File system that stores location of file in Pi

Not too much, just one thing: If we could simulate the universe then of course there would be a simulation in the simulation, etc... And maybe there is a fundamental yet undiscovered 'law of computation' that a sufficiently complex simulation can embed itself only on a slower timescale, so even if everything is deterministic, we even theoretically cannot calculate fast enough to calculate the future.

Wow, great article!

Does a number that represents a range within Pi, get also coloured as copyrighted if your intent while computing it was the search for a copyright coloured sequence of bits within Pi ?

I think that for a lawyer it doesn't really matter; it doesn't matter which technique you're using to encode your data, as long as somebody can access that content and you did that on purpose. They're good at dealing with loosely defined things like intent, better than with formally defined things.

I wonder what amount (and progress) of AI research has been done in this area; not all illogical things are bullshit, however you might want to feel about them. Anti-digital-rights sentiment (disclaimer: I personally deplore much of the consequences about enforcement of digital rights, so I share that sentiment at many levels) sometimes can cloud judgement, and I've seen many people invoke rational thinking so well they successfully miss the point.

As many pointed that out using Pidgeon Hole principle, it is not practical to create a compression index(A lookup index where you map actual data with some kind of adresses preferably smaller than sequences), using every possible n byte sequence of your data!

Because your index size would be at least equal or higher than your original data.

The only way you get a smaller compression index, you have to look for recurrences, and try to only include most recurring sequences up to a number(there would be a tradeof and an optimal number for compression ratio) and left other sequences uncompressed. Only this way you can achieve compression ratio's smaller than 100%.

It isn't proven to be "normal" (http://en.wikipedia.org/wiki/Normal_number). There is no guarantee that any particular sequence is in pi until you've searched and found it. It's a very common fallacy that because the expansion is infinite and non-repeating it should contain every possible sequence, very simple counter examples exist.

Pi can be infinite and non-repeating (as it's irrational) and only sparsely contain 5s after the 100 trillionth digit (or whatever we've calculated it to so far), unlikely.

There are some normal numbers that are known but they seem hard to construct (to me, not a number theorist), like Champernowne's number which is the concatenation of all natural numbers (clearly any number will be in it's expansion by definition but it won't be very good for compression purposes due to the indexing issues highlighted elsewhere).

Some further reading: http://math.stackexchange.com/questions/216343/does-pi-conta..., http://mathoverflow.net/questions/51853/what-is-the-state-of..., http://en.wikipedia.org/wiki/Complexity_function.

This is genius!

Am I right in assuming that the decompression step is several orders of magnitude faster than the compression phase?