Monday, May 21, 2007

 
A Shield Against The Power Rangers Of Occam
or Just a few random ideas as a late birthday present to the late Bertrand Russell

Occam is best known for a maxim which is not to be found in his works, but has acquired the name of “Occam’s razor.” This maxim says: “Entities are not to be multiplied without necessity.” Although he did not say this, he said something which has much the same effect, “It is vain to do with more what can be done with fewer.” That is to say, if everything in some science can be interpreted without assuming this or that hypothetical entity, there is no ground for assuming it. I have myself found this a more fruitful principle in logical analysis.

Bertrand Russell: A History of Philosophy

In order to apply the “razor” to a difference of belief between two people or to find the truth or untruth of a general idea you first have to have an agreement on the definition of the problem, without that you can’t exclude things from the solution. Exclusion is the purpose of this “razor”. And it can exclude only those aspects of a problem you know about. You wouldn’t be able to deal with any unknown aspects. If you doubt that one, please explain to me how you would exclude something you didn’t know about. While logical analysis is very useful and sometimes impressive it doesn’t encompass the entire universe of possibilities, it can’t include those unknown to it but which, nonetheless might be there, and it can’t include those which could contribute but which aren’t known and necessary to the immediate solution of the problem at hand. And unskilled use of the razor, rampant in some of its make believe masters, runs the risk of cutting out things that are relevant and even necessary.

A fun thing to think about, but which we don’t know to be of much practical use, are the extra dimensions of the universe which are being examined. How many of these dimensions exist? Are they really there? What qualities do they impose on existence? Do they impinge on our universe of sense? Could their effects permeate our lives unknown? Perhaps there are aspects of our lives too subtle for us to have discovered yet but which are understandable only through the added, as yet unknown, qualities of these extra dimensions. Just to throw one in for the entertainment of the atheists in the audience, maybe one of them has a quality that bridges the physical universe and the non-physical. Notice I said “maybe” before you fly off the handle.

For most of the problems we deal with those aren’t important considerations, we might cut out their consideration but that’s only a matter of the necessities imposed by contingency, not a definitive exclusion. As the math and perhaps someday the science done with these develops maybe that will change, though I doubt it will turn out to be a closed matter. The difficulties of dealing with just the equations might outstrip the efforts of the entire body of scientists and mathematicians to discover them before the species goes extinct. Maybe some of the less “knowable” aspects of human experience really are impinged on by these dimensions. Consciousness, for example. Maybe that’s why it escapes those would be-scientists who attempt to work around it. Who knows?

You’ll notice that Russell said, “if everything in some science can be interpreted.” That great master of logic used a conditional construction, he certainly would have known the implications of doing so and would have done that for a good reason. Science is a very specialized activity, many things in life can’t be discovered through science. My favorite example this week is to try to find “the separation of church and state” with science. To start with, there isn’t a discreet “thing” , defined and bounded, that is “the separation of church and state”. Just the lack of unanimity of the legal definitions of it clearly demonstrates that to be true. You would have to have a “discreet thing” there to do real science about it. “The separation of church and state” is there, or at least I hope it is, it has an impact on our lives and I hope it is preserved and strengthened but it is entirely outside of the reach of science.

I’m not sure if he meant to imply it, but Russell’s endorsement of this mainstay of modern materialist fundamentalists seems more of a conditional endorsement than a final requirement. You’ll notice Russell called it a maxim, not a foundation of logic. I’m guessing he meant it less as law and more as tool. The “razor” is really more of a convenience than an infallible tool, it doesn’t do everything necessary. And it might have been called a “razor” by people with painful experience that those tools are often not sufficiently sharp and prone to go farther than they should. He also endorsed it as a tool of logical analysis, formal logic reduces the complexity of real life to analyze the form of the problem. It can be useful but the possible solution of many real life problems are too complex to fit into its forms.

The kind of pop-materialists, cultists of scientism, etc. who are always ready to pull out the old chestnut “Occam’s razor” often mistake their wielding of pat assertions of prejudice and dismissive bigotry for this tool. That is an advertisement of their fundamentalism, not their mastery of logic. They often can’t get to step one of the use of the razor, finding out if it is useful in the question at hand.

A less than honest use of the form of the razor popular these days is to apply it to a question beyond its ability, the question of the existence of God. “The material world is most simply explained without a God so the idea of a God is false”, or some such construction. This begins by assuming that our knowledge of the physical universe and the methods we know to analyze it are effectively comprehensive, when they certainly aren’t. It also assumes that a God, by definition supernaturally outside of the physical universe, would be susceptible to the known limits of the physical universe and answerable to its laws. They do this even on those occasions when they assign qualities to “God” such as “all powerful” “all knowing”, etc. Just the first of these “all” qualities would include the ability to surpass the known laws of nature.

