Shaving Science with Occam's razor

This post is about Occam's razor, i.e. the statement, that when presented with competing explanations for the same phenomenon, the one with the fewest assumptions is likely the correct one. It is often used prescriptively in its abbreviated form - "Choose the simplest explanation."

Occam's razor is not a law, it is a rule of thumb. It is often useful and leads to the right answer. This post is about some major exceptions to the statement. I wrote it because I find people often use Occam's razor as if it is a law (rather than a heuristic).

Doing so can lead to flat mistakes (mainly because of overemphasis on simplicity), something every researcher and indeed human being should be aware of. Carelessness in using Occam's - or anyone's - razor can result in shaving off parts that are actually critical.

1. Physics: There are many examples. I will mention a few.

a) Cosmology: It is simpler to assume that the Earth, rather than any other heavenly body, is the center of the universe. In fact it was possible at one time, to explain the observed motion of the heavens quite well using that assumption. Nonetheless, it is not correct.

Another example was the observation of perturbations in the orbit of Mercury. Simplest explanation as per Newtonian dynamics? The presence of a nearby planet. But no one found such a planet. Mercury's behavior was later explained by Einstein's theory of general relativity: a more complicated explanation.

Yet another example: the steady state model of the universe is simpler than the big bang model. For a long time it was consistent with the observed data. But it is wrong.

b) Thermodynamics: The phlogiston theory assumed there was fire inside every combustible

object, which was merely released on burning. Lavoisier proved this simple theory wrong by

demonstrating weight gain during burning and the crucial role of oxygen in the process.

Ergo: the real explanation was much more complicated.

c) Atoms: Scientists like Mach (opposing Boltzmann, among others) argued there was no need to postulate the existence of atoms, since physical and chemical laws known at the time could be described without them. 'nuf said.

d) Neutrino: In the case of radioactive (beta) decay, the simplest explanation was a violation of the law of conservation of energy. The more complex, but real answer: the existence of a completely new particle, the neutrino, which carried away the missing energy. Confirmed by experiment (1995 Physics Nobel).

e) The standard model: The best, experimentally confirmed, working theory we have of the universe seems to be complicated and ad hoc. It is hard to argue that it is simple in any sense.

2. Geology: The theory of continental drift was initially thought as too complex an explanation for the observed distribution of biological species. Turns out to be right, though.

   
   

3. Mathematics: One example from pure, and another from applied, math.

a) Non-Euclidean geometry: Two parallel lines only meet at infinity, says Euclid's 5th proposition. After many centuries, Bolyai, Lobachevsky and others showed this was not true for non-Euclidean geometries. A relevant example is Riemannian geometry, which provides the framework for Einstein's theory of gravitation.

b) AI: Occam's razor fails spectacularly here. Reality is complex. That's we need large language models for learning it. In machine learning complex models are easier to train than simple models.

4. Biology: This is a field where Occam's razor, as Crick pointed out, is especially dangerous to use (because natural selection does not always pick simple or minimalistic solutions).

a) DNA: DNA (which has only 4 nucleotides) was not considered seriously as the vehicle for genetic transmission in contrast to proteins (which have 20 amino acids) for a long time. Here the razor worked in reverse - DNA was thought to be too simple to be the answer to life.

b) Stomach ulcers: Simplest explanation? Stress and excess stomach acid. The more complex, but correct, explanation, involves the bacterium Helicobacter pylori. Barry Marshall and Robin Warren got the 2005 Nobel for finding the right answer.

Afterword

I do not advocate against the careful use of Occam's razor. It is a useful but crude tool. Unthinking use of it can represent intellectual laziness. It would probably be good to keep in mind Einstein's warning: "Everything should be as simple as possible, but not simpler." And it is also good to remember that what is simple is actually a subjective opinion. Thus also Oscar Wilde: "The truth is rarely pure, and never simple."