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Archive for category 'mathematics'

The Unimaginable Mathematics of Borges' Library of Babel

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Sounds fantastic. From a review by Brian Hayes in American Scientist:

In William Goldbloom Bloch’s mathematical companion to “The Library of Babel,” the first task is to calculate the number of distinct books that can be created in this way. There’s not much to it. Borges tells us that the alphabet of the books is restricted to 25 symbols (22 letters, the comma, the period and the word space). He also mentions that each book has 410 pages, with 40 lines of 80 characters on each page. Thus a book consists of 410 × 40 × 80 = 1,312,000 symbols. [...]

These combinatorial exercises are the most obvious instances where mathematics can illuminate the Borges story, but Bloch finds much else to comment on as well. [...] Borges describes the library as a close-packed array of hexagonal rooms. Four walls of each hexagon are lined with bookshelves, holding a total of 640 books; the other two walls provide portals to adjacent hexagons. Vertically, the levels of the library are connected by ventilation shafts and spiral stairways. This design has some curious consequences. For example, Bloch points out that somewhere in the library there must be at least one hexagon whose shelves are not full. The reason is that 251,312,000 is not evenly divisible by 640

For me the biggest surprise in Bloch’s commentary comes in a chapter that applies ideas from graph theory to the layout of the library. [...]

Ed Felten: You Can Own an Integer Too!

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45 69 5C CF 9D 6C 3C 19 BB 98 71 41 5E 54 BC 58 is mine.

Who Can Name the Bigger Number?

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You have fifteen seconds. Using standard math notation, English words, or both, name a single whole number--not an infinity--on a blank index card.

Interesting, accessible journey through some of the mathematics of really big numbers, from "9999..."-repeating through to curious constructs you never learned the names of in school. See also MeFi.

Small things, links and miscellany, sparkling with light. Sam's tumblelog.

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