

Converting Pi to binary: Don't do it - joeyespo
http://www.netfunny.com/rhf/jokes/01/Jun/pi.html

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out_of_protocol
πfs? [https://github.com/philipl/pifs](https://github.com/philipl/pifs)

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lutusp
The author's remarks apply to computing Pi in any base, not just base two.
Also, all square roots of numbers that aren't perfect squares are irrational,
and normal, and therefore contain every imaginable sequence within them, just
as Pi does.

~~~
syncerr
Would we assert that Pi contains Pi?

~~~
lutusp
Pi can only be expected to contain a subset of itself. Specifically, if we
choose a finite digit sequence of length N, for any value of N there are an
infinite number of copies of that sequence within Pi.

Let's try this with an experiment. Let's say we want to find the first four
digits of Pi (3141) within Pi. For the first 100,000 digits of Pi, we find the
substring "3141" at these index locations (skipping the first match):

    
    
        3497
       26613
       42126
       45903
       53277
       68919
       88009
       91355
    

For the substring "31415", one more digit in length, within the first 100,000
digits of Pi we find only one example, at index 88009. This makes sense, since
the binomial theorem provides a probability of 0.632 for one or more successes
within 100,000 normal digits and a substring length of 5.

Binomial theorem calculator:
[http://arachnoid.com/binomial_probability](http://arachnoid.com/binomial_probability)

Based on this example, with an arbitrarily large set of Pi's digits, it's
reasonable to say that any reasonable digit sequence can be found within it.
And for Pi's infinite sequence, any subset of Pi -- or any other numerical
sequence of any length -- can be located within it.

One more example. For the substring "33333", within the first 100,000 digits
of Pi we find occurrences at indices 28468 and 89086. I include this to
suggest that any digit sequence, for that matter any sorts of numbers, for
example representing letters, can be found. The old saw about finding the
works of Shakespeare within Pi is obviously true, if difficult.

