base 10
(23:56:24) SquallMage: No, ‘7 and 1′ is not different than ‘1 and 7′ also.
(23:56:32) OneTrueCalculus: of course not
(23:56:39) SquallMage: Just checking.
(23:56:42) OneTrueCalculus: I wouldn’t use a cheap technicality like that
(23:56:44) SquallMage: Since I’m a language bastard.
(23:56:49) SquallMage: And I completely would.
(23:56:54) OneTrueCalculus: okay
(23:57:13) OneTrueCalculus: If you even honestly feel that it was a cheap technicality, I wouldn’t expect you to pay me.
(23:57:22) SquallMage: Anyways.
(23:57:23) OneTrueCalculus: Under those conditions, will you accept my offer?
(23:57:33) SquallMage: Yes.
(23:57:37) OneTrueCalculus: Okay.
(23:57:44) SquallMage: Tell me how I owe you $100 now
(23:57:48) OneTrueCalculus: you don’t
(23:57:52) SquallMage: Good.
(23:57:56) OneTrueCalculus: now
(23:58:03) OneTrueCalculus: will you accept the same offer, but for 11 this time?
(23:58:05) SquallMage: Not for 81241
(23:58:34) OneTrueCalculus: i.e. if you ever find out that 11 is not prime, you will give me $100
(23:58:49) SquallMage: I would make that deal under equivalent conditions
(23:59:00) OneTrueCalculus: okay. I’m asking you to make that deal.
(23:59:44) SquallMage: I did say that I would.
(00:00:00) OneTrueCalculus: okay, thanks
(00:00:04) OneTrueCalculus: how about 13?
(00:00:20) SquallMage: Yes.
(00:00:48) SquallMage: 17 also, and 19, and 23.
(00:00:54) OneTrueCalculus: thanks.
(00:00:57) OneTrueCalculus: What about 27?
(00:01:02) SquallMage: No thanks.
(00:01:05) OneTrueCalculus: 29?
(00:01:11) SquallMage: sure.
(00:01:13) OneTrueCalculus: 31?
(00:01:17) SquallMage: Yep.
(00:01:20) OneTrueCalculus: 33?
(00:01:24) SquallMage: Nah.
(00:01:26) OneTrueCalculus: 37?
(00:01:29) SquallMage: Yah.
(00:01:31) OneTrueCalculus: 39?
(00:01:35) SquallMage: Nah.
(00:01:37) OneTrueCalculus: 41?
(00:01:42) SquallMage: Yah.
(00:01:45) OneTrueCalculus: 43?
(00:01:51) SquallMage: Yah.
(00:01:54) OneTrueCalculus: 47?
(00:02:06) SquallMage: Yah.
(00:02:09) OneTrueCalculus: 49?
(00:02:17) SquallMage: Nah.
(00:02:20) OneTrueCalculus: 51?
(00:02:28) SquallMage: Yah.
(00:02:36) OneTrueCalculus: Thank you. I win.
(00:02:48) SquallMage: You know I’ve been up since this time yesterday.
(00:02:51) OneTrueCalculus: You can donate your money to the Singularity Institute for Artificial Intelligence
(00:03:06) SquallMage: I’ll forward you their message of receipt.

16 Comments »

  1. It took me way too long (about a minute) to figure out 51=17*3. I need to practice my mental arithmetic more.

    I haven’t talked to you in a long time. We should.

    /H.

    Comment by Herbert — March 2, 2008 @ 12:34 am

  2. Why did he even play? What was in it for him?

    Comment by Will Pearson — November 6, 2008 @ 9:52 am

  3. 81241 = 127*593

    Comment by Paul Crowley — April 22, 2009 @ 1:39 pm

  4. 137 * 593, Paul Crowley.

    Comment by Robin Z — January 18, 2010 @ 4:40 pm

  5. >What was in it for him?

    Amusement, maybe. With 100% subjective probability, he should be completely indifferent even if there’s nothing in it for him at all. Theoretically.

    Comment by Toby Bartels — December 16, 2010 @ 8:55 pm

  6. I tried doing this on my friend. He claimed prime numbers don’t exist “because every number but 0 is divisible by 2.” He’s 15.

    Comment by Chloe — April 15, 2011 @ 7:36 am

  7. >What was in it for him?

    A valuable lesson (see 23:53:37).

    Thanks for giving that one to us for free.

    Comment by Jordi Salvat i Alabart — April 17, 2012 @ 9:59 am

  8. Moronic and somewhat useless. To establish mental ‘focus’ varies in a human or humans is a moot point really. The same person, might have, if slept better apparently, not made the ‘delayed’ calculation error. The point supposedly argued for here, is how confident someone is (read: biased) about their opinion on something, right? And what? That famous example of Ramanujan in hospital when Henry? (ah, Hardy) visited him and instantly could state that 1729 was… etc.

    All you sum up is the two persons in the chat are not geniuses and thus will have some limited focus at some point. Subjective probability… give me a break… you are trying to make hens out of feathers.

    Seriously.

    Comment by M. Switalski — May 11, 2012 @ 9:44 am

  9. Actually, the point being made is that your computation device – whether it’s a wonderfully faulty human brain, or even a highly deterministic computer chip – will get randomly hit by a cosmic ray well before you test a proposition ten quintillion times, nevermind an “infinite” number.

    Comment by linkhyrule5 — July 30, 2013 @ 9:16 pm

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