Saturday, June 16, 2007

Occam, with razor

All mathematical models of physical reality are approximations in lieu of an exactly solved theory. There are few cases in science of exact, complete theories,* so models are unavoidable. But there are models, and then there are models, and they're not all made equal.

Everything else being the same, simpler models are better models. A good model captures every significant physical mechanism in play and respects general physical principles (like energy and mass conservation), but avoids uncontrolled complexity. The most complex numerical computer models are approximations and in some sense caricatures. The simple climate model picture used in these last months there is also a caricature - an approximation that captures every important mechanism at work in the lower atmosphere only one or two steps beyond mere bookkeeping (kinematics). But the complicated computer models of climate invoke a mix of approximations, some controlled and some not. There is no way to check many of the assumptions made; when they can be checked, they're often wrong.

A simple model like the one used here, by design, ignores important climate subtleties and doesn't directly address dynamical questions. But while it's a carefully sketched caricature, it's a caricature under full theoretical control. It doesn't make many assumptions, and those it does, can be checked and, if necessary, modified. Complex models with uncheckable assumptions and many moving parts are difficult to understand. Teaching a computer to solve those models as rapid numerical simulations doesn't magically make them right; it just means that the modelers are committing sophisticated theoretical mistakes faster than they would if they were solving the models with pen and paper backed by brainpower. Computer scientists have a name for this: GIGO, meaning "garbage in, garbage out."

Since the 1980s, the much larger, more complex climate computer models (called "general circulation models," or GCMs for short) have given a wide range of answers to the question of "global warming" (enhanced IR opacity due to CO2), with changes ranging from small to much larger than the simple estimates. These models are impressively complex - they're the Pyramids or Saturn moon rockets of computer models - but for precisely that reason not to be trusted - they make uncontrolled approximations and far more uncheckable assumptions than do the simpler estimates. But the place to discuss the GCMs is later.

"As simple as and whenever and wherever possible" is a modern form of a principle first enunciated by the medieval philosopher and Franciscan friar William of Ockham (1288-1348) as entia non sunt multiplicanda praeter necessitatem, which means "entities should not be multiplied beyond necessity." The principle was dubbed "Occam's Razor" by Ockham's fellow scholastics. Here's a medieval doodle of William from a 1341 manuscript copy of his Summary of Logic.

Medieval manuscript sketch of William of Ockham

Over on the upper right the Latin says frater Occham iste, which means "that's Brother Occam."

William was an early representative of the nominalist school of philosophy, which holds that universals or abstract concepts are strictly mental constructs and words; only particulars are reals - this dog, that dog, not Dog-in-general. This seems to have been an English specialty and closely related to the English taste for empiricism and individualism; it appears again and again later in Hobbes, Locke, Hume, Darwin, etc.

In modern terms, Occam's sharp blade means that, the fewer assumptions you make, the less likely you are to be wrong. And it is a lot easier to be wrong than to be right, especially if you're guessing.
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* In physics, there are only three: the harmonic oscillator, the Kepler problem (two-body gravitational problem), and the ideal gas.

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