Simplicity plays a crucial, but frequently overlooked, role in the scientific method (see the posters in my previous post). Considering how complicated science can be, simplicity may seem to be far from a driving source in science. Is string theory really simple? If scientists need at least six, seven or more years of training past high school, how can we consider science to be anything but antithetical to simplicity?
Good questions, but simple is relative. Consider the standard model of particle physics. First, it is widely agreed upon what the standard model is. Second, there are many alternatives to the standard model that agree with the standard model where there is experimental data but disagree elsewhere. One can name many: Little Higgs, Technicolor, Grand Unified Models (in many varieties), and Super Symmetric Grand Unified Models (also in many varieties). I have even attended a seminar where the speaker gave a general technique to generate extensions to the standard model that also have a dark matter candidate. So why do we prefer the standard model? It is not elegance. Very few people consider the Standard Model more elegant than its competitors. Indeed, elegance is one of the main motivations driving the generation of alternate models. The competitors also keep all the phenomenological success of the standard model. So, to repeat the question, why do we prefer the standard model to the competitors? Simplicity and only simplicity. All the pretenders have additional assumptions or ingredients that are not required by the current experimental data. At some point they may be required as more data is made available but not now. Thus we go with the simplest model that describes the data.
This is true across all disciplines and over time. The elliptic orbits of Kepler (1571–1630) where simpler than the epicycles of Ptolemy (c. 90 – c. 168) or the epicyclets of Copernicus (1473–1543). There it is. We draw straight lines through the data rather than 29th order polynomials. If the data has bumps and wiggles, we frequently assume they are experimental error as in the randomly chosen graph to the left where the theory lines do not go through all the data points. No one would take me seriously if I fit every single bump and wiggle. Simplicity is more important than religiously fitting each data point.
Going from the sublime to the ridiculous consider Russell’s teapot. Bertrand Russell (1872–1970) argued as follows: If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense. But what feature of the scientific method rules out the orbiting teapot? Or invisible pink unicorns? Or anyone of a thousand different mythical beings? Not observation! But they fail the simplicity test. Like the various extensions to the standard model, they are discounted because there are extra assumptions that are not required by the observational data. This is otherwise known as Occam’s razor.
The argument for simplicity is rather straight forward. Models are judged by their ability to describe past observations and make correct predictions for future ones. As a matter of practical consideration, one should drop all features of a model that are not conducive to that end. While the next batch of data may force one to a more complicated model, there is no way to judge in advance which direction the complication will take. Hence we have all the extensions of the standard model waiting in the wings to see which, if any, the next batch of data will prefer – or rule out.
The crucial role of simplicity in choosing one model from among the many solves one of the enduring problems in the philosophy of science. Consider the following quote from Imre Lakatos (1922 – 1974) a leading philosopher of science from the last century: But, as many skeptics pointed out, rival theories are always indefinitely many and therefore the proving power of experiment vanishes. One cannot learn from experience about the truth of any scientific theory, only at best about its falsehood: confirming instances have no epistemic value whatsoever (emphasis in the original). Note the premise of the argument: rival theories are always indefinitely many. While rival theories may be infinitely many, one or at most a very few are always chosen by the criteria of simplicity. We have the one standard model of particle physics not an infinite many and his argument fails at the first step. Confirming instances, like finding the Higgs boson, do have epistemic value.