## Learnability

You sometimes hear people say that syntax is not important. Not true: syntax is one of the most important things there is. (Maybe what they really mean is that their syntax is better than yours...) They probably refer to the fact that there are multiple ways to write down the same model. That is true, but it by no means follows that all ways are equivalent. It is a philosophical debate whether a person's language determines his mental model of the world or whether the language is merely the surface structure of a deeper model that is essentially the same for everybody. For human languages we leave the debate to others, but for our formal, limited languages we must follow the advice from mathematics: there is nothing like a suggestive notation for understanding the model.

The standard example from mathematics is dt/dx, which looks like (and is treated by physicists as) an infinitesimal change of t divided by an infinitesimal change of x. Mathematicians can tell you exactly in what ways it behaves like a division and it what ways it doesn't, but the fact is that for nearly all formulas that occur in physics it does behave like a division. And it makes life very easy for physicist that they can simplify (dx/dt)(dt/dy) to dx/dy. It is easy because it looks the same as simplifying (2/3)(3/7) to 2/7. The notation for differential equations hasn't always been like that, but it is not for nothing that all other notations are forgotten.

Learnability, then, has a lot to do with readability.