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The Ghost in the Machine

May 16, 2008 Posted by Emre S. Tasci

Yesterday, during Alain P.’s “From Quantum to Atomistic Simulations” titled presentation, there was an argument over one of his comments on the generation of potentials, particularly the EAM potentials. He listed “No physical meaning (‘Any function is good as long as it works’)” as one of the specifications (or, more accurately as a freedom) which drew objections from the audience since they -naturally- insisted that when dealing with a physical problem at hand, we ought to keep in mind the physical aspects and reasoning – blindly determining some parameters in order to fit the data is surely not the correct procedure to follow.

This reminded me of some debate program we used to have back in Turkey called Siyaset Meydanı (can be translated as “Political Grounds”, maybe?). Most of the time, the participants would defend two opposing but in their own terms, surely agreeable opinions, for both of which you could easily find supporters. But on one of the sessions, they were discussing smoking. You can pretty guess that, nobody would defend smoking and that session was intended to be a “light” session and for that reason, the party in favor of smoking was made of artists and showmen. Now, it is like a sham fight at first because everybody already knows who the winner side is but then, one of the anti-smokers who happens to be a chairman of some anti-x thing, stands up and in minutes she’s like defending the hardest cause of all: smoking kills you, kills your loved ones, kills the children, kills the world… Her attitude triggered those who were initially “in favor of smoking” and they also began actually defending their cause. Since they were composed of popular artists and showmen, meaning they knew how to effectively present the ideas, at the end of the session, a strange triumph was achieved.

Actually, the related part of the anecdote I gave above ends with the debate topic being an already won cause. Definitely, when doing physics, we must keep in mind that we’re doing physics. But..

Before going into that “But…” and all the advances in computational tools plus the information theory, I’d like to include two contradicting(?) quotes on the subject. One of them comes from a physicist while the other belongs to a biologist:

“A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data.”
Paul Dirac

“The great tragedy of science is the slaying of a beautiful hypothesis by an ugly fact.”
Thomas Huxley

Maybe -but maybe- you can pave a way between this two by introducing another physicist:
“Make everything as simple as possible, but not simpler.”
Albert Einstein

So, back to the subject: It is natural and obvious to think in terms of the discipline’s domain that you are actually researching in but it’s getting more and more tempting to pull yourself back one step, look at the problem from above and treat it as mere data. I do not mean this in a context like “Digitalize everything! NOW!”, but more like a transformation where you carry the problem unto another realm where you can exploit that realm’s properties and tools, tackle the problem from a different angle, and after solving it, transform it back to where it belongs. In the “digital realm” it’s possible to violate, for example, causality principle since -from a mathematical point of view- you have two equally valid solutions but just go on, fork the results, solve for both of them and when you return from your trip to the 101010 (42, btw) make sure you check the implications, now.

Can I offer a quasi-solution to this conundrum? Yes, “any function is good as long as it works” but “as long as there is no objection from the physical side of view and also as long as there is no violation – now or ever, however unlikely it may be.” Black holes and dislocations: if you happen to step on them in silico and you didn’t know about them until then, and the physicist in you tells you that there is no such thing, what to do? The medical point of view clearly states that, in order to be successfull most of the time, you should stick to the regularizations in treatment. Yes, maybe a 5% that are exceptions will die because of the justifications but you’ll save the 95%. And I second that. You can’t spend your (calculation) time trying to comprehend every anamoly. If it was theory, again, don’t worry to much… Remember Einstein, Bose? Guess who got the Nobel for that, yes, things happen (Cornell, Wieman, Ketterle)…

An overheated argument which I should have included in the beginning of this entry:
“Woe unto those who hath sold their souls to silica! For they gave up their intution in return for some toys.”

Wishing that you always manage to return to your green land after your trip to 42 (6x9_13) land,
Yours truly.

“[…]Note that these concerns have nothing to do with the importance of messages. For example, a platitude such as “Thank you; come again” takes about as long to say or write as the urgent plea, “Call an ambulance!” while clearly the latter is more important and more meaningful. Information theory, however, does not involve message importance or meaning, as these are matters of the quality of data rather than the quantity of data, the latter of which is determined solely by probabilities.” (I was trying to find some already formulated essay about the “stripping of the knowledge from its content and thus treated solely as a data” but took the easiest way and copied from the wikipedia – sorry.

One more thing I wanted to write about but maybe some time later: David J.C. MacKay proposes a very insightful application of the Bayesian Interpretation on how it naturally follows after Occam’s razor principle [*]. The simple solution is indeed preferable to the complex one and having this principle formulated, one can now use this efficient fact in model comparison. So, if you accept that “nature will follow the simplest path among possibilities” as a priori, the algorithm can also make this distinction for you. Whether assume that there is “no physical meaning – any function is good as long as it works” or don’t assume it but eventually, and with the help of the Bayesian Interpretation, you’ll arrive at the same point, regardless of your assumptions (and if nature indeed favors the simpler form 8).

[*] – MacKay D.J.C. “Probable Networks and Plausible Predictions – A Review of Practical Bayesian Methods for Supervised Neural Networks” – http://www.inference.phy.cam.ac.uk/mackay/network.ps.gz | http://www.inference.phy.cam.ac.uk/mackay/BayesNets.html

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