Occam's Razor

Occam's Razor

This is a problem-solving principle attributed to the 13th Century theologian William of Ockham. The principle can be stated thus:

Among competing hypotheses, the one with the fewest assumptions should be selected.

It can also be written as two principles:

The Principle of Plurality - Plurality should not be posited without necessity

The Principle of Parsimony - It is pointless to do with more what is done with less

Occam’s razor means one doesn't add wasteful things to an explanation.  If you have a few hypotheses that could explain an observation, it is usually best to start with the simplest one.  Note that Occam's razor is not a law, but a rule of thumb, used to guide research down the easiest course.

In physics and mathematics,  what's important is the simplicity of equations, not the simplicity of the solutions. Currently it is possible to describe the physical world using two equations. That's parsimony. (One equation would be even better!)

Example 1

The turbulent flow of water can be described by the Navier-Stokes equations.  These are very simple. But the solutions of those equations for say, Niagara Falls, is extremely complicated. 

Example 2

Imagine I leave a saucer of milk outside overnight, and in the morning the milk has gone. No one saw what happened to the milk. Let's consider two possibilities:

1. The neighbour's cat drank it

or

2. Loki the god of mischief made the milk disappear.

Occam tells us to reject option 2, not because it refers to Loki, but because it requires the introduction of an entity that might not exist. There is a plausible explanation that requires only existing entities (the cat next door, which is a fact). Both solutions are equally simple but the Loki hypothesis includes an entity that is not necessary (and hence contravenes the principle of plurality). However - it could have been Loki - it's impossible to prove it wasn't (unless we used CCTV to monitor the milk overnight. But even then, maybe Loki was disguised as a cat).

Example 3

There are conspiracy theories surrounding the NASA moon landings where some people argue that the Moon Landings were filmed in a studio, as part of an elaborate hoax. But the conspiracy theories contain hundreds of suppositions, requiring millions of people to tell lies or hide the truth.  There are hundreds of "ifs".  The NASA argument on the other hand, is straightforward. That doesn't mean it's true, but it is more likely to be correct.

Example 4

Ptolemy's epicycle model of the solar system included multiple/ elements, and every time an observation didn't fit the model, more elements were added. This was replaced by a much simpler theory (the earth is not the centre of the solar system but rather, the planets orbit the sun) which explained the same facts as Ptolemy's model.