Circa 1980 someone at MIT showed me a little pamphlet floating around, created by Gian-Carlo Rota, of all the integers between I think 1 and 1000, listed purely in English, alphabetically. The idea that this could have any conceivable use struck me as so absurd that I could not stop laughing for quite a while. --Dan Hans wrote: << Don Knuth & Allan Miller: A Programming and Problem-Solving Seminar, . . . . . Chapter 1 of the seminar (Alphabetized Integers) provides a good background discussion, contextualizing the problem.
Sometimes the brain has a mind of its own.
It appears that j, k, and z are not used in the American way of writing positive integers. Is there a positive integer that uses all 23 of the other letters? If so, what's the smallest? Kerry
I'll start the bidding with one octillion, one septillion, one quadrillion, one million, one billion, two hundred twelve thousand, four hundred sixty eight (1,001,000,000,001,001,001,212,468). I bet I missed a trick or two, though. On Wed, Oct 12, 2011 at 3:56 PM, Kerry Mitchell <lkmitch@gmail.com> wrote:
It appears that j, k, and z are not used in the American way of writing positive integers. Is there a positive integer that uses all 23 of the other letters? If so, what's the smallest?
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Kerry Mitchell:
It appears that j, k, and z are not used in the American way of writing positive integers. Is there a positive integer that uses all 23 of the other letters? If so, what's the smallest?
Allan Wechsler:
I'll start the bidding with one octillion, one septillion, one quadrillion, one million, one billion, two hundred twelve thousand, four hundred sixty eight (1,001,000,000,001,001,001,212,468). I bet I missed a trick or two, though.
Your number being 1001000000001000001001212468 actually. (Some missing zeros.) I get 1001000000001000001001002568: one octillion, one septillion, one quadrillion, one billion, one million, two thousand, five hundred, sixty-eight. The 'octillion' is the smallest number for 'c'. The 'septillion' is the smallest number for 'p'. The 'quadrillion' is the smallest number for 'q'. The 'billion' is the only number for 'b'. The 'million' is the smallest number for 'm'. That leaves us looking for 'f', 'g', 'v', 'w', 'x', 'y' and I believe 2568 is the smallest number containing those.
Actually, that "Alphabetic Number Table" was done by Radia Perlman (I think when she was a freshman), possibly from a suggestion by Rota. The vaguely amusing side story is that it had to be printed twice, because she spelled "forty" wrong the first time. --ms On 10/12/2011 2:51 PM, Dan Asimov wrote:
Circa 1980 someone at MIT showed me a little pamphlet floating around, created by Gian-Carlo Rota, of all the integers between I think 1 and 1000, listed purely in English, alphabetically. The idea that this could have any conceivable use struck me as so absurd that I could not stop laughing for quite a while.
--Dan
Hans wrote:
<< Don Knuth& Allan Miller: A Programming and Problem-Solving Seminar, . . . . . Chapter 1 of the seminar (Alphabetized Integers) provides a good background discussion, contextualizing the problem. Sometimes the brain has a mind of its own.
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Random trivia: the word 'forty' is the only integer such that its English representation is alphabetically ordered. Anyway, why are we using 10^66 as the highest named power of 1000? Can't we call 10^99 a 'dotriacontillion', for example? That system extends up to 10^600 ('enneanonacontahectillion') quite easily. It appears that any similar systematic naming of all integers must surely use recursion, resulting in a number N having a representation of length: O(N log N log log N log log log N ... 2^log* N) Sincerely, Adam P. Goucher
Actually, that "Alphabetic Number Table" was done by Radia Perlman (I think when she was a freshman), possibly from a suggestion by Rota. The vaguely amusing side story is that it had to be printed twice, because she spelled "forty" wrong the first time.
--ms
On 10/12/2011 2:51 PM, Dan Asimov wrote:
Circa 1980 someone at MIT showed me a little pamphlet floating around, created by Gian-Carlo Rota, of all the integers between I think 1 and 1000, listed purely in English, alphabetically. The idea that this could have any conceivable use struck me as so absurd that I could not stop laughing for quite a while.
--Dan
Hans wrote:
<< Don Knuth& Allan Miller: A Programming and Problem-Solving Seminar, . . . . . Chapter 1 of the seminar (Alphabetized Integers) provides a good background discussion, contextualizing the problem. Sometimes the brain has a mind of its own.
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If we are talking about creatively extending the existing, attested system, see *The Book of Numbers*, by funsters Conway and Guy. On Wed, Oct 12, 2011 at 4:31 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Random trivia: the word 'forty' is the only integer such that its English representation is alphabetically ordered.
