Math Mojo - Making Math Meaningful

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Professor Homunculus' answer:

Great question! It gives us a chance to explore what math really is and what it isn't.

First the "isn't." Math is not a "reality." It did not come down from the mountain on tablets written by God or anything. It isn't something you can point to and say, "Look, there goes a two. There goes another two! They are making a four!"

Math is simply a description of a reality. A great author once called math, "The grammar of size, shape, and order." It describes the things we see, and tells us those things about them.

It is, in that way, like any other language. "Chair" for example, is just a word. You can point to something and call it a chair, but someone in Germany might call it a "Stuhl." It is still the same thing. The reality of the object is the same. You can still sit on the thing, but "Chair," and "Stuhl" are just names we gave them. The reason we choose the word "chair" might have a linguistic reason, but that reason has nothing to do with the object itself. The object doesn't know what we call it, and it doesn't care. If we had no word for it, it would still exist
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The reason we name things is so we can communicate with other people, and make remarks about reality. So, as a society, we agree to accept certain names for the things and actions which happen around us. Each culture accepts the same names for the same things, and then they can talk about them.
So far it makes sense, right?

Numbers are the same. Numbers are just names for things that happen. For example, if you hold out two fingers, and then hold out two more, something happens. There is a certain amount of fingers out, and it is the same amount every time. So we give that amount a name. We call it "four." Germans call it "vier", people who come from Wales (not whales!) sometimes call it "pedwar," and I don't know what people from Burundi call it. But I think you get the Idea.

Eventually mankind figured out that if you have two of anything, and you get two more of anything, you always get the same amount of anythings. So they figured that the name the gave to the " two-plus-two-finger-problem" would work for anything. And it seems to, doesn't it?

Giving labels to things is one of the ways that humans make it easy to communicate with each other. It doesn't always work, because, as you know, "sometimes words have two meanings," (as Led Zeppelin has told us, in "Stairway to Heaven," the lyrics to which, by the way, did come down from on tablets).

You know that if you take the word, say, "Patriotism", it means 20 things to 10 different people. Remember, the words are not the things themselves, just descriptions, which can be more or less accurate.

Luckily, in math, the rules (or the grammar) is so clear, that we usually don't have problems understanding what is meant - if we understand the grammar. And when we do, we tend to settle the arguments by logic and understanding, rather than terror or sabre-rattling.

So, in times of stress, you can actually take comfort in arms of a well-defined, totally democratic system like math.

Hotcha!

Professor Homunculus

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