Dick, perhaps you can enlighten me on this.
People marvel at the way we can use math to model reality but I'm not too excited about it as I'm not sure it's simply a matter of our time scale. Let me clarify. To take that simplest case, 1 + 1 = 2 is a mathematical truth. It is truth simply because we say so, and we consider it an eternal (metaphysical?) truth because again simply because we define it so. Nothing to be amazed at.
Now comes the interesting part. Our 1+1 truth, which is truth by convention, seems to apply to the world. We take one apple plus one apple and we get two apples all the time. You can never get something other than two apples when you add, well, two apples. The real magic in the universe is that it is perfectly logical, that is the only reason our mathematical conventions can be successfully used to describe reality.
But, wait a minute. One apple plus one apple does not always equals two apples. Leave the apples unattended for a few years and see what happens: one apple plus one apple = zero apples! OK, so it's only a matter of applying math "the right way". The apples are gone but all their constituent atoms are still out there in the world. The validity of logic is preserved. Or is it? Aren't we simply shifting the logical inconsistency to a time scale where it can't be invalidated, in other words, restricting the amount of data so that it conforms to our theory? I'm not sure what modern physics says about it but my understanding is that particles are not logical at all, that is, 1+1=2 does not apply.
I guess my point is that logico-mathematical descriptions of the universe only apply to specific time spans, and the time spans are arbitrarily chosen by us to make the models work, and given a large enough time span all models eventually break. So there's no reason for jubilation at our ability to explain the universe using mathematical models, we are only explaining a very small portion of it, the portion of space and time in which we live.
Does that make sense? |