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Two Kauffman's

I’ve been reading The Present Moment in Quantum Cosmology: Challenges to the Arguments for the Elimination of Time by Lee Smolin of loop quantum gravity fame (phil-sci archive). Mostly I’m reading because I’m an addict for anything involving the notion of “the present.” In the article he discusses two questions raised by Stuart Kauffman in the context of biology and economics which Smolin has ported over to physics:

  • Is it possible that there is no finite procedure by means of which the configuration space of general relativity or some other cosmological theory may be constructed?
  • Even if the answer is no is it possible that the computation that would be required to carry out the construction of the configuration space is so large that it could not be complete by any physical computer that existed inside the universe?

I’m not much of a fan of the first, (Penrose-ish) question…I find it hard to imagine noncomputability being of any practical consideration because it seems to me that one always needs an “infinity” of sorts to make the noncomputable arguments. (Apologies to Michael Nielsen quant-ph 9706006.) How do I verify that the universe is doing something noncomputable with my finite means?
The second question also strikes me as a bit odd. What I like about the question is that it talks only about the construction of the “configuration space.” This is, in a way, a specific computational problem. But it also seems that it glosses over a lot because in order to use a physical theory one needs a lot more than just the configuration space. The way in which I present a configuration space has a lot to do with what I can do with this space. And even if the full physical configuration space is not tractable, this doesn’t render it useless…there are probably tractable configuration spaces. Indeed, in a beautiful universe, the tractable configuration spaces will correspond to the tractable experiments. But this is wrong in some way: we know that we can use a quantum computer to simulate a quantum experiment, but this doesn’t mean we can use a quantum computer to output the amplitude of a particular basis state: there are nontractable questions about the theory even though we can use the theory to simulate the system.

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Quicksilver

I’m about halfway through Quicksilver, Neil Stephenson’s new novel. This book is going to appeal to a lot less people than Cryptonomicon, mostly because you have to be a real hard core geek to love what he’s doing in this novel, not just some half-ass computer nerd who built his last computer. That being said, and unhumbly labeling myself as a member of the former class, so far the book has me hooked.
But what I’m really writing this entry about is not to give a review of the book (see the New York Times review or Lundblad’s review.) …especially considering I haven’t finished it yet! What really struck me in reading Stephenson is how his books remind me of the best conversations I’ve had. You know one of those conversations at a party where the ideas flow like spittle from a rabid dogs mouth (hee hee!) Where you lose track of time and how cold it is standing outside on the back porch in the middle of winter but wouldn’t give up your company or the conversation for anything. In fact, when I think about all of the authors that I consider my favorites, all of them, Philip Dick, Thomas Pynchon, Jorge Luis Borges, etc. give me this same feeling.
Well in honor of Stephenson, I don’t know how to end this entry.

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Physics Will Save Us!

Much hubub is made about how uncomfortable everyone feels with quantum theory. So much hubub that there are now a plethora of different “interpretations” which are all supposed to make you feel less uncomfortable with quantum theory. There are basically two things which make quantum theory interesting: contextuality and nonlocality. The first of these is really not to disturbing. Sure, philosophically, having a realistic theory with really hidden variables (meaning you’ll never get access to them) is disturbing (why the extra structure?) but its not something which is completely incompatable with our everyday conception of reality. We operate fine when we interact with our PC’s without knowing the exact details of the currents and voltages inside of these machines (this being an analogy and not a precise comparison: of course we could go in an measure the currents and voltages and therefore understand why the hell the blue screen of death just popped up on the monitor.) Nonlocality is disturbing in a different way. It says that there is no way we can have realistic descriptions which are always local (but will be hidden, of course, as a consequence of the contextuality of quantum theory.)
OK, so here is my point. The issue of nonlocality arises due to the combination of relativity and quantum theory. It is perfectly reasonable to consider all sorts of notions of locality and then do quantum theory on them. Our notions of locality arise due to a physical theory: relativity. So perhaps the way out of the nonlocality mess is not via some hand-wavy philosophical smoothing over of emotions, but instead is due to actual real hard core physics. What physical theories can we derive which produce quantum theory? Can physics save us from the quantum quagmire?

