Sunday, August 13, 2006
Occam's Razor
Occam's razor is a thorn in my flesh. I sometimes get pained with the beautiful and simple statement of intent that the razor is: "Entities should not be multiplied beyond necessity." Most of science and philosophy swears by it and it has really worked wonders in clearing up thought through history. When confused, with many possible hypotheses to explain a set of facts, pare away those that rely on excessive external entities and whatever remains, however improbable, must be the truth! Basically, it is a whole philosophy, this principle of parsimony - a refusal to believe there can be wastefulness - which has become an aesthetic and ethical theory as well, saying what is wasteful is ugly or bad. Anyway, this has worked beautifully in both information-complete and information-limited systems where we might or might not know everything that is to be known(there are exceptions as there always are but very few on the margin). All that has to be absolutely known is that the system to be analyzed is complete - that there is nothing else that will come in like a deus ex machina and cause radical changes like, for example, a teeny-weeny new fact. This, of course, is a direct consequence of the chaotic nature of life/complex systems, which are highly sensitive to initial conditions and can be affected to a large extent by small disturbances(butterfly effects!). Take the case of Newton's theory of light - it was nice and explained a lot of things until diffraction was observed and suddenly it was no good. And the wave theory(which was actually the older one) went the same way after photoelectric emission and Planck came along. Anyway, the point is, the razor is good when we know what to cut - just throw away the entrails - but if the butcher should reveal a new piece of breast-meat hidden near the leg, what do we do? get a whole new chicken? Scientists and philosophers have embraced the principle so very happily in spite of this basic robustness problem with the principle. Acceptedly the problem arises not internally but as a result of external factors and new data, which can again be carved into a new theory using the same razor. But the fact is we need a more robust principle and, for example, not believe in the superfluity of god just because we have very few facts and invoke William of Ockham vehemently and learnedly!
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5 comments:
The Occam's Razor is surely an interesting principle, and many of those things you say there are indeed true. Perhaps Einstein also referred to the Occam's razor when he remarked on conveying ideas in theoretical physics, when he said that things should be made as simple as possible, but not simpler. I have two things to convey here - the concept of self organizing criticality, as discovered by Per Bak, and the concept of Zipf's Law.
http://en.wikipedia.org/wiki/Self-organized_criticality
http://philramble.wordpress.com/2005/08/04/brains-brain-drains-and-zipfs-law/
Self organized criticality connects the mechanics of sandpiles to the organization of systems and rules of formal languages or constructs. Its effect is essentially similar to the Occam's razor, in that it enforces simplicity in systems to a practical extent. It is intriguing, since it seems to be a limiting of order in the universe. It is perhaps a construct of ordered reality which maintains a slow rate of entropy increase, since the effective "communicability" of and subsequently the enforcement of one axiom across a framework of many derived postulates would constitute a system of great "novelty". Such a system of novelty will probably require a great deal of energy to maintain, which in turn will lead to large changes in the entropy gradient. Let me know your thoughts on these ideas.
There are a couple of points which I would like to convey to you, which I forgot to include in that comment which I put up:
http://esd.mit.edu/symposium/pdfs/papers/wengenroth.pdf
Thats an interesting paper by Ulrich Wengenroth who has worked on problems of managing complexity in life in general.
I guess you have heard of Arthur Iberall and his science of homeokinetics as well. He combined the frameworks of non linear dynamics and chaos with system of system approaches to give solutions to systems of physics, sociology, chemistry, gas dynamics and other systems in which particle approaches or swarm approaches can be taken into account. I stumbled on the concept of Homeokinetics a couple of years back when I was looking online for information on psychohistory, the fictitious science developed by Hari Seldon in the sci-fi novel "Foundation" by Asimov.
http://www.trincoll.edu/depts/ecopsyc/homeokinetics/
What intrigues me continually is that the systems in which we all live have these limitations beyond which any abstractions which are made through them are broken down and beyonfd which things start to make very little sense. It is the thin line between sense and nonsense which we seem to be treading, when we consider techniques like Occam's razor or Iberall's homeokinetics.
hey wealth of info man.. will go thru it sometime soon.. unfortunately am into something right now so have to put this after a couple of other things in the priority list
Ocassionally write for the regular joes too buddy.We are a visible minority.
Occam's razor is only one of the necessary principles in science. The way I would define a good scientific theory (and maybe you will disagree) is that it should follow three principles:
1) It should have a self consistent set of axioms which can be considered obvious through experience or observation or definition.
2) It should be able to predict results which can be verified by unbiased, repeatable experiments or observations.
3) It should judiciously use Occam's razor, but without compromising on the previous two principles.
Since one could sometimes make mistakes in either choosing axioms or in performing experiments, it isn't fair to blame Occam's razor when a theory fails because of it's simplicity. I feel that if new facts or insights are discovered which are inexplicable by present theories, the only way forward is to try and modify the existing theory or to build an entirely new one with fresh axioms(as in the case of relativity vis-a-vis newtonian mechanics).
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