February 19, 2018

How to Understand Ockham’s Razor

“More things should not be used than are necessary.” Common translation of text attributed to William of Ockham, 14th century English theologian.

“Everything should be made as simple as possible, but not simpler.” Often attributed to Albert Einstein.

Ockham’s Razor is a mental tool for reasoning about scientific theories. It’s often oversimplified to something like “The simplest theory is usually the best.” The idea is that if you have two theories, and you don’t know which is correct, you can do pretty well by just choosing the simpler one.

But is this really a good idea?

I will admit up front that I don’t have the credentials to say anything new or surprising about Ockham’s Razor. I’m not a logician, philosopher, or historian, and I gave up my scientist aspirations a few years ago. I’m not even sure how to spell “Ockham” (“Occam” is one alternative). But I know a little bit about scientific inference, and I’ve given this subject some thought. So here we go.

First, let’s dispose of the idea that the simplest theory is usually the best. While a popular interpretation, this is neither a good translation of any text attributed to William of Ockham, nor a useful rule of thumb in practice. Yes, simplicity is a desirable property in scientific theories. But if you have to rely on comparing absolute levels of simplicity between two dissimilar theories, then you’re in very bad inferential shape. It’s useless as a rule of thumb, because there’s no objective absolute measure of simplicity. Just about any two theories can be described in a way to make the one you like seem simpler. It’s probably only a hair better than comparing two sports teams on the basis of how intimidating their mascots are.

So what is Ockham’s Razor good for? Actually, quite a bit. There’s a simple interpretation that is valid and quite useful, even if it’s not such a great sound bite.

Suppose you have a theory, composed of various postulates, that is sufficient to explain (predict) some data. As an explanation for that data, you should prefer that theory by itself to the combination of that theory and any additional postulate. Or in plainer terms: don’t glom extra stuff onto your theory that doesn’t help explain the data.

Here’s an illustration. Suppose we’re interested in why stuff falls down. One theory might be gravitational forces. If I tell you that my theory of gravity is a good explanation of things falling, you might examine the evidence and determine that it does an awfully good job of explaining the data. If, however, I tell you that my theory also postulates that Francis Ford Coppola is the finest director in the history of cinema, we might have a good use for the razor. Use it to strip away the parts of my theory that are superfluous, or (to echo one translation) “beyond necessity.” In this case, you would be right to look me squarely in the eye and ask, “Are you sure the bit about Coppola is really essential to explaining falling objects?” And after you establish that gravity alone does just a good job as gravity + Coppola, you would be entitled to do some slicing. It may very well be true that Coppola is a great director. But this fact probably doesn’t have a place in anyone’s theory of falling objects.

The razor is really not for comparing disparate theories. It’s most useful when you have a single theory, and you want to pare its formulation down to the essentials. It can be tricky. Maybe you have some genuinely puzzling data, and a complex, well-articulated model that does a surprisingly nice job of explaining the data. It will be tempting to regard the data as support for the entire model. Ockham’s razor admonishes you to keep only the parts that are doing the explanatory work, and discard the rest. If your model is a giant arithmetic hairball, it may take some work to figure out which features are just window dressing and which are essential. But you are obligated to do this work for any facet you want to claim is supported by data.

If you are somehow in the unfortunate position of having two theories to consider, with absolutely nothing but parsimony to go on, then although it’s very sad, you really don’t have any business choosing. Choosing the simpler one may be slightly better than flipping a coin, but only slightly. In fact, it’s unlikely you’ll even have an objective way of deciding which is simpler. You need more to go on before cutting anything with a razor.

So there you have it. I don’t know if this is exactly what William of Ockham had in mind 700 years ago, but it’s easily described and intuitively sensible. This is the kind of interpretation that tends to show up in writings geared towards scientists and philosophers. So that’s how I like to think about it, and I think you should too.

And for the record, although I do think Coppola has produced some deeply wonderful films, I don’t think it makes sense to pick a single finest director in the history of cinema.