3 ms·
I approve of you giving this some thought, but entropy doesn't care about Kolmogorov complexity at all. A box full of helium where exactly half of the helium i
by Symmetry 13y ago
I approve of you giving this some thought, but entropy doesn't care about Kolmogorov complexity at all. A box full of helium where exactly half of the helium is on one side and half is on the other is not appreciably more likely than one where there are 17 more helium atoms on one side the box than on the other despite requiring less bits to describe.
The regions of the Canonical Ensemble corresponding to a "A Brain" are much smaller than those corresponding to "A brain that's inside a body". And the incompressibility of phase space means that it's therefor proportionally less likely in the steady state. Just be very glad that the universe we live in is such that we seem due for a Big Crunch or Big Rip before getting anywhere near steady state.
EDIT: A little bit of help for the intuition. In a long run steady state universe pretty much all matter is going to be inside black holes. Sometimes you get a spontanious particle/anti-particle pair forming near the radius and one happens to escape. The odds of this happening enough times to accumulate a brain's worth of mass outside a black hole are staggeringly unlikely. Each additional brain's worth of mass decreases the odds exponentially. So I hope you can see that an entire solar system's worth of mass forming outside a black hole is so unimaginably unlikely that it dwarfs the unimaginable unlikely-hood of some mass happening to assemble into a brain.
- schiffern 13y ago>A box full of helium where exactly half of the helium is on one side and half is on the other is not appreciably more likely than one where there are 17 more helium atoms on one side the box than on the other despite requiring less bits to describe. Plus, how does one decide which information is counted ("which of two distinct volumes the atoms occupy") and which information is not ("full position & velocity of every particle constrained only by uncertainty")? Because if we don't make that [artificial] distinction, each box has exactly the same amount of information.