A Case of the Mondays: Science is Cumulative

Crossposted to Abstract Nonsense

Science is a cumulative process. Although as Thomas Kuhn noted, scientific paradigms overthrow earlier paradigms and bring forth brand new theories, the process remains almost linearly progressive. Facts get tacked onto other facts; new observations falsify theories or prove them more solid; methods improve as scientists' understanding of measurement and statistics becomes more complete.

In The Structure of Scientific Revolutions, Kuhn explains that there is normal science and revolutionary science. Normal science is completely cumulative, and is based on just one paradigm, or way of viewing things. Physics had Newtonian mechanics, and then General Relativity; chemistry has atomism; biology has the gene-centric view of evolution. The basic paradigm then colors the experiences of scientists, who modify it a little bit whenever a dissonant fact comes up. Revolutionary science occurs when the body of dissonant facts becomes so huge that the paradigm becomes more of a liability than an asset, at which point a new paradigm, which incorporates that body of facts, crops up and replaces the old one.

The above description is nearly trivial. The only observation that would distress a positivist is that initial dissonant facts are incorporated into the theory instead of falsifying it. But in reality, rational people make generalizations all the time, switching to different frameworks only when the body of conflicting facts becomes too massive to ignore. In scientific terms, the modified paradigm is usually still able to make falsifiable predictions. For example, the epicycles that were invented to account for observational discrepancies between the Ptolemaic model and astronomic observations were a perfectly understandable invention, at least before the evidence piled up that the epicycles were centered at the Sun. Paradigms that remain even though they outlive their predictive power tend to be like the theory of the luminiferous ether, which took a few decades to be discarded because it took that long for someone to come up with a better alternative.

But where Kuhn makes a nontrivial statement is when he says that paradigms are in a way incomparable. It's impossible, he says, to just decide based on evidence, since evidence itself depends on the framework you see it in. If you are a proponent of a deterministic physical theory, in particular classical physics, you will be inclined to ignore statistical mechanics.

However, in reality, classical physicists did consider statistical mechanics, and paradigms are comparable. Even Kuhn admits that given an unordered list of paradigms, it's always possible for the historian of science to tell the order they appeared in. In that sense, and in several more senses, science is the accumulation of a body of facts and theories, as opposed to the phoenix-like creature Kuhn imagines it as.

At this point, I would like to take a detour and show cumulativity in two other areas of science. Science can be viewed as a body of observed and inferred facts, a body of tested theories strung together to explain the facts and predict future facts, or a body of methods to test theories and discover new facts. I am going to focus on the first and third formulations first, and only then come to the second, the one Kuhn deals with.

In a certain trivial sense, facts are invariably cumulative. Existing facts may be emphasized or deemphasized, but they are only stricken out when they're discovered to be the result of misunderstanding, experimental error, or fraud, none of which is common. What can change is the body of facts inferred by theory. Evolution, even speciation, is an observed fact, but the large-scale evolution of phyla and kingdoms—including, for example, events like the Cambrian Explosion and the Permian Extinction—is merely inferred from a gigantic body of geological evidence. Advances in technology can promote inferred facts to observed facts, as the discovery of the parallax effect promoted heliocentrism. More rarely, they can overthrow inferred facts that are based on relatively little evidence; in the early 1920s, physicists considered it a fact that the Sun was primarily composed of iron, based on faulty inference. But they cannot overthrow directly observed facts, and have yet to impeach any fact based on overwhelming inference such as the fact of evolution or the existence of black holes.

Similarly, methods may become better or worse than others because of technological improvements, but on their own they never become worse. It may be considered silly to make astronomic observations using tools developed in the 19th century, but modern technology will ensure that even so, the observations will be at least as good as the ones the same tools produced when they were invented. It's far more common for a new tool to suddenly shed light on a theory—the telescope, the electron microscope, the supercollider—than for a theory to dictate the use of a tool. The standard scientific method, which dictates how to interpret experiments using these tools, doesn't change when a paradigm changes; the closest thing to a real change it has undergone is the incorporation of observational sciences to a method that was invented for use in experimental sciences.

What is nontrivial is how theories influence the choice of which facts are to be emphasized. But whenever a paradigm is in crisis—that is, whenever it can no longer easily adapt to new evidence while remaining predictively relevant—the deemphasized facts can come into play. Especially when scientists only hang on to a theory because nothing else is available, as in the case of the Standard Model in quantum physics, they look for every possible avenue that will give them a new theory. They may be attached to the old ways of thinking, but they are even more attached to the fame they will get if they are the first to discover the next paradigm. Evidently, quantization did succeed as a method in a continuous world; at first Planck thought it was just a convenient trick, but once that trick became acceptable, it wasn't hard to realize that it underlay a real phenomenon.

It's telling that the final arbiter in a scientific crisis tends to come from a new discovery. Heliocentrism would have never gotten anywhere if Kepler hadn't discovered that planetary orbits were elliptical, disposing of the need for epicycles once and for all. Neo-Darwinian evolution became a lot more powerful once the structure of DNA was discovered; and even the original Neo-Darwinian synthesis came about because biologists had rediscovered Mendel's laws of inheritance. Darwinian evolution was dominant long before then, but that was because its best competitor, Lamarckian evolution, was a lot more self-evidently flawed than geocentrism was in the 1600s.

What this suggests is that even the succession of theories is cumulative. This is especially true in physics, where new theories don't so much overthrow their predecessors as expand them: Einstein showed Newtonian mechanics was an approximation valid when speed was negligible compared to the speed of light, Planck and Einstein showed that continuous light emission was a large-scale approximation of a discrete structure, and physicists after them showed that General Relativity was a large-scale approximation and the Standard Model a low-gravity one. But even in other sciences, there is a similar cumulativity of theories. The neo-Darwinian synthesis proved neither Darwin nor Mendel wrong; it only said that Mendel's genetics was the mechanism of inheritance Darwin had been looking for.

A change in paradigm may make theory an approximation of reality from another angle. But it is nonetheless a better approximation, so in a way science is cumulative, even linearly. Beyond the trivial sense, in which the scientific knowledge of 1960 was clearly better than this of 1900 and this of 1900 was clearly better than this of 1800, both kinds of science only usher in further progress. Normal science is clearly cumulative; and revolutionary science replaces a paradigm that outlived its usefulness with an objectively better one.