Unreasonable Effectiveness

I've recently become a fan of Peter Leithart, thanks to the recommendation of my brother. I was perusing some old posts and came across this one on the comprehensibility of the universe. Of course I am always flattered to hear about "the unreasonable effectiveness" of mathematics.

It is a beautiful mystery, that mathematics, which is pure thought, can lead to advances in understanding the natural world. (This is dear to my heart, given that I study that's actually applicable to science and engineering.)

But on the other hand, I've heard it argued, with some merit, that there is no reason to think that we humans genuinely understand the world around us. The universe is "rational" only insofar as we force it to be, i.e. we subjectively interpret it as rational.

For instance, Newton came up with a beautiful model in his mind, and then applied it to the universe around him. The power of his model is that it really is so predictive and helps us to manipulate the world around us so effectively. Is it "correct"? Does it really enable us "to discern the inner structure and beauty of the physical universe?"

Obviously not, because Einstein supersedes Newton. But now that we have Einstein, do we now truly understand the universe? Well, why would it be any more so with Einstein than it was with Newton? Again, the power of Einstein is that his mental construct provides us with such excellent predictions of real-world phenomena.

I don't think that one can argue that of necessity humans developed intelligence that allows us such power over our surroundings. However, I do think it can be argued that power is all we're getting from our ability to do science. There is no guarantee that what we obtain in our theorizing is some direct understanding of the universe, as if we've truly unlocked its secrets.

Leithart ought to appreciate this, as there surely will always be some mystery in the universe.

I see mathematics as a creative act. It is almost as if, instead of discovering a system that already runs the world, we are actually building a system by which the world ought to be run. People might be surprised how often mathematicians say something like, "Morally speaking, this is the answer we're looking for." The idea is to look for what should be true, and then see if the universe obeys.

We are learning to have dominion over the world. Yet it cannot be an arbitrary or cruel dominion, because only by truly loving the material world can we master it. Any old scientific model will not do. It can only be one that truly captures the heart of reality.