December 27, 2009

On abstraction

Because Physics, you see, deals with forces, and matter, and motion. And for many kinds of system, the classical model of Physics provides us a clear, consistent picture and throws in reliable tools to predict future behaviour. The literature that defines the classical model is an imposing body of work, prepared by some of the greatest minds in history.

Yet, when we study complex interactions between exceedingly small particles, this model proves cumbersome. We find it difficult to cope with the sheer number of variables involved, with the errors in the measurement of each variable, and with the myriad parameters that remain entirely unaccounted for and yet interfere with the results that Physics predicts.

So, without entirely forsaking Physics, we try a new model to help us understand these interactions. This time we abstract a step higher. We consider collections of similar particles - substances - instead of their elementary constituents. We experiment, as the scientific method demands, and we develop this new model to explain the interaction between these substances. Soon enough, we find an entire discipline in front of us - this we call Chemistry.

When we apply Chemistry to intricate hydrocarbon molecules, however, we find it unequal to the task and decide that we must move to a newer model. We abstract a step higher and train ourselves to think in terms of organic structures, to which we give names in our new vocabulary, and whose behaviour we determine through observation, and soon enough we are in the realm of Biology.

Yet, when we try to analyse the neural system, notable for its heavily interconnected, highly convolved architecture, even Biology comes up short and we shift to the empirically-derived model of Psychology, abstracting away those fiddlesome neurons and dealing only with the consciousness that they engender.

But when a number of organisms interact, each consciousness distinct and yet influenced by others in unimaginably warped ways, Psychology too proves insufficient. We must now think in terms of the community and the choices it makes, and cease to consider the all-too-often irrational individual - we approach the social sciences, and the domain we call Economics.

Of course, it's still essentially about forces, and matter, and motion. We realize that it is only the inadequacy of our models that, along with the feebleness of our computation and our inability to account for every single variable, prevents us from deriving economic laws from the first principles of physics. And each model, a venerable Science in its own right, is but a rough draft, constructed only to place our observations within a context, to create repositories of if-this-then-that axioms that prove valuable in some situations, repositories that we call Knowledge.

But Physics is a Science too, and a model - perhaps, then, reality is not fundamentally about forces and matter and motion at all. Perhaps these, too, are merely abstractions. Perhaps a model, whatever its level of granularity, is but a caricature of a deeper reality, and this reality a caricature of another, and so on ad infinitum, the interminably-cocooned Truth safe from prying eyes.