λ - programming

I'm sorry to burst your bubble, anon, but this is pretty much completely useless. Still very cool from a mathematical perspective, but I doubt it will ever have any practical implications in computer science. In fact, the sources that you linked say that more or less.

It's a fun idea. But as you can see from your links, folks just mess around with it for fun, not seriously.

>>10831
I've watched the pifs source code.
Atm, the guy simply looks for a series of matching bytes in pi. You could in theory look for sequences of bytes in pi. So, instead of saying "My data is byte 503, 685 and 38.", you could say "My data is byte 758 to 760." You would save a lot of space
However, you would need a lot more computing effort to find such sequences than you need for just single bytes.

https://oeis.org/wiki/Disjunctive_numbers
>It is not known whether π = 3.1415926535897932384626433832795... is a disjunctive number.[3]
So we don't even know if it works. Useless.

Won't work.
This, and ideas like it, pop up all the time.

https://en.wikipedia.org/wiki/Kolmogorov_complexity

>>10831
the problem is that, assuming the digits are random, on average it takes a number of length n to point to a message of length n. And, since pi is iterative, you'd be incurring gigantic computational cost as well.

Proof:

let your message be m1, m2, m3, ... mn

the probability that a series of random digits matches your message is 1/10 * 1/10 * 1/10 * ... = 1/10^n

therefore if we take a sample of all messages of length n in the random sequence, on average you would have to sample 10^n sequences to get a matching sequence. (10^n * 1/10^n = 1)

It just so happens that it takes n digits to represent 10^n in a base-10 system. This could not be compressed to base-exponent notation because in most cases the number would not be 10^n.

Therefore, on average there would be no compression performed.

>>10953
It works, it is just unbelivealy slow, as I think your link was supposed to show. But the proposition is just for fun.

>>10847
The problem is, the indices would be massive - larger than the data itself, in most cases.