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The best explanation for this paradox and one that should be especially convincing to computer scientists is that the kolmogorov complexity of any brain aware e

by Dn_Ab 13y ago

The best explanation for this paradox and one that should be especially convincing to computer scientists is that the kolmogorov complexity of any brain aware enough to have consistent memories is higher than the universe which contains it. A Boltzmann brain might not be impossible but it is far,far less likely than arbitrary universes occurring as fluctuations. It makes sense if you think about it. It's also consistent with the fact that 17th century mathematics could make so much headway unravelling the laws of physics and we're still fumbling trying to understand bacteria. Suppose you were playing with procedural generation. Which would be harder: a procedural universe, a procedural universe with a generated AI able to interact with it or an isolated AI which has learned to act optimally in some arbitrary but specific universe? It is not clear that the last program, meant to represent a Boltzmann Brain with a memory of interactions with the universe is any less difficult than the one with the complex generated AI. The isolated AI might be even harder since a dumb algorithm could, given enough time and feedback, produce something fairly intelligent. So it would take more bits to describe a brain with your specific memories than to specify a universe which could end up with someone similar to you and easiest of all is the program which generates all possible universes. Schmidhuber goes into this here: http://www.idsia.ch/~juergen/computeruniverse.html http://www.idsia.ch/~juergen/computeruniverse.html. Even if the universe is not some automaton, the argument is still valid. Shorter programs are more likely and a program specifying you with memories of being embedded in some specific universe requires more bits than evolving a universe which has the laws required to support and eventually evolve someone like you.

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.
Florin_Andrei 13y ago
> It's also consistent with the fact that 17th century mathematics could make so much headway unravelling the laws of physics and we're still fumbling trying to understand bacteria. Keep in mind that's pretty relative. 17th century physics was low-energy, newtonian, and euclidian. No insight into the microcosmos whatsoever. No insight into the high-energy macro-structures. No science of complexity. In other words, a very narrow slice of the whole range of existence.

by Dn_Ab 13y ago

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.

Florin_Andrei 13y ago

> It's also consistent with the fact that 17th century mathematics could make so much headway unravelling the laws of physics and we're still fumbling trying to understand bacteria. Keep in mind that's pretty relative. 17th century physics was low-energy, newtonian, and euclidian. No insight into the microcosmos whatsoever. No insight into the high-energy macro-structures. No science of complexity. In other words, a very narrow slice of the whole range of existence.