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The Equation

Today while shopping for books at Borders I notice that “The God Equation” was shelved right next one of Feynman’s books. Of course, I had to correct this and moved the God book a few spaces to the right (I hope no librarians are reading this.) Of course the irony of this is that Feynman is the place where I first saw how you could right a single equation to represent a theory of everything (assuming that such a theory can be written down in terms of our algebraic notation…something which I feel shows quite a bit of hubris!) To do this, first notice that all equations can be written as A=0 where A is some probably nasty equation. A theory of everything, i.e. a set of equations describing all physics, will just be a collection of such equations, say A_1=0, A_2=0, … A_n=0: it’s important to make sure all of these equations are over real numbers, but this is easy to do. Now we can combine all of these equations into one by specifying

A_1^2+A_2^2+…+A_n^2=0

which is true iff all of the A_i=0! I’m not sure if Feynman was the first to pull this little slight of hand, but it was the first place I saw this trick.

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Job Hunt, Second Season

Today I officially started the hunt for my next job. After much procastination, I finally sat down and tried to formulate a strategy for landing my next job. Of course this failed miserably. I am totally clueless when it comes to applying for jobs/fellowships/positions scrubbing the floor. Last year’s job hunt (season one) was such an abysmal failure that it doesn’t really give me anything to build on (I would have like to at least gotten a foot in the door for one of the positions I applied to, but my foot was so far out of the door, you’d need a good pair of binoculars to even if I had shoes on.)
All of this reminds me of an idea for a new reality television show: “Survivor: Academia Island” Twenty overqualified Ph.D.’s stranded on a presitigious university campus all competing for a single tenure-track position. A no holds barred fight for one faculty position. Who will survive the first round and get an interview? Will anyone backstab and trash their fellow contestants? Whose shmoozing will increase their chances beyond their academic qualifications? And of course, we need to add a twist: when one of the contestants finally wins, it turns out the position has been canceled due to lack of funding!

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European Christian Union?

Currently there is a debate in the EU about whether to include in the new EU constitution a statement as to the common christian heritage of the continent:

Josep Borrell Fontelles, a Spanish Socialist, appeared more doubtful about the inclusion of a Christian-heritage clause, commenting…”Many of our values were forged against the Church,” he said. “And when it comes to democracy, the rights of man and equality, God is only a recent convert.”

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Paul, Paul, Paul

No Paul, you’ve got it wrong. What this downtown property is good for is not a biotech center, but a new research university, a.k.a. the Washington Institute of Technology

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Searching for Bobby Fisher

One of the cool results of computer science which I recently learned is Levin’s universal search. Suppose you have a function f from a set X to a set Y. Many problems in computer science ask for you to invert this problem, i.e. given a y in Y, find x such that f(x)=y (there may be multiple such x’s but let’s not worry too much about that let’s just say you want to find an x such that f(x)=y.) Further lets assume that we have an efficient method for evaulating f(x). Thus, we may efficiently test whether a possible solution, x, satisfies the desired f(x)=y. OK, so that’s the problem. How do you solve it?
Well here is what Levin proposed. Consider running all possible programs which can solve this problem. We will do this serial, but with the time spent running each program which is proportional to 2^(-l(p)) where l(p) is the length of the program p. So we will be running shorter programs more often than we are running longer programs. There is a program q, which is the fastest program for solving our problem. This program runs in time T(q). Eventually our program will execute this program and get the correct result. How long does this take? A quick calculation shows that this time is at works 2^(l(q)) (T(q)+Tv) where Tv is the time to verify that the answer is correct (not included in T(q)). Thus, up to 2^(l(q)) the program is the fastest possible. Think about a class of programs now: notice that we will have produced an algorithm for this inversion problem which is, up to this huge multiplicative constant optimal. If we were to use big-O notation, this constant would be hidden and we would say assymptotically we have the most efficient algorithm!
Needless to say, the multiplicative constant DOES matter and in most cases is ridiculously large. But the story doesn’t end here. Recently Marcus Hutter has shown how to make this multiplicative constant 5 (Hutter’s work also solves a broad classes than the one described above.) What’s the catch this time? The catch this time is that there is an additive constant which is huge!