Algorithm about Counting Letters and Words in TextDate: 01/03/2007 at 20:47:38 From: Ruben Subject: Math involved in language texts - algorithms Some years back in a magazine, Martin Gardner drew attention to a phenomenon involving, as he later disclosed, an algorithm on the text of language. To illustrate the results that could be gotten, he reproduced the first paragraph of the Declaration of Independence, as follows: When in the Course of human Events, it becomes necessary for/ one People to dissolve the Political Bands that have connected/ them with another, and to assume among the Powers of the Earth/ the separate and equal Station to which the Laws of Nature and of/ Nature’s God entitle them, a decent Respect to the Opinions of Mankind requires that they should declare the causes that impel them to the Separation. Gardner then gave the following instructions: 1) Select a word from any of the first twenty words 2) Count the number of letters in that word; call that number n 3) Starting with the NEXT word, move ahead n words in the text 4) Upon reaching the nth word, count the number of letters in it 5) Move ahead as many words as the new letter count 6) Continue in this way, counting letters and moving ahead words using the latest letter count, until you end a count on a word beyond the 4th line of the text 7) What word is it? (The word will be the same irrespective of which of the first twenty words you selected to start) I have lost the magazine where I found this phenomenon described by Gardner. In the Answers column, he mentioned that the procedure is based on an algorithm discovered by a certain mathematician; an associate regarding Math applied to texts. I would like to know the names of the mathematicians, the name of the algorithm, and if possible Gardner’s brief explanation, verbatim, of how it works. The “text-puzzle” was presented in the May 1999 issue of "Games Magazine", but although the answer (the first word on which the counting stops, beyond the 4th line) is given, Gardner’s comments are omitted. Date: 01/04/2007 at 13:33:25 From: Doctor Douglas Subject: Re: Math involved in language texts - algorithms Hi Ruben, I also remember reading about this very interesting phenomenon. A web search (Google) using the search terms "Martin Gardner" text word count gives some helpful web pages: Ross Eckler, Word Trees in Running Text http://wordways.com/wtrees.htm John Allen Paulos - An Old Card Trick and New Biblical Hoax http://www.math.temple.edu/~paulos/bibhoax.html The name of the mathematician and physicist that is associated with the origins of the idea is Martin Kruskal. Here is a list of some other resources that might be helpful in finding how Gardner described the phenomenon of the "Kruskal count": C. Fulves and M. Gardner, The Kruskal Principle, The Pallbearers Review, June 1975. M. Gardner, Mathematical Games, Sci. Amer. 238 (1978) No. 2 (February), 19-32. M. Gardner, From Penrose Tiles to Trapdoor Ciphers, W. H. Freeman Co., New York, 1988. (Chapter 19) The basic idea is that these chains of linked elements running through the entire sequence will, with high probability, intersect. Once they intersect, they will coincide forever thereafter. For explanations by others of how the phenomenon arises, try: Ivars Peterson, Science News for Kids: Mathemusements http://www.sciencenewsforkids.org/pages/puzzlezone/muse/muse1003.asp Ivars Peterson's MathTrek at MAA Online http://www.maa.org/mathland/mathtrek_12_24_01.html and for (much) more mathematical detail and rigor, J. C. Lagarias, E. Rains, and R. J. Vanderbei, "The Kruskal Count", http://arxiv.org/PS_cache/math/pdf/0110/0110143.pdf - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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