", he became convinced of something he came to call the Dust Theory, which holds that there is no difference, even in principle, between physics and mathematics, and that all mathematically possible structures exist, among them our physics and therefore our spacetime. These structures are being computed, in the manner of a program on a universal Turing machine, using something Durham refers to as "dust" which is a generic, vague term describing anything which can be interpreted to represent information; and therefore, that the only thing that matters is that a mathematical structure be self-consistent and, as such, computable. As long as a mathematical structure is possibly computable, then it is being computed on some dust, though it does not matter what dust actually is, only that there be a possible interpretation where such a computation is taking place somehow. The dust theory implies, as such, that all possible universes exist and are equally real, emerging spontaneously from their own mathematical self-consistency."
While I'm not sure every number is in pi (see my other comment to grandparent), there is a similar really weird feeling I get when I consider all digital data is really just numbers. That means there is a number, that when turned into a .avi (or format of your choice), shows anything you can imagine. Imagine yourself talking with Plato. There is a number that produces a 1080p video of you doing just that. Actually, there are a lot of numbers that do that, as every little difference in the setting would be a different number.
There is a number that produces a high def photo of when you married your high school sweetheart, even if you never actually married her. There is one of you being awarded the Nobel prize. If there is a proof that P = NP, or that it doesn't, or even a proof that it can't be proven either way, then there is a number that would be the PDF version of that document.
Oh no! I sketched up a script to gzip the chunks, hashsum them, and then find out how many collisions there are before the real occurrence starting from an approximate address in the PI digits chain, so that I could have: ($address*1e12)$hash$collisioncount
The resulting string is 10% of size of the gzipped string, at the expense of CPU. But when I read you achieved 100% compression I just deleted the script and got out to get a beer. :-(((
Also, assuming that it is, if 'start as position X and read Y bits from pi' produced an illegal image (top secret document, abuse images, etc), what would be the legality of trading such information?
", he became convinced of something he came to call the Dust Theory, which holds that there is no difference, even in principle, between physics and mathematics, and that all mathematically possible structures exist, among them our physics and therefore our spacetime. These structures are being computed, in the manner of a program on a universal Turing machine, using something Durham refers to as "dust" which is a generic, vague term describing anything which can be interpreted to represent information; and therefore, that the only thing that matters is that a mathematical structure be self-consistent and, as such, computable. As long as a mathematical structure is possibly computable, then it is being computed on some dust, though it does not matter what dust actually is, only that there be a possible interpretation where such a computation is taking place somehow. The dust theory implies, as such, that all possible universes exist and are equally real, emerging spontaneously from their own mathematical self-consistency."
Great book!