I guess the question is
"does an 'infinite' number of patterns imply 'every' number of patterns?"
For instance, if you could quickly calculate the decimal sequence of π, could you not (in theory of course) come up with an algorithm to search that sequence for some pre-determined sequence?
Then you could do this:
start = findInPi(sequence)
So "sequence" in theory could be a decimal representation of the movie "The Life of Pi". The implication is that all digital knowledge (past, present and future) is bound up in irrational numbers (not just the group of irrational numbers, but each irrational number), and we just need to know the index to pull data out.
Once you know the index and length of data, then you could simply pass this long.
From an encryption standpoint, you could pass the start, length pair around, and the irrational number would be known only by the private key holder.
Am I off base here?