Wednesday, December 23, 2009

On Understanding Complexity (or, Looking Inwards)*




As a scientist**, I often find myself turning to works of philosophy to consider questions that science cannot answer.  Contrary to popular belief in some corners, we freely admit that those questions exist -- because, by necessity, there must be first principles and science only deals with matters that follow from them.

For example, what does it mean to live a correct life?  This is partially a question of morality, but what is morally correct?  Why, for example, is the Golden Rule any better, from a moral standpoint, than Might Makes Right?  There is no easy answer.  One's choice is simply a preference than cannot be "proven" to be superior.  The christian bible is essentially an historical collection of first principles (the Old Testament) with errata and appendices (the New Testament) that provides a convenient starting point, but one which is not really usable by anyone who does not accept that morality is what God says it is, particularly when He had such a penchant for contradiction and His Children have such a tendency for picking and choosing.

Lately I've been reading a lot of Dennett, particularly his musings about determinism and free will.   The nice thing about Dennett, beyond his readability, is his thoroughness.  It's not enough, for example, to say that we have free will because we can make personal choices -- Dennett probes the source of those choices.  He uses the clever example of the spex ichneumoneus wasp, which lays eggs next to a paralyzed cricket.  When the time comes for egg laying, he quotes a biologist, the wasp Spex builds a burrow for the purpose and seeks out a cricket ... She (then) drags the cricket into the burrow ... and the wasp grubs feed off (it).  To the human mind, (this) seemingly purposeful routine conveys a convincing flavor of logic.  He then goes on to describe how the nefarious biologists vex the poor wasp by moving her paralyzed cricket around, to which the wasp can only respond by going through apparently preprogrammed biological actions that -- had she actually been using logic and reasoning -- she would not have done, for apparently the wasp inspects the burrow first, before dragging the cricket inside.   If the cricket is moved a few inches away while the wasp is inside making her preliminary inspection, the wasp ... will bring the cricket back to the threshold, but not inside, and will repeat the prepratory procedure. ... On one occasion, (the biologists moved the cricket) forty times, always with the same result.  "The poor wasp is unmasked," writes Dennett: "she is not a free agent, but rather at the mercy of brute physical causation, driven inexorably into her states and activities by features of the environment outside of her control."

There was a time, long ago during the Age of Reason and the young ascendency of empiricism, when it was thought that the time would come when the future could be predicted through mathematics.  Physics, went the reasoning, was guided by fixed laws, and hence the path of a particle through space (and thereby its future) was predetermined by the position and velocity of of every other particle in the universe.  All that was needed was the precise identification of the latter two quantities.

Today, we know that prediction of the behavior of something as simple as a quadratic mapping -- practically the 2nd most simple type of nontrivial equation known to mathematics -- is fundamentally unknowable, given the basic limits on precision in the real universe and our inability to capture anything except the finite in an empirical sense.   Long ago, I once wrote something along these lines regarding the number of problems in the universe: how not only that the number of provably solvable problems is finite, but that the number of humanly indescribable (much less solvable) problems is uncountably infinite***.

We are meek and small animals, we are.  Well, small, anyhow.

*This line of thought actually has a point and is going somewhere, I think, someday, although the ride may take innumerable side trips.  Who knows.  It makes some kind of weird sense to me.

**I use that term loosely these days, given that I have long since sold out, as it were.

***That particular statement is provable, too.

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