Implicitly, Frank Wilczek is suggesting that the problems he poses should be pretty simple (the properties of a proton, for example). But many people have pointed out that this may not be right.

We think of smaller things being simpler, but that may just be a prejudice. One can argue that as we get to smaller regions of space and higher energies we are just "going out the other end of the uncertainty principle". Instead of momentum/energy being small and size/time being big, particle physics deals with big momentum/energy and small size/time values. Why should we expect this side of the uncertainty principle to be simpler than the side we see every day?

One of the most persuasive arguments along these lines I've read was made by solid state physicist P.W. Anderson several years ago in a Physics Today column. If I remember right, he was arguing that particle physicists' claim to being the only "real physicists" was misplaced, and that other disciplines such as his own should not have to put with being seen as somehow "less fundamental".

And, for what it's worth, I agree.

Perhaps I'm confused: On the one hand Mr. Wilczek worries that simulating natural phenomena has outpaced our computational abilities. Was his grandfather as worried before computers were created to handle ballistics computations during WWII? Nature seems to get results from those actions pretty well, too.

Then, he wonders if the inability to create such simulations "suggest[s] some limitation to the universality of computation?"

I'm a little surprised that he hasn't heard of NP-complete problems, but some of them don't seem to require more than a Travelling Salesman. Pretty far afield from simulating subatomic particles.

I would be very surprised if Wilczek hasn't heard of NP-complete problems. The point is that we seem to have horrible difficulties computing these things at a good speed while Nature does it without any real problem. How is that? Is nature not computing? If not, what is it doing?

I'm not sure the question has any meaning, but I don't really know.

We don't need to go to something as fancy as QCD. The Navier-Stokes equation (the basic equation of fluid mechanics) is even more computationally-intractable.

But, when we stir a glass of water, the water molecules sure as heck don't solve the Navier-Stokes equation to know how to move!

Pardon my (utter) ignorance but is there any convincing reason to rule out the possibility that even Mathematical Physics may go through paradigmatic changes in the not necesseraly so close future? Don't deficient paradigms typically tend to make solutions look significantly more complicated than they have to be?

>>The Navier-Stokes equation (the basic equation of fluid mechanics) is even more computationally-intractable. <<

Not really. Not since about 1989 and the invention of lattice-gas automata as a method of solution. This sort of thing is what Stephen Wolfram's "New Kind of Science" book is all about, for those who took a peep at the last page.

To be fair to Wilczek, Brad should have quoted the sentence before the quote:

"There [sic] some aspects of QCD I find deeply troubling - though I'm not sure if I should!"

To be fair to Brad, Wilczek did write the rest after his disclaimer. Personally, as a physicist in P.W. Anderson's field, I would at this point take Wilczek's opinions a lot more seriously than Anderson's. One thing to realize is that Wilczek does condensed matter physics, too. He's not exactly an "out of touch with the everyday world particle theorist."

Still, I was fairly surprised by the comments. He's now the smartest person I'm aware of who has taken Wolfram's ideas seriously (though he disclaimed with "I don't think they've got very far...").

When clocks were the be-all and end-all of human inventiveness, our great thinkers worked very hard to make all of naturte over in the model of a clock. Now that computers are wowing us with their abilities, all of nature must be a big computer. Though not at all familiar with the problems being discussed here, I am interested in how long it will take before we drop the computer metaphor (as J-P Stijns also suggests), and then find ourselves utterly untroubled by natures failure to work like an abacus. There is no reason to think human insistance that nature fit into our metaphors has reached a workable pinnacle with the computational model.

Isn't reality the only computer that is powerful enough to carry out the calculations? I'm
not sure why our little computers would be
considered powerful enough.

Let me argue that we should look in the other end of the telescope.

We don't even need physics to find computationally intractable problems. Surely the simplest category of math problem is "choose a number." But numbers that can be specified by a finite algorithm are almost nonexistent compared to numbers that can't be computed.

The difference between QCD and classical mechanics, or even "choose a number," is not the existence of intractable problems. It's the nonexistence of tractable ones. It's the world "almost."

In a sense, this difference is infinitesimal. And do we know the difference is real? Maybe we simply haven't stumbled on the simple QCD problems.

In any case, I think we have inflated expectations of how well we should be able to do QCD, because we have inflated beliefs about how well we can do classical mechanics.

I thiought most advanced fluids codes were based on clever finite element routines, which are themselves a very clever evolution of simple matrix math.

Computationally difficult is more true, but not intractable. So long as meshes can be made sufficiently small, and automatic meshing algorithms sensible, the computation is not fundamentally intractable. I just takes quite a few resources.

Why is it at all suprising that 10^23 molecules can do more clever computations than 10^8 transistors? That is why the Buckingham Pi theorem is so useful.

B

"He's now the smartest person I'm aware of who has taken Wolfram's ideas seriously (though he disclaimed with "I don't think they've got very far...")."

I'm sure Wolfram would take offense at this statement, as it implies that Wolfram himself is not the smartest person to take his ideas seriously.

Philosophy is an occupational hazard of physicists. And, believe me, it's a hazard. Physicists can make the worst philosophers.