It compounds those follies with the assumption that only a yes-no answer is possible when neither are. The only honest answer to the question of God’s existence is “I don’t know”. You can go on from there to believe, not believe or abstain from voting on the existence of God. But belief isn’t considered to be the same thing as knowledge.

Comments:
The problem, of course, in applying Occam's Razor is defining what is the "simplest explanation". The computer scientists come up with a scheme to compute the answer to problem X, an instance of which is described in Y bytes in 0.01*Y^2 + 3*Y + 135 steps. They say it's the simplest solution as any other method takes more steps for anything but the smallest instances of the problem.

I say their solution is more complicated than mine, 'cause mine takes 50 lines of code whereas theirs takes 100. But my method takes more computations on most reasonable data sets. Which method has fewer multiplied entities? My method which has 50 rather than 100 "lines of code" entities?

Or there method which has fewer "calculation step" entities? Or my boss's method which takes 2 sentances to explain well enough for any person to do the calculation, whereas both my method and the computer scientist's method take as many words to explain as to write them out in computer code. Yet implimenting the method my boss claims is simple as he can describe it in two sentances requires 150 lines of code and, unless you have a dedicated pattern-recognition chip equivalent to those found in our brains, takes 0.01*Y^2 + Y*log(Y) + 5*Y + 170 calculation steps.

Consider that the problem is to describe numerically some sort of physical system -- my boss's method might have the fewest entities in its description, at a human level, but to actually use that method requires that the human level entities be proliferated into many code-level entities and many calculation step level entities.

So which method does Occam's razor tell us to use?

Of course Alberich's razor says "use the method told to you by the person paying you" ;)
 
I bow down, Alberich's razor is brilliant, I'd imagine that there is more evidence of its existence in the world and it is one that few would deny using.

The rest of this reasoning isn't to bad either. That piece I promised is coming. I'm going to limit my "agnostic" blogging to one day a week. Odd for someone who isn't officially an agnostic to find himself in this position.
 
This begins by assuming that our knowledge of the physical universe and the methods we know to analyze it are effectively comprehensive, when they certainly aren’t.

Nah, it begins by saying "we know our knowledge of the universe isn't comprehensive, but we can only work with what we have so let's go from there".

It also assumes that a God, by definition supernaturally outside of the physical universe, would be susceptible to the known limits of the physical universe and answerable to its laws.

Not that I can see. We're really only assuming that it makes sense to use epistemological rules of thumb when talking about God. And, like I said before, we can only work with the understanding we have. Claiming at the beginning that the entity in question is beyond our understanding so any ordinary rule that we might use to determine the existence of God is useless strikes me as disingenuous. I mean, yes, you could posit such a being, but it would be completely beyond us to know how to react to such a being, because we wouldn't be able to know anything about it if it was completely beyond our understanding. So why bother with it?

It compounds those follies with the assumption that only a yes-no answer is possible when neither are.

We don't know for certain, but I would argue that we can still have a strong indication in one direction.
 
Nah, it begins by saying "we know our knowledge of the universe isn't comprehensive, but we can only work with what we have so let's go from there".

-- Lynet, if you're talking about the big one, the question of the exitence of God, then, no, the knowledge necessary isn't there. There is no way to know anything about it.

We're really only assuming that it makes sense to use epistemological rules of thumb when talking about God.

-- There is no way you can know that. There is no possible rule for dealing with anything outside of the physical universe, there is no data that could support it, no experience, no methodology. In the absence of those anything you do, even if you call it "epistemological rules of thumb" are anything more than a hunch, and most likely just a bunch of assertions to get where you wanted to go in the first place.

We don't know for certain, but I would argue that we can still have a strong indication in one direction.

- I maintain that with the argument that just preceeded that section there is no logical way that you could maintain this. Not if you wanted to use logic.
 
To address Alberich's question "So which method does Occam's razor tell us to use," the formal razor doesn't really apply to specific mathematical problems. Ignoring that, number of steps is not a factor for the formal razor; merely the input program and input data sizes. Correctness of output, however, is required to be eligible for consideration. Thus, for a finite output set the trivially generated case of a program simply printing pre-computed output is "correct", if not necessarily preferred. For large (including "infinite") data sets, the formal razor prefers the smaller input.

olvlzl's claim that "a God, by definition supernaturally outside of the physical universe, would be susceptible to the known limits of the physical universe and answerable to its laws" begs the question of what "supernatural" is, and appears to misunderstands the character of what science considers "law". The laws of inertia and gravitation may govern the motion of uncharged newtonian bodies, but that does not make the motions of charged bodies supernatural. It just means there are additional laws. Essentially, science presumes there is a pattern to our experience... and mathematically, a pattern in one area put together with another pattern in a different area nonetheless compose a single combined pattern. Science tries to find the "best" pattern for describing human experience (aka, "the evidence").

For most of the irritating math, see doi:10.1109/18.825807 (or the free postscript copy from the author).
 
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