The issue here is you would need to have an infinite amount of memory to store Pi.

Actually, no. Given sufficient resources,

**π** can be calculated to arbitrary precision and you’d only need to inspect a finite subset of its expansion at a time, discarding it if it doesn’t encode anything worthwhile. One would likely use a sliding window of variable length that starts at successive digits to parse the string, appending new digits as needed if at any point the window shows anything promising, otherwise discarding the leading digit and moving to the next one. (As an aside, there’s an ongoing informal competition among those in the mathematical sciences to develop algorithms that converge on

**π** faster than all the previous ones.)

What you would need are enormous amounts of time and energy because statistically the information content (as Claude Shannon defined it) of a string of digits is proportional to its length, whereas the chance of finding that string in an infinite jumble of digits, decreases exponentially with its length. A stark illustration of this is that if you captured every Joule of energy the Sun ever emitted and will ever emit until it burns out, and harnessed it 100% efficiently, that would be the minimum energy required to generate all possible 45-letter strings drawn from a 26-letter alphabet. If you generated them at a rate of 1,000,000,000,000,000,000 (= 10

^{18}, a billion billion) a second, to do them all would take about 10,000,000,000,000,000,000,000,000,000 (= 10

^{28}, ten billion billion billion) times the present age of the universe.

And these are just some of the simpler quirks that bedevil efforts with large numbers.

But you could say that an infinite combination of {0,1} contain everything.

What is “an infinite combination of {0,1}”? If you mean an infinitely long string of effectively random binary digits (0’s and 1’s) then that is saying the same as what was said about

**π** because we can just as well use its binary expansion instead of its decimal one. If on the other hand “{0,1}” indicates the interval of all real numbers between zero and one, then all you need to do is pick any one of the infinitely many

transcendental numbers in that interval, and use its expansion as with

**π**.

'Luthon64