Data Compression Explained
mattmahoney.net
mattmahoney.net
"The universe has a finite age, T, about 13.7 billion years. Because information cannot travel faster than the speed of light, c, our observable universe is limited to an apparent 13.7 billion light years, although the furthest objects we can see have since moved further away. Its mass is limited by the gravitational constant, G, to a value that prevents the universe from collapsing on itself.
A complete description of the universe could therefore consist of a description of the exact positions and velocities of a finite number (about 10^80) of particles. But quantum mechanics limits any combination of these two quantities to discrete multiples of Planck's constant, h. Therefore the universe, and everything in it, must have a finite description length. The entropy in nats (1 nat = 1/ln(2) bits = 1.4427 bits) is given by the Bekenstein bound as 1/4 of the area of the event horizon in Planck units of area hG/2πc3, a square of 1.616 x 10^-35 meters on a side. For a sphere of radius Tc = 13.7 billion light years, the bound is 2.91 x 10^122 bits.
We now make two observations. First, if the universe were divided into regions the size of bits, then each volume would be about the size of a proton or neutron. This is rather remarkable because the number is derived only from T and the physical constants c, h, and G, which are unrelated to the properties of any particles. Second, if the universe were squashed flat, it would form a sheet about one neutron thick. Occam's Razor, which the computability of physics makes true, suggests that these two observations are not coincidences."
I'm not qualified enough to find the possible error but I consider that speculation intriguing!
There has been some speculation that we're really living in a 2D universe projected onto a 3D surface, or similar.
Is this a tautology or does 'squished flat' mean something other than 'squished flat'?
This sounds wrong to me. My understanding of QM is that the underlying physics is actually continuous (as apposed to quantized), and it is only when we attempt to make measurements that we run into planks constant.
1) The "Universe" we talk about when we observe the limits is "the visible universe for us" and not "the whole infinite universe" we're part of.
2) Even if the universe is 13.7 billion years old, we can observe more at the moment:
https://en.wikipedia.org/wiki/Observable_universe
"According to calculations, the comoving distance (current proper distance) to particles from the CMBR, which represent the radius of the visible universe, is about 14.0 billion parsecs (about 45.7 billion light years), while the comoving distance to the edge of the observable universe is about 14.3 billion parsecs (about 46.6 billion light years),[1] about 2% larger."
(http://prize.hutter1.net/index.htm)
It would be interesting to see if enwiki8 can be compressed further.
(http://mattmahoney.net/dc/textdata.html)
Matt Mahoney has a lot of great information about compression!
The compression curiosities page has some nice gimmicks. A file that compresses well in with one software, but hardly at all with another; a tiny compressed file (115 bytes) that expands to 5 MB; compressed files decompressing to themselves.
Let's say we were to somehow define all the information that makes up us as individuals (map all the atoms in our body or something). All that information is algorithmically compressed into DNA. If the universe is a giant computer, DNA is the code and we are the output. Geneticists, in a sense, are just studying how this compression works.