4 ms·
> "infinite compression", in which it is claimed that every possible input can be reduced in size. It's computationally intractable (in fact, I'm pretty sure i
by a1369209993 5y ago
> "infinite compression", in which it is claimed that every possible input can be reduced in size.
It's computationally intractable (in fact, I'm pretty sure it's computational-intractability-complete), but if you live in a deterministic universe, it actually is possible to compress any input to at most a psuedo-constant number of bits.
Just run every possible program in some Turing-complete language in parallel, and pick the shortest program that outputs your input. In the worst case, this will be a program that simulates the entire history of your universe up to the point where you were provided with the input and then reads out the simulated input. No matter how large the input is, this will only take (U+logXYZT) bits, where U is the number of bits to describe the laws of physics and initial state of the universe, and logXYZT is the number of bits to describe your position in space and time (among other things, it's logarithmic in the current age of the universe).
(Caution: there may be elditch abominations in your universal prior[0], but as long as you stick to programs that output a fixed input and don't try to fiddle with them to decompress more data than you originally put in, they probably can't hurt you.)
0: https://ordinaryideas.wordpress.com/2016/11/30/what-does-the-universal-prior-actually-look-like/ https://ordinaryideas.wordpress.com/2016/11/30/what-does-the...
- AndrewDucker 5y agoThat assumes an infinite univerise, which means your coordinates are also theoretically infinite, which means that they aren't a fixed number of bits.
- deleted 5y ago[deleted]
- a1369209993 5y agoUh, no? It assumes a effectively finite universe (perhaps with something like the speed-of-light limit rather than strictly finite, but effectively). It can be infinite in time if you're okay with your compressed data potentially being somewhat larger the later you compress it, but that's not strictly necessary.