Since there don't appear to be too many serious physicists here, let me propose a truely whack theory of physics based on taking Wolfram, and few other people, seriously. It's an idea I've been tinkering with, semi-seriously, but I can't ask anyone else to treat it as anything but (in Wilczek's words) "[speculation] in reckless disregard for facts", especially since I've long let my qualifications in physics expire.

(N.B. I have not read A New Kind of Science. Some sort of "evil knows its own" kind of instinct leads me to suspect that Wolfram is a smarmy know-it-all. His book is a little long for light reading, and far outside my usual field. I'll get to it eventually, probably about when it hits the remaindered table at Waterstone's.)

Wolfram proposes that we take seriously the notion of the universe as a cellular automata and that physics at our scale emerges from the computational properties of such automata. Laurent Nottale thinks physical laws should be scale-invariant and proposes a fractal space-time to make it so. David Wolpert seems to me to have proved that there are either inherent limitations on the explanatory power of physical theories or that the universe places an upper limit on computational power. (Thanks to D^2 for pointing Wolpert out to me indirectly, via a link to J. Barkley Rosser.)

I propose to take them all seriously. Imagine for the moment that the universe is a cellular automata in a fractal medium. What good is it? Well, non-local phenomena may be explained by fractal paths through space-time, without allowing time travel (which creates a contradiction identical to the one Wolpert uses to prove his point.) Entanglement could be treated as a restriction on simultaneous solutions to some set of equations, without having to explain the equations physically. We could even consider a physics where phenomena may depend on Turing non-computable outcomes (because a fractal automata is provably more powerful than a Turing machine) without fearing for our sanity. And - and this is the good part - physicists would need never fear unemployment. There could never be a foundational reductive level at which all physical phenomena could be explained.

Is it falsifaible? Is it science? Beats me. Like I said, take it with a grain of salt.

Philosophy is an occupational hazard of physicists. And, believe me, it's a hazard. Physicists can make the worst philosophers.

Since there don't appear to be too many serious physicists here, let me propose a truely whack theory of physics based on taking Wolfram, and few other people, seriously. It's an idea I've been tinkering with, semi-seriously, but I can't ask anyone else to treat it as anything but (in Wilczek's words) "[speculation] in reckless disregard for facts", especially since I've long let my qualifications in physics expire.

(N.B. I have not read A New Kind of Science. Some sort of "evil knows its own" kind of instinct leads me to suspect that Wolfram is a smarmy know-it-all. His book is a little long for light reading, and far outside my usual field. I'll get to it eventually, probably about when it hits the remaindered table at Waterstone's.)

Wolfram proposes that we take seriously the notion of the universe as a cellular automata and that physics at our scale emerges from the computational properties of such automata. Laurent Nottale thinks physical laws should be scale-invariant and proposes a fractal space-time to make it so. David Wolpert seems to me to have proved that there are either inherent limitations on the explanatory power of physical theories or that the universe places an upper limit on computational power. (Thanks to D^2 for pointing Wolpert out to me indirectly, via a link to J. Barkley Rosser.)

I propose to take them all seriously. Imagine for the moment that the universe is a cellular automata in a fractal medium. What good is it? Well, non-local phenomena may be explained by fractal paths through space-time, without allowing time travel (which creates a contradiction identical to the one Wolpert uses to prove his point.) Entanglement could be treated as a restriction on simultaneous solutions to some set of equations, without having to explain the equations physically. We could even consider a physics where phenomena may depend on Turing non-computable outcomes (because a fractal automata is provably more powerful than a Turing machine) without fearing for our sanity. And - and this is the good part - physicists would need never fear unemployment. There could never be a foundational reductive level at which all physical phenomena could be explained.

Is it falsifaible? Is it science? Beats me. Like I said, take it with a grain of salt.

"God integrates empirically" -- Einstein

On August 8, 1900, David Hilbert presented ten yet-unsolved problems at the Second International Mathematical Congress in Paris. Here is problem number six in its entirety:

Can physics be axiomized?

Physicists do make the worst philosophers, but philosophers make the best physicists. The quickest way to solve a problem is to have a specific goal in mind, rather than the randomized 'quest' for knowledge. Since most of the solid axioms we use daily were found in the pursuit of appied physics, what we need is a program goal that encompasses all that is known of the macro behavior of stable chaotic local phenomena and use that information to build something useful, rather than using only what the physicists can calculate to build something and then try to find a use for it.
Nature doesn't 'calculate' anything. It just happens. There is a fundamental flaw in trying to simplify the perceived data when we don't know if the particular level we are trying to simplify is actually an axiomatic structural level, or if it is a chaotic level of strange attractors supported on a lower axiomatic level of structure. Our relative success with weather analysis should be considered as a model of alternating chaotic and axiomatic levels of complexity. Natural systems have a closed feedback loop that retains structure from chaotic systems in alternating layers (DNA, matter, tornadoes, the Great Red Spot). We need to think in terms of stable feedback occurrances in chaotic background environments, rather than unnecessary construction in controlled laboratory mathematical inventions. And why do we want to know, anyway? Where does the madness begin, and where's the feedback that should be controlling the research funding paradigm? It's time to consider what closes the loop in all systems.