I’ve got a better idea for you to chew on after the LHC finds nothing and people start to get really desperate when the funding for crackpot research goes away:

http://www.lns.cornell.edu/spr/2006-02/msg0073320.html

The pre-inflation past would be high-entropy in any case.

I’d assign a rather low probability to that. Physics is thought to be reversible – and the idea has stood up well over the centuries. For an early entropy decrease, you’d need irreversible physics – or enormous spans of time. I am not currently aware of any evidence favouring irreversible physics – and I don’t think you can argue that the universe is likely to have started in an arbitrary state, and then stumbled upon a low-entropy zone by chance – since that hypothesis would not predict the incredibly-low entropy beginning we seem to see. Also, complex initial conditions would themselves need explaining in the face of Occam’s razor.

I tend to agree with you. Have you perchance read Greg Egan’s “Permutation City”? The “dust theory” of that book – patterns finding themselves (which is what you are essentially saying) – is very intriguing, and the more I’ve been thinking about all the metaphysical problems involved in “traditional” theories, the more I find a “dust theory” attractive.

Cheers,
Günther

1. There is a high probability that the Universe is very large.
2. If the Universe is very large, then there is a high probability that we are in a low-entropy region.
3. Any low-entropy region will lead to an asymmetry in time.

This is interesting, but it’s sure a lot of extra machinery for this kind of claim. The claim you’re interested in would be the past-hypothesis: the initial conditions of the Universe pick out a low-entropy state. Why not simply posit this as a fact about the Universe, instead of going through the exercise of (1) and (2)? Here’s two reasons why it’s worth considering:

First: there is no probability space in which (1) makes sense; and
Second: (2) seems to be false.

No matter what interpretation of probability you adopt, defining a probability measure on the “space of possible Universes” will be completely meaningless. This suggests there is no meaningful way to precisely state (1), if one has any empiricist scruples. And if the Universe is infinite, as our best models now suggest, then the probability that you’ll end up in any finite region is 0. So (2) would simply be false. I suspect there are no bullets to be bitten here, before these problems are worked out more carefully.

Thanks for the interesting post!
Bryan

For your allusion to Copernicus, cite the source directly – he begins with beauty and with art in his introduction. It is so nicely written I take the liberty of quoting the opening in full:

“Among the many various literary and artistic pursuits which invigorate men’s minds, the strongest affection and utmost zeal should, I think, promote the studies concerned with the most beautiful objects, most deserving to be known. This is the nature of the discipline which deals with the universe’s divine revolutions, the asters’ motions, sizes, distances, risings and settings, as well as the causes of the other phenomena in the sky, and which, in short, explains its whole appearance.

What indeed is more beautiful than heaven, which of course contains all things of beauty? This is proclaimed by its very names [in Latin], caelum and mundus, the latter denoting purity and ornament, the former a carving. On account of heaven’s transcendent perfection most philosophers have called it a visible god. If then the value of the arts is judged by the subject matter which they treat, that art will be by far the foremost which is labeled astronomy by some, astrology by others, but by many of the ancients, the consummation of mathematics.

Unquestionably the summit of the liberal arts and most worthy of a free man, it is supported by almost all the branches of mathematics. Arithmetic, geometry, optics, surveying, mechanics and whatever others there are all contribute to it.”

- N. Copernicus, De revolutionibus, Introduction, Book One

This preoccupation with the beauty and elegance in science is not a solely a Western phenomenon, it can also be found in Abhinavagupta and in Buddhist natural philosophy as well.

Note also that Copernicus is interesting in that he begins to separate science from what was then called “natural philosophy,” when he later says:

“However, since different hypotheses are sometimes offered for one and the same motion (for example, eccentricity and an epicycle for the sun’s motion), the astronomer will take as his first choice that hypothesis which is the easiest to grasp. The philosopher will perhaps rather seek the semblance of the truth.”

What is the difference to Copernicus between the practitioner of this new science – astronomy – which he distinguishes from its Medieval name “astrology” – and the philosopher? Yet even as Copernicus struggles to create science, he insists on retaining beauty!

Thus I ask you mjgeddes, would you agree that Robin’s foray above meets Copernicus’ criteria of being both “beautiful” and “easy to grasp,” despite being perhaps unexpected?

Similarly others argue that a correct counting makes ordinary brains more common than Boltzman brains, though this also isn’t entirely clear.

Since ‘ordinary’ brains are a subset of Boltzmann brains, that would have to be a truly extraordinary redefinition of ‘correct’.

whatever it is that’s encoding me seems to be encoding rather more regularity and so on then is necessary to just encode, well, a few minutes of me.

The order you perceive is a property of you, the information processed by your algorithm. Not the environment running the algorithm.

The walks through Libraryspace that do not preserve the illusion of continuity far, far outnumber those that do. But in worlds where that continuity is not preserved, either you do not exist at all or you do not perceive the discontinuity. The more properties of the algorithm that aren’t preserved in ‘switching’ from one instance to another, the less likely it is that the two fit the criteria for a valid continuity.

Maybe you’re seeing some obvious thing here that I’m missing, but, well, if so, then there’s something I’m missing. I remain confused on this issue.

Robin: That paper you mention, does it explain about proper counting solving the Boltzman Brain problem, or do you mean that’s something that others have done entirely separately. If so, if you happen to know the basic idea, well, what is the basic idea about that? Thanks.