jgardn's Journal: Numbers Aren't Real

I am drawn back to this concept again and again as I encounter the application of physics, math, and science in reality.

The concept is pretty fundamental to understanding exactly what correlation math and reality have with each other. That correlation can be summed up as follows.

Mathematics applies to reality inasmuch as it correctly describes reality.

That's a pretty basic statement. But it has a deep meaning.

For instance, what does "1+1=2" have to do with anything? The answer is nothing at all.

But what does "1+1=2" mean when the 1 represents 1 apple, and the 2 represents 2 of them? It means what you have been taught it to mean. If you take a group of 1 apple, and combine it with another similar group, you get a group of 2 apples.

So we see that this mysterious behavior of numbers we name "addition" has a correlation with reality.

Now, numbers themselves have no meaning. They are as meaningful as letters, blotches of ink, or scribblings on the corner of the paper. It is only when they are used to represent things, or symbolize something, that they become meaningful. It is at this point that the mathematical properties of the numbers have meaning as well.

This is why something like "irrational numbers" are really pretty rational. This is why something like "imaginary numbers" are befitting of reality as "real numbers" are. They are numbers that do indeed correspond with reality if applied correctly. The behavior of these numbers reflect the behavior of reality.

I am amazed at how far we have progressed as a society. We live out our lives with numbers on a piece of paper representing our worth. We buy and sell things by adding and subtracting numbers. We make predictions with numbers as our guide, and entire nations are built and prosper on mere theory.

We live in a world that only makes sense when we abstract it out into a bunch of symbols that live most unnatural lives. Reality is subdued by the imaginary.

Nowhere is this best demonstrated than in the industry of software development. We move numbers about and talk about them as if they were real. We make fortunes on making our numbers dance better and faster than someone else's. And we live as kings because we can see farther than the average man, and delve deeper into the maze of the imaginary than they can imagine.

We are real people, living imaginary lives. And somehow, it all works out in the end.