Does math exist outside of the universe? I mean, if there were less than four atoms that existed, would 2 + 2 still equal 4? It would, because math is conceptual. It exists outside of, and independent of, the physical properties of the universe. Let’s think about it.
I laughed once when I read about a fellow who said: “I believe in positive numbers. I’m not sure if I believe in zero or not. I guess you could say I am agnostic about zero. I certainly don’t believe in negative numbers. And don’t even get me started on imaginary numbers!”
I can’t remember who said the quote above. It seems like a kind of a loopy thing to say, but the guy would have a point, if math depended entirely on the physical universe. “2” is a positive number. I can have two apples. But how could I ever have negative two apples? It doesn’t really make sense.
Still, we have many good uses for negative numbers; they express real-life situations. At NASA, if we are launching a rocket at 8:00, we have a countdown clock that starts before 8:00 with a negative number (“T minus” a certain value) and counts up to zero. Then when the rocket launches at 8:00, that clock then crosses over to positive territory and counts upward, becoming what we call a Mission Elapsed Time. Financial statements often record debts as negative numbers and assets as positive numbers. So at least we have some uses for negative numbers.
In Europe, mathematicians began using zero commonly around the 11th or 12th century A.D., though much of the population continued to use Roman numerals (which do not have a zero) into the 15th century. Using a zero makes math a lot easier, even if it’s just a representation for nothing.
So I think we can say that positive numbers, negative numbers and zero all have some kind of real representation in a natural universe. However, math can be extended far beyond what we see in the natural universe.
Currently, we have three-dimensional mathematical models that we use to predict the weather. They are three dimensional because we live within three dimensions. However, we could extend our mathematical models to model a four, five, or six dimensional world – or any number of dimensions. The math isn’t constrained by natural reality. There wouldn’t be any way to check our six-dimensional model against real-world weather to see how accurate it is, but there’s nothing preventing us from developing a model.
We can use math to design things, producing things which may not even be present anywhere in nature, yet are still beautiful. Fractals are an example.
Math is a product of the mind. But it is not the product of a human mind. Human minds can discover mathematical laws, and if different people discover the same thing, they may use different terminology, but the laws remain the same. So if math is a product of the mind, but not the human mind, whose is the mind that came up with math? Math came from the mind that is outside the universe – the mind of God.
So if math originates from outside of the universe, here is a very strange fact: the universe obeys mathematical laws. Why should the universe obey laws that are not part of the universe? And yet it does. The force due to gravity is the gravitational constant times the mass of an object divided by the distance between the objects squared. That’s a law, and all bodies in the universe were obeying that law long before we discovered it. The reason the universe obeys mathematical laws is that the mind that created the mathematical laws was the same mind that created the universe – the mind of God.
Perhaps the reader may be thinking about an objection to this argument about reason and math – an objection based on computers. Computers do math, and they reason (or at least appear to), but computers don’t get that ability from anything outside the universe. There is nothing extra-natural about a computer. This is a serious objection and I will deal with it in the next chapter.
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