gridverse
http://twitter.com/WCGrid/status/24028589385
Team “Dinosaur Comics – qwantz dot com” has added over 1,100 new members in the last 7 days! WOW! http://bit.ly/4GrCsk
1 year and 293 days of CPU time were logged yesterday from team Dinosaur Comics. My account contributed 1 day and 19 hours of that. GRID COMPUTING IS FUN. Also it keeps your room warm.
I was browsing Wikipedia’s multiverse page today and came across the following interesting quote by a cosmologist called Max Tegmark:
The algorithmic information content in a number is, roughly speaking, the length of the shortest computer program that will produce that number as output. For example, consider the set of all integers. Which is simpler, the whole set or just one number? Naively, you might think that a single number is simpler, but the entire set can be generated by quite a trivial computer program, whereas a single number can be hugely long. Therefore, the whole set is actually simpler.
This is an interesting observation. He uses this to defend that the multiverse hypothesis does not fall afoul of Occam’s razor. Occam’s razor literally says “do not needlessly multiply entities” but in common usage it just means “the simplest answer is probably right” or rather, a bit more strictly, “the answer which introduces the least number of new things (weighted against their improbability) is probably right”. Something which would fall afoul of Occam’s razor is an answer that raises more questions than it answers or just seems to introduce new things for no real justifiable reason.
The answer given by Occam’s razor may only be changed when new information becomes available. Thus Occam’s razor works very well if you have a lot of information, not so well if you don’t, but there is never a more reliable alternative.
But if Occam’s razor is to be used rigorously, an important question is raised: how exactly do we measure simplicity or complexity? Max Tegmark above opts to use Kolmogorov complexity, which defines a measure of complexity of a piece of data in terms of how much data is required for a computer to generate it. And he is right in that it takes a shorter program to generate the whole set of integers than to just generate one arbitrary one (because the average integer is pretty damn long). Elegantly in Python,
f = lambda n: [n] + f(n+1) print f(0)
At n=infinity it all collapses beautifully into a list of all the integers. And this is in 37 characters. One single 40 digit number can’t be expressed in 37 characters*, but somehow I’ve managed to express every 40 digit number, and a whole lot more, in just 37 characters.
Of course in practice, n is never infinity and it gives you a recursion depth exception, or you run out of memory and it crashes. I am unclear on whether Kolmogorov complexity requires the answer to be generated in a finite time, but I think the overall point stands regardless. We can see and trivially prove (assuming I didn’t make a mistake) the above program generates the set of all integers. It’s a valid mathematical description whether or not it could be evaluated by a machine with finite resources.
I am not a physicist (obviously) but I think there’s a case for the multiverse which basically equates to Occam’s razor.
There are apparent contradictions in choosing between either a single universe arising from an unintelligent mechanism or a single universe arising from an intelligent design mechanism. If it was unintelligent, how did it get so much right? By which, I refer to the so called fine tuned constants of the universe. Whilst I hesitate to accept that no other form of life could occur in a universe with different tuning, I am prepared to accept that there are more ways to make a universe uninhabitable than inhabitable. But if the design was intelligent, what is everything else doing here? It’s a wasteland. Neither explanation is satisfactory. The multiverse addresses the shortcomings of both.
Given that life exists, this universe must be inhabitable. The range of “inhabitable” spans from something which is the bare minimum to support life, to something which has no wasteful elements whatever and appears to be completely designed for life. To assign each a probability makes no sense for a single universe, because probability talks about average cases, but if there is only one case then this is by definition the average one. But if we consider a multiverse probability becomes a much more powerful tool: We expect the former (a just about adequate universe) to occur with much higher frequency than the latter (a perfect universe). Note that I shan’t assess the probability of any given universe being inhabitable, it’s not relevant to the argument, we just assume it’s non-zero.
The nearest we get to testing the multiverse hypothesis is to assess in its context how likely our own universe is. Our own is not so perfect as to be improbable by the multiverse hypothesis, in fact, outside of isolated pockets our universe is simply a wasteland which is very hostile to life, hostile through negligence rather than any concerted effort. Even the part we are in will only be friendly for a short amount of time relative to the timespan of the universe. So our own universe is safely towards the ‘bare minimum’ for life, and so it is within the expected probabilistic bounds for an inhabitable universe of a multiverse. This was only one test, but for now the hypothesis is unscathed.
It seems like introducing many universes should be a prime candidate for the accusation of “multiplying entities”, but I disagree. The example above shows that the set of all integers may be represented very concisely and more easily than one arbitrary integer. This is because the entity of importance is not the integer itself, but the method which generates it. And this parallels the universe: The universe isn’t the important entity, it’s the creation process we care about. We already accept that a creation process must exist, we merely specify a detail about that process. That detail could well be an extra entity, I agree, but in return this extra entity grants us a neat explanation. It beats the god/design argument because we replace actual intelligence (which requires a whole GREAT BIG explanation for itself) with an unintelligent pseudo-randomised process (which also still requires an explanation, but if it does not need to ‘think’, then it’s simpler). It beats the idea of a single universe because otherwise we would have to account for how an unintelligent process could pop into existence a universe which just happens to have all the settings tuned such that our physics and chemistry set the stage for the evolution of complex biological systems (i.e. us), and why it was invoked exactly once.
Even if the fine tuning assumptions turn out to be wrong, the idea that only one universe can exist is still baffling. One is a very arbitrary number. Having zero universes existing would be neat. Going from zero to one is very strange, but apparently it happened, so there we have it. But going from one to two is not so strange. And in fact not going to two implies some form of limit, which demands to be explained.
It seems to me that the multiverse is the best candidate to respect Occam’s razor.
In the interests of false trichotomies, I should also point out that another possibility is possible that there are actually infinite universes but they’re all identical. This still has the fine tuning issue, though.
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* Obviously some integers are factorable or otherwise reducible into shorter representations, but let’s assume this one isn’t. And if it is, make it 10 million digits and keep picking random numbers until you find one that definitely can’t be expressed in fewer than 37 characters.
grid computing wooo
I joined… the Dinosaur Comics distributed computing team! We’re a team on a so-called computing grid, which uses volunteer’s idle CPU cycles to perform calculations and modelling which is used for medical research. It might be an exaggeration to say we’re curing cancer, but that’s the basic idea. I believe most of these things are interested in interactions between proteins, which is what your computer models for them. On the Dinosaur Comics team we are currently pulling in over a year of CPU time PER DAY! PRETTY AWESOME. This house is now contributing 8 cores to the project.
But the real excitement is in the membership drive Ryan North has been campaigning on Qwantz. We’re in 7th place when ranked by the total number of members. Yesterday we demolished the dastardly L’Alliance Francophone and have just this very evening surpassed the team of Slashdot. We’re 240 members short of the next biggest team, but still growing. WATCH OUT IBM, 6th place shall be ours presently.
