Sunday, 5 August 2012

The Occam–Einstein Incongruence


No, this is not an episode of The Big Bang Theory you missed, but instead the seeming tension between two of science's best-loved heroes: William of Occam (who, incidentally, was a Franciscan friar and is revered in the Anglican Church as a saint) and Albert Einstein.

Let’s set the ground first by seeing what these two guys say about simplicity versus complexity, that is often applied also to scientific theories. Occam is almost exclusively known for his razor, which goes as follows:
“Plurality must never be posited without necessity” (which he also expressed by saying that “[i]t is futile to do with more things that which can be done with fewer.”)
while Einstein has, among many other things, warned that:
“Everything should be kept as simple as possible, but no simpler.”
and that
“For every problem there is a solution which is simple, obvious, and wrong.”
At first sight it may seem like Occam is arguing for simplicity, while Eistein is warning against its excessive application, but a closer reading suggests to me that Einstein is simply being cautious of simplicity in the absolute. Just looking at some theory and judging it to be complex does not automatically make it a candidate for being cut to size with Occam’s razor. Instead, it is its simplicity relative to the simplicity of the entities and events that it refers to that needs to be considered. Neither is it the case that two theories can be compared solely on the grounds of simplicity, with the conclusion that Occam would side with the simpler one. It is only when the competing theories have the same level of descriptive/predictive performance that the razor comes into play.

Bringing Occam and Einstein together, we can say that problems of varying degrees of simplicity require solutions of commensurate complexity – if a solution’s simplicity exceeds that of the problem’s, it is likely not to be a solution, while if it falls short of it, there is room for simplification and the added baggage is unnecessary.

Instead of being a battle axe, Occam’s razor looks more like a surgical implement, requiring careful deliberation both before and during application. As for our protagonists, they are more likely to star in an episode entitled ‘The Occam-Einstein Equivalency’ :).