[aprescott]

(Edit: I emailed them and the article has been corrected.)

> a Library that contains 251,312,000 volumes of random sequences of letters (1,312,000 being the number of characters in any given book, each of which admits of twenty-five variations)

This seems to be a typo of sorts. I believe the correct number is 25^1312000 (sequence length m, n possible values for each, n^m distinct possible sequences).

Having hit this in the past, my guess is it was originally written with a superscript, then the text lost the formatting (leaving 251312000), and an editor left it as 251,312,000. Always worth checking final rendering for any text you expect to include superscripts.

[anvandare]

Correct.

>"... each book is of four hundred and ten pages; each page, of forty lines, each line, of some eighty letters which are black in color."

>"The orthographical symbols are twenty-five in number."

25 ^ ( 410 * 40 * 80 ) = 25^1312000 ≈ 10^1834097 possible books.

There are an estimated 10^80 atoms in the known universe.

[SamBam]

It's always staggering to really meditate on the unimaginably vast size of the universe, and then come up with some simple idea such as every combination of letters arranged in books, and realize that our universe could never fit all the books that would require, even if stacked side-by-side between all the galaxies.

(The observable universe is also on the order of 10^80 meters cubed.)

[phreeza]

Something similar happened to me once when submitting a scientific paper. The publisher merged a line number into the number I was trying to write. Caught it in the proofs, luckily.