Ive got this odd idea... that you could use a quantum computer and an equation making system, and you have infinite storage space.
Because each and every sequence of numbers repeats infinite times in pi, every peice of data ever known to man is contained in pi an infinite number of times. All you have to do is record what decimal place this sequence starts and stops, and you have the file. All you need is some enourmous computing power, because large sequences of numbers that you want do not happen too often in pi.
here is a simple example.
I want to store the number 1415926535.
All I do, is write this down : "1,10"
Now, I could give the "1,10" to any computer in the world, and it could calculat pi to the first place, the tenth place, and everywhere inbetween, and it would have my sequence of numbers.
Since we would probably not want to store that number (when converted into binary/hex it probably uncompresses to complete gibberish), we would need to find out what deciumal place a say, 4 trillion digit long number starts at in pi, and the number it stops.
The resulting file would probably be around 100 megs, because sequences of numbers we want dont happen to often.
The way to calculate this would of course be quantum computers, which could calculate each of these problems in exactly zero seconds flat.
We could compress files in a ratio billions to one.
Yea, I know there is probably a gigantic flaw in this that any amateur mathematician could spot, but its my two cents on the limitations of computing.