Jerry Coyne posted this video at his blog:

Presumably Coyne was making a point about alternative truths. The video clip is quite exaggerated. I don’t expect anything like that to actually happen. But, of course, exaggeration is often a good way of making a point.

However, I see the video as also making a very different point. And that’s what this post is about.

**Mathematics as culture**

To be a mathematician is to be a member of a culture. To do mathematics, is to follow the conventions of that mathematics culture.

That 2+2 = 4 is a convention within the mathematics culture. It has been argued that mathematics is entirely a matter of convention (or cultural practices). Quine argues against that in his paper “Truth by Convention”, which I suppose I should discuss some day.

So yes, you could have an alternative-math culture where the convention is that 2+2 = 22. You would not be able to use alternative-math in the same way that you use standard math. In alternative-math, addition would not be connected with counting unless you also came up with an alternative form of counting.

We follow the conventions of standard mathematics, because they have proved very useful. The conventions themselves were developed for their usefulness. So the conventions of mathematics are not random. They are chosen for their usefulness. I very much doubt that alternative-math could be developed into as useful a system of conventions. But, strictly speaking, I am only guessing when I say that.

**Conventions are important**

The take away from this should be to recognize the importance of social conventions. Our traffic laws are conventions. The rules of baseball are conventions. Our banking systems depend on conventions. Our markets (stock markets, food markets, etc) all follow social conventions that have been honed over many years.

The importance of social conventions has, I think, been under appreciated.