Occam's Razor, Without the Mystique: Where the Idea Came From and What It's Good For

Picture a quiet evening in a kitchen. The fridge has stopped humming, and you only notice because the silence is suddenly so large. Then you see that the clock on the microwave is dark too. I'm telling this as an imagined scene rather than a diary entry, because the details matter less than its shape. Some version of it happens in most households sooner or later.

Two stories are available. In the first, one thing has gone wrong: the power to that part of the kitchen has been cut off. In the second, three separate things have gone wrong at once: the fridge's motor has failed, the microwave's display has failed, and the oven clock has failed. Both stories fit what you can see. So which do you try first?

That is the question Occam's razor answers, in plain words: when two explanations fit the facts equally well, begin with the one that needs fewer separate assumptions. It is a rule for where to start looking, not a ruling on what is true. The rest of this piece is about why that starting point is sensible, where the idea came from, and where it stops helping.

Who was Occam, and what was he trying to do?

The name belongs to William of Ockham, an English friar and philosopher who lived from the late thirteenth century until about 1347. Historians are not certain of his exact birth date, so I'll leave it there. He worked in medieval philosophy, and one of the arguments of his day was over what exists. Do general things, such as "humanity" or "redness", exist as realities of their own, over and above the individual people and red objects? Ockham leaned towards saying they do not. As I understand his position, we can talk about individual things and the words we use for their likenesses without adding a further layer of invisible entities. Where an extra entity does no explanatory work, he saw no reason to posit it.

His problem, then, was less about fridges than about clutter in an argument. If you can explain something without a new ingredient, adding the ingredient only makes your account harder to check.

The famous slogan is not quite his

Here is a small correction I find reassuring, because it is an easy mistake and I would have repeated it myself before checking. The tidy Latin slogan usually attached to him translates roughly as "entities are not to be multiplied beyond necessity". Scholars generally note that this exact wording does not appear in his surviving writings, though he did write sentences with a similar spirit. The neat form seems to have become standard later. The "razor" image is also a later flourish, coined in the centuries after him.

Nor did the idea begin with him. Aristotle, as I read the Posterior Analytics, already suggests that, other things being equal, an argument resting on fewer assumptions is the better one. Isaac Newton, in the opening of the reasoning rules in his Principia (1687), says we should admit no more causes for natural things than are both true and sufficient to explain them. I like the word "true" in that rule. It reminds us that being sufficient was never the whole test.

So the razor is less a single invention than a habit that several careful people wrote down in their own words, and it has been handed on and sharpened ever since.

Why fewer assumptions is a sensible place to start

Now back to the kitchen. The reason to prefer the one-cause story is not that simplicity is beautiful. It is arithmetic about coincidence.

Every separate assumption you make has to be true at the same time, and each one has a chance of being true that is less than certain. When independent things must all hold together, you multiply their chances, and multiplying numbers below one gives a smaller number each time.

Let me make up some numbers, which are invented purely to show the shape. I'll also handicap the simple story to be fair to the complicated one. Suppose a safety switch tripping on a given evening has a 1 in 1,000 chance (0.001), while each appliance failing independently has a 1 in 100 chance (0.01).

• One cause: the switch has tripped. Chance of this whole pattern of darkness: 0.001, or 1 in 1,000.
• Three causes: fridge, microwave display and oven clock all fail independently on the same evening. Chance: 0.01 × 0.01 × 0.01 = 0.000001, or 1 in a million.

Even with the simple story made ten times less likely than each of the appliance failures, it comes out a thousand times more probable (0.001 ÷ 0.000001 = 1,000). The result does not depend on my exact figures. The three-cause story must pay a "coincidence tax" three times over, and that tax is heavy.

Two cautions keep this honest. First, I've assumed the three failures are independent, and in a real kitchen they might not be. Second, the comparison only works because both stories explain the same facts equally well. If one story left something unexplained, we'd be comparing unlike things.

Where the razor meets statistics and curve-fitting

The same logic reaches into other fields, and that is the part I find most pleasing.

In the eighteenth century Thomas Bayes wrote an essay on probability, published after his death in 1763, which gave us what we now call Bayes' theorem. It is the rule for updating how much you believe a story once you see evidence. Used to compare explanations, it builds the coincidence tax into the calculation: a story that needs many things to line up gets a lower score unless the evidence strongly favours it. Later statisticians turned this into practical tools. The Akaike information criterion (1974) and the Bayesian information criterion (1978) both score a model by how well it fits the data and then subtract a penalty for each extra adjustable part. I only know these at a surface level and am still learning, but the idea is clear enough: the razor became a sum.

