Math is as Arbitrary as Language

As an interesting exercise, try and think of all the mathematical concepts that can be derived from themselves, or first principles. Go ahead, I can wait.

If you came up with anything besides arithmetic, you're wrong. Anything that involves measurements of any kind are arbitrary. Which means, to a certain extent, physics and chemistry are arbitrary.

Now, what I mean by arbitrary is this: the numbers do not have to be what they are. Take Density as an example. Density, if I remember correctly, is mass divided by volume. Now, take mass. It is an arbitrary principle. What makes a gram a gram other than what people have decided it was. Take volume. What is volume but a liter but a meter to the third? And what is a meter? Another arbitrary principle.

For language, it's the same thing. What sound does an A make? Why? Why is a B the shape that it is?

But for all the arbitrariness of both math and language, so much is built upon it. Math has given us physics which has given us so many things. Entire theorems are based around what could have been completely different and language shows what could have been. Each language is based on arbitrary, yet universal, components and from there and entire way to communicate is created.

Think of it in an interesting way. The math for an alien planet could, and probably would be, completely different from our math, but the principles would be exactly the same. The only difference would be the symbols and measurements used. It's the exact same thing with language. Spanish and English are radically different but each shares prepositions, clauses, nouns, adjectives, etc.

I'm not really sure what the point of this post was. One point is to get people to understand how arbitrary everything in our lives really is. Another is to show that while it's arbitrary there are still universal things.