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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