Why would you want that penalty? Imagine you have ten measurements on a graph that roughly follow a straight line, with the small wobbles you'd expect from imperfect measuring. A line is a two-number story (its tilt and its starting height). A wiggly curve of the ninth degree has ten adjustable numbers, and it can pass exactly through all ten points. On the data you already have, the wiggly curve looks perfect. But it has bent itself around the wobbles as well as the pattern, so its predictions for the eleventh measurement are often wild. This is called overfitting. The line, which "explains less", frequently predicts more.

That's the deeper reason for the razor. Extra assumptions can always be tuned to fit what you've already seen. The risk is that they were fitted to the noise, and you pay for it when the next piece of evidence arrives.

Simple is a starting guess, not a verdict

A common misconception is that Occam's razor says "the simplest explanation is usually correct". As a slogan it is catchy, but it overstates the case. The razor says that, when fit is equal, simpler is the sensible first thing to check. It guides your order of investigation. It does not settle the matter.

Notice what a good response to the kitchen puzzle looks like. You don't announce that the switch has tripped. You walk to the switchboard and look, which is a cheap test. If the switch is down, you flip it back and the appliances may wake up. If the switch is fine and the microwave works at another point, the one-cause story has failed, and you move to the next story without embarrassment.

There is also a twist worth keeping. Suppose the switch had tripped. That's still not the whole truth, because something made it trip. A fault inside the fridge could have caused it, in which case the fridge really is the problem and the other two appliances are innocent. The simple story was a good first step and an incomplete final answer. This is normal. A simple explanation usually opens the next question instead of closing the last one.

When the world really is complicated

The razor has honest limits, and history shows a few.

Take Copernicus. In 1543 he published a sun-centred model of the planets. The usual telling says it won because it was simpler than the old earth-centred scheme. The truth is more mixed. He kept the old device of circles riding on circles (epicycles), so his picture wasn't the tidy clean-up that later textbooks suggest, and what counted as "simpler" was itself arguable. A clearer simplicity came later, when Johannes Kepler (his Astronomia nova appeared in 1609) showed that planetary paths are ellipses. Simplicity existed in that story, but it arrived by degrees, and people disagreed about where it lay.

Another case is the planet Neptune. In the 1840s astronomers saw that Uranus wandered slightly from its predicted path. One option was to alter Newton's law of gravity. The other was to add something new: an unseen planet. By a plain count of new entities, the razor might have favoured changing the law. But Urbain Le Verrier calculated where such a planet should be, and in 1846 astronomers at Berlin found Neptune near that position. A similar puzzle in the orbit of Mercury suggested another hidden planet, which was never found. That one was settled only when Einstein's general relativity changed the law itself, in the 1910s. The same style of reasoning gave opposite answers, and no one could have told in advance which was which. "Which is simpler?" was not an easy question to answer, and the razor couldn't settle it.

Biology offers a gentler version of the lesson. Living things are shaped by long histories of small, untidy changes, and what exists is not always the neatest design. When something in nature has many interacting causes, the simple story may simply be wrong. Weather, bodies and ecosystems tend to humble anyone who expects the answer to be short.

A small habit worth keeping

If you'd like to use the razor, here is a version that worked for me in ordinary life, and I'd call it a habit rather than a rule:

1. List the stories that fit everything you've noticed.
2. Count what each story needs to be true at the same time, and whether those things are likely to come together by chance.
3. Start with the story needing fewer coincidences, and design a cheap test for it.
4. Let the test overrule your taste. If the simple story fails, drop it kindly and carry on.

Mistakes in this are normal. I've often grabbed a favourite explanation first and been wrong, and nothing terrible has followed beyond a slightly longer evening.

A question I'm still turning over

The razor seems to work best when we can count assumptions and say how likely each one is. In the kitchen that is possible. In many parts of life it isn't. What counts as "one assumption" depends on how you describe the problem, and two careful people can carve it up differently. Is a hidden planet one extra thing or a very large one? Is a changed law one small change or a sweeping one?

I don't have a tidy answer, and I'm not convinced anyone does. It makes me wonder whether simplicity is a property of the world, of our descriptions of it, or of how much our minds can hold at once. When the next small mystery turns up in your house, it might be worth noticing which of those feels true to you.