Anyway, why are we using 10^66 as the highest named power of 1000? Can't we call 10^99 a 'dotriacontillion', for example? That system extends up to 10^600 ('enneanonacontahectillion') quite easily.
It appears that any similar systematic naming of all integers must surely use recursion, resulting in a number N having a representation of length:
O(N log N log log N log log log N ... 2^log* N)
Sincerely,
Adam P. Goucher
Actually, that "Alphabetic Number Table" was done by Radia Perlman (I
think when she was a freshman), possibly from a suggestion by Rota. The vaguely amusing side story is that it had to be printed twice, because she spelled "forty" wrong the first time.
--ms
On 10/12/2011 2:51 PM, Dan Asimov wrote:
Circa 1980 someone at MIT showed me a little pamphlet floating around, created by Gian-Carlo Rota, of all the integers between I think 1 and 1000, listed purely in English, alphabetically. The idea that this could have any conceivable use struck me as so absurd that I could not stop laughing for quite a while.
--Dan
Hans wrote:
<< Don Knuth& Allan Miller: A Programming and Problem-Solving Seminar, . . . . . Chapter 1 of the seminar (Alphabetized Integers) provides a good background discussion, contextualizing the problem. Sometimes the brain has a mind of its own.
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It looks like you're using Greek. It is more common to use Latin, following Chuquet and the standard dictionary words like "tredecillion" and "vigintillion". "duotrigintillion" for 10^99 is pretty standard ([1] and [2]). For 10^600, [1] gives "novenonagintacentillion" and [2] gives "cennovemnonagintillion". Broken up to show they are made from the same pieces: nove-nonaginta-cent-illion and cen-novem-nonagint-illion. I don't see your O(N log N log log N...) claim. The name of 2^32=4294967296 is not twice as long as the name of 2^31=2147483648. It seems the first N should be removed: O(log N log log N ...) - Robert [1] Conway and Guy, "The Book of Numbers", ISBN 0-387-97993-X or my own web page, http://mrob.com/pub/math/largenum.html#conway-wechsler [2] http://isthe.com/cgi-bin/number.cgi On Wed, Oct 12, 2011 at 16:31, Adam P. Goucher <apgoucher@gmx.com> wrote:
Anyway, why are we using 10^66 as the highest named power of 1000? Can't we call 10^99 a 'dotriacontillion', for example? That system extends up to 10^600 ('enneanonacontahectillion') quite easily.
It appears that any similar systematic naming of all integers must surely use recursion, resulting in a number N having a representation of length:
O(N log N log log N log log log N ... 2^log* N)
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
Yes, I meant O(log N log log N ...). Oops. Sincerely, Adam P. Goucher ----- Original Message ----- From: Robert Munafo To: math-fun Cc: Adam P. Goucher Sent: Wednesday, October 12, 2011 10:45 PM Subject: Re: [math-fun] Zillions It looks like you're using Greek. It is more common to use Latin, following Chuquet and the standard dictionary words like "tredecillion" and "vigintillion". "duotrigintillion" for 10^99 is pretty standard ([1] and [2]). For 10^600, [1] gives "novenonagintacentillion" and [2] gives "cennovemnonagintillion". Broken up to show they are made from the same pieces: nove-nonaginta-cent-illion and cen-novem-nonagint-illion. I don't see your O(N log N log log N...) claim. The name of 2^32=4294967296 is not twice as long as the name of 2^31=2147483648. It seems the first N should be removed: O(log N log log N ...) - Robert [1] Conway and Guy, "The Book of Numbers", ISBN 0-387-97993-X or my own web page, http://mrob.com/pub/math/largenum.html#conway-wechsler [2] http://isthe.com/cgi-bin/number.cgi On Wed, Oct 12, 2011 at 16:31, Adam P. Goucher <apgoucher@gmx.com> wrote: Anyway, why are we using 10^66 as the highest named power of 1000? Can't we call 10^99 a 'dotriacontillion', for example? That system extends up to 10^600 ('enneanonacontahectillion') quite easily. It appears that any similar systematic naming of all integers must surely use recursion, resulting in a number N having a representation of length: O(N log N log log N log log log N ... 2^log* N) -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
participants (7)
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Adam P. Goucher -
Allan Wechsler -
Dan Asimov -
Hans Havermann -
Kerry Mitchell -
Mike Speciner -
Robert Munafo