[math-fun] A question about the "is this prime?" game
This week I made a game which has turned out to be like crack to maths fans - http://isthisprime.com/game/. You're shown a number, and you have to decide if it's prime or not. The aim is to correctly sort as many numbers as possible within a minute; the game ends as soon as you get one wrong. So, I thought that would appeal on its own merits to math-funsters, but I have a question which occurred to me while talking about it with Colin Wright: since primes become rarer the higher you go, at what point is just clicking "No" as good a strategy as doing any thinking? I suppose I could rephrase and slightly change the question to: if the maximum number you can be shown increases by a factor of X each time you make a correct decision, what's the expected score of a strategy that just clicks "no" every time? And finally, I'm collecting data on each attempt made at the game. I expect to be able to come up with some interesting statistics about people's intuitions on primality. So far, 51 seems to be by the far most "primey" composite, before factoring in the likelihoods of particular numbers being shown.
Oliver Sacks (z"l) wrote in one of his books about some twins who were remarkably good at factoring numbers. Does anyone remember the details? I remember being a little bit suspicious, because at least one of the feats seem to require more parallel processing power than I imagine human brains to be capable of (leaving aside sensory processing, which is hard-wired). But I also felt that we don't know enough about brains to know what brains can or can't do. Jim Propp PS: z"l is a Hebrew abbreviation for "may his/her memory be a blessing". On Wednesday, March 9, 2016, Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
This week I made a game which has turned out to be like crack to maths fans - http://isthisprime.com/game/. You're shown a number, and you have to decide if it's prime or not. The aim is to correctly sort as many numbers as possible within a minute; the game ends as soon as you get one wrong.
So, I thought that would appeal on its own merits to math-funsters, but I have a question which occurred to me while talking about it with Colin Wright: since primes become rarer the higher you go, at what point is just clicking "No" as good a strategy as doing any thinking? I suppose I could rephrase and slightly change the question to: if the maximum number you can be shown increases by a factor of X each time you make a correct decision, what's the expected score of a strategy that just clicks "no" every time?
And finally, I'm collecting data on each attempt made at the game. I expect to be able to come up with some interesting statistics about people's intuitions on primality. So far, 51 seems to be by the far most "primey" composite, before factoring in the likelihoods of particular numbers being shown. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Here's a short paper about the twins: http://goertzel.org/dynapsyc/yamaguchi.htm On Wed, 9 Mar 2016 at 17:15 James Propp <jamespropp@gmail.com> wrote:
Oliver Sacks (z"l) wrote in one of his books about some twins who were remarkably good at factoring numbers. Does anyone remember the details? I remember being a little bit suspicious, because at least one of the feats seem to require more parallel processing power than I imagine human brains to be capable of (leaving aside sensory processing, which is hard-wired). But I also felt that we don't know enough about brains to know what brains can or can't do.
Jim Propp
PS: z"l is a Hebrew abbreviation for "may his/her memory be a blessing".
On Wednesday, March 9, 2016, Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
This week I made a game which has turned out to be like crack to maths fans - http://isthisprime.com/game/. You're shown a number, and you have to decide if it's prime or not. The aim is to correctly sort as many numbers as possible within a minute; the game ends as soon as you get one wrong.
So, I thought that would appeal on its own merits to math-funsters, but I have a question which occurred to me while talking about it with Colin Wright: since primes become rarer the higher you go, at what point is just clicking "No" as good a strategy as doing any thinking? I suppose I could rephrase and slightly change the question to: if the maximum number you can be shown increases by a factor of X each time you make a correct decision, what's the expected score of a strategy that just clicks "no" every time?
And finally, I'm collecting data on each attempt made at the game. I expect to be able to come up with some interesting statistics about people's intuitions on primality. So far, 51 seems to be by the far most "primey" composite, before factoring in the likelihoods of particular numbers being shown. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
That paper is very annoying in its lack of specificity. "Oliver Sacks (1985) reported that autistic twins, who were already famous for calendar calculation, also had extraordinary number abilities." Repeatedly, the author (Yamaguchi) uses the phrase "autistic twins" *without* saying whether he means ALL, MANY, SOME, or JUST ONE PAIR. (And if "many" or "some", then about what fraction would that mean.) I presume that I could figure out what he means by reading further into the paper. But I have completely lost interest in this author. —Dan
On Mar 9, 2016, at 9:22 AM, Christian Lawson-Perfect <christianperfect@gmail.com> wrote:
Here's a short paper about the twins: http://goertzel.org/dynapsyc/yamaguchi.htm
On Wed, 9 Mar 2016 at 17:15 James Propp <jamespropp@gmail.com> wrote:
Oliver Sacks (z"l) wrote in one of his books about some twins who were remarkably good at factoring numbers. Does anyone remember the details? I remember being a little bit suspicious, because at least one of the feats seem to require more parallel processing power than I imagine human brains to be capable of (leaving aside sensory processing, which is hard-wired). But I also felt that we don't know enough about brains to know what brains can or can't do.
