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.


  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.


    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.


    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

  10. Because watches can tell time accurately which includes a microchip space and games » Infinite Certainty as well LCD screen, tons of noname watches with cheap plastic or metal cases have flooded sales, offering discounts for lowquality products. You may find out bins of watches at many discount retailers, not being totally sure large enough . サッカースパイク watch will often last a quarter or so. Through which to take into consideration brand watches.

    Comment by サッカースパイク — January 17, 2014 @ 10:10 pm

  11. Very shortly this web site will be famous amid all blogging and site-building users, due to it’s nice articles|
    My brother suggested I might like this blog. He used to be totally right. This put up actually made my day. You can not believe simply how so much time I had spent for this info! Thank you!|
    Very nice post. I just stumbled upon your blog and wished to say that I’ve really enjoyed surfing around your blog posts. After all I’ll be subscribing to your rss feed and I hope you write again soon!|
    Hello there! Would you mind if I share your blog with my myspace group? There’s a lot of people that I think would really appreciate your content. Please let me know. Many thanks|
    Since the admin of this web site is working, no question very quickly it will be well-known, due to its quality contents.|

    Comment by RonaldMaw — March 3, 2014 @ 2:51 pm

  12. This is getting a bit more subjective, but I much prefer the Zune Marketplace. The interface is colorful, has more flair, and some cool features like ‘Mixview’ that let you quickly see related albums, songs, or other users related to what you’re listening to. Clicking on one of those will center on that item, and another set of “neighbors” will come into view, allowing you to navigate around exploring by similar artists, songs, or users. Speaking of users, the Zune “Social” is also great fun, letting you find others with shared tastes and becoming friends with them. You then can listen to a playlist created based on an amalgamation of what all your friends are listening to, which is also enjoyable. Those concerned with privacy will be relieved to know you can prevent the public from seeing your personal listening habits if you so choose.

    Comment by recette crepe — April 12, 2014 @ 2:03 am

  13. Oleh : Sabrina Hamid“Fifi! Tunggulah aku. Janganlah lari.” Jerit Farah sambil lari lintang pukang ingin mendapatkan Fifi yang jauh dihadapan. Mereka berdua takut dimarahi oleh Cikgu Syah jika terlewat masuk kelas. “Hish. Dahlah kita terpaksa tunggu…

    Comment by Toms Shoes Outlet — April 26, 2014 @ 12:03 am

  14. Pourquoi avoir intégré M. Miyagi dans Reality Fighters ?

    Comment by air jordan xx8 — May 5, 2014 @ 2:44 am

  15. Notre dessinatrice m’a regardé d’un air de dire “Mais ?a va pas??”, mais j’ai coupé court?: “?coute, t’as pas idée à quel point je supporte pas les clowns.”

    Comment by maillot de jordan — May 5, 2014 @ 2:44 am

  16. Today, while I was at work, my cousin stole my apple ipad and
    tested to see if it can survive a thirty foot drop, just so
    she can be a youtube sensation. My apple ipad is now broken and she has 83 views.
    I know this is completely off topic but I had to share it with someone!

    Comment by how to get rid of anxiety stress — May 6, 2014 @ 5:14 am

  17. [...] [24] Suppose that near certainty in your ability to assess a set of propositions equals a 1 in a million chance of being wrong about an assessment of a particular proposition. This means that given a million similar statements, you would have to be correct (on average) about 999999 such assessments while being wrong only once. Can you possibly be this accurate? An amusing example: [...]

    Pingback by Alexander Kruel · Interview with Michael Littman on AI risks — February 6, 2015 @ 11:39 am

RSS feed for comments on this post. TrackBack URI

Leave a comment

Powered by WordPress