? in Base-26 Will Produce All the Works of Shakespeare

Base 26 is one of two fairly natural ways of representing numbers as text using a 26-letter alphabet. The number of interest is expressed numerically in base 26, and then the 26 different base-26 digits are identified with letters as 0=A, 1=B, 2=C, ... 25=Z. Here are the first 100 digits of pi expressed in this way:

D.DRSQLOLYRTRODNLHNQTGKUDQGTUIRXNEQBCKBSZIVQQVGDMELM UEXROIQIYALVUZVEBMIJPQQXLKPLRNCFWJPBYMGGOHJMMQISMS...

Lo! At the 6th digit we find a two-letter word (LO), and only a few digits later we find the three-letter ROD embedded in the four-letter TROD. How many other English words can be found if we continue looking?

First, a few ? facts are in order. The digits of ? (in any base) not only go on forever but behave statistically like a sequence of uniform random numbers. (Mathematically proving that this is the case - the "? is normal conjecture" - is a deep unsolved problem, but numerical analysis of several billion digits suggests that it is true.) Consequently, ? in base 26 emulates the mythical army of typing monkeys spewing out random letters. Among other things, this implies that any text, no matter how long, should eventually appear in the base-26 digits of ?!

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We should expect to need about 2.5 x 1018 letters in order to find the phrase TO BE OR NOT TO BE (without the spaces) once. We can only get as far as TO BE in the first million.

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That the first 6-letter word is OXYGEN suggests that ? is truly the very stuff of life!

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Though this does not seem to be a useful way of looking at all the digits of ?, we mustn't fail to note one last logological property. Write ? as usual in decimal, and group the digits as follows:

3. 14 15 9 26 5...

and then make the obvious substitution A=1, B=2, etc. You get C.NOIZE, which is rather fitting, because the random nature of ?'s digits means that when you look at it you SEE NOISE!

By assigning letters to numbers in the irrational number, we can produce the effect of a million monkeys on a million typewriters for a million years.