Take a circle, for instance. Is there any such thing? You might point to grapes, or the Earth itself, or the spots on a ladybug, or the geostationary orbit belt. Those are all roughly circular, I’ll admit, but they’re not actually circles. They don’t use (h-k)2 – (y-k)2 = r2 to guide their formation, nor does that equation describe them exactly. A circle is an ideal construct, a human simplification in a wild, complex world of infinite imprecision and variety.
The real world itself doesn’t use math. A ball doesn’t fall in a parabola because s = -16t2 + 32t + 128. In fact, any single thrown ball won’t follow that equation. That equation only works in a vacuum. On a perfectly spherical Earth. With no moon, sun, or planets. With a perfectly spherical ball. Even then, the throws will probably only average, approximately, to the motion described by the equation, because we can never perfectly know the quantum interactions of the underlying particles.
The extraordinary thing is that it works. It works so well that you may be scratching your head, wondering what word games I’m playing. Mathematics is so ingrained a part of our thinking that we take for granted that the universe follows its rules, forgetting that the rules are of our own devising. The human race has, over the course of centuries, not only noticed patterns in nature, but has invented ideal versions of those patterns that can be manipulated according to ideal rules. We then turn around and use our imaginary models to predict nature . . . and succeed in doing so, again and again.
It begs the question: which came first? Does the universe really have mathematics at its core, like a plaster sculpture on a wire frame? Or is its apparently predictable nature a fraud, just as likely to fail tomorrow as to succeed? If you’ve read this blog before, you know what I think: that the reason mathematics is successful is because the world declares the character of its Creator. The universe is predictable, its basic nature changeless, because the God who made it is as reliable as the mathematics that describes his world.