Jim Propp
PS: z"l is a Hebrew abbreviation for "may his/her memory be a blessing".
On Wednesday, March 9, 2016, Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
This week I made a game which has turned out to be like crack to maths fans - http://isthisprime.com/game/. You're shown a number, and you have to decide if it's prime or not. The aim is to correctly sort as many numbers as possible within a minute; the game ends as soon as you get one wrong.
So, I thought that would appeal on its own merits to math-funsters, but I have a question which occurred to me while talking about it with Colin Wright: since primes become rarer the higher you go, at what point is just clicking "No" as good a strategy as doing any thinking? I suppose I could rephrase and slightly change the question to: if the maximum number you can be shown increases by a factor of X each time you make a correct decision, what's the expected score of a strategy that just clicks "no" every time?
And finally, I'm collecting data on each attempt made at the game. I expect to be able to come up with some interesting statistics about people's intuitions on primality. So far, 51 seems to be by the far most "primey" composite, before factoring in the likelihoods of particular numbers being shown. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Conversely, are there "compositey" primes?
The most commonly misidentified prime is 5, I assume because people are applying an "if it ends in 5 it's composite" rule, but after that 79 and 59 are closely tied for second place. I suppose they both look like multiples of 3 if you're, to quote British legal precedent, a moron in a hurry.
It's from "The Man Who Mistook His Wife For A Hat". Here's the excerpt: http://empslocal.ex.ac.uk/people/staff/mrwatkin/isoc/twins.htm The Yamaguchi paper casts some doubt on the accuracy of the account. Tom James Propp writes:
Oliver Sacks (z"l) wrote in one of his books about some twins who were remarkably good at factoring numbers. Does anyone remember the details? I remember being a little bit suspicious, because at least one of the feats seem to require more parallel processing power than I imagine human brains to be capable of (leaving aside sensory processing, which is hard-wired). But I also felt that we don't know enough about brains to know what brains can or can't do.
Jim Propp
PS: z"l is a Hebrew abbreviation for "may his/her memory be a blessing".
On Wednesday, March 9, 2016, Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
This week I made a game which has turned out to be like crack to maths fans - http://isthisprime.com/game/. You're shown a number, and you have to decide if it's prime or not. The aim is to correctly sort as many numbers as possible within a minute; the game ends as soon as you get one wrong.
So, I thought that would appeal on its own merits to math-funsters, but I have a question which occurred to me while talking about it with Colin Wright: since primes become rarer the higher you go, at what point is just clicking "No" as good a strategy as doing any thinking? I suppose I could rephrase and slightly change the question to: if the maximum number you can be shown increases by a factor of X each time you make a correct decision, what's the expected score of a strategy that just clicks "no" every time?
And finally, I'm collecting data on each attempt made at the game. I expect to be able to come up with some interesting statistics about people's intuitions on primality. So far, 51 seems to be by the far most "primey" composite, before factoring in the likelihoods of particular numbers being shown. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
="Christian Lawson-Perfect" <christianperfect@gmail.com> ... people's intuitions on primality. So far, 51 seems to be by the far most "primey" composite, ...
''... the legend of the so-called "Grothendieck prime". In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. "You mean an actual number?" Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, " All right, take 57." ...'' -- http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf Conversely, are there "compositey" primes? Sort of similarly, I've recently become fond of 343 and 2401. Generally, all these might be called "camouflaged numbers" -- their appearance disguises or misleads intuition of their true nature. Primey numbers have many primey substrings, like 3773. Can we quantify how well "primeyness" predicts primality?
participants (5)
-
Christian Lawson-Perfect -
Dan Asimov -
James Propp -
Marc LeBrun -
Tom Karzes