The Unreasonable Effectiveness of the Human Brain

Eugene Wigner famously wrote about "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."

Though he was indeed speaking about two miracles

"[...] the two miracles of the existence of laws of nature and of the human mind's capacity to divine them."

And while a lot has been said and written about the fact that the laws of nature seem to be formulated in the language of mathematics, I always found the larger miracle to be that we simple humans are able to grasp these laws, to write them down, and to use this knowledge to shape Nature according to our liking. As far as mathemetics is concerned, if it wasn't unreasonably effective to that end would we be wondering about it? If mathematics wasn't good to describe the real world it would just be a bizarre form of art with a nerdy cult. The actual question is why is there anything so unreasonably effective that the human brain can comprehend. Understanding, say, cosmological perturbation theory or the representations of Lie Groups isn't such a large survival advantage. (And then there's those who claim we just do it all for the sake of reproduction, obviously.)

Let me highlight two extreme points of view one can take on our ability to describe Nature. Max Tegmark's hypothesis of the "Mathematical Universe" puts forward the idea that mathematics is really all there is, claiming that mathematics is the only thing that is ultimately "free of human baggage". And if we find that counterintuitive or disturbing, that's because our brains didn't evolve to understand the fundamental nature of reality. In fact, according to Tegmark, we should be disturbed if we did not find the fundamental description of reality puzzling.

I wrote previously that though the hypothesis can of course stand as such, the justification Tegmark gives is either empty or logically faulty. If one defines what is free of human baggage to be mathematics, then it's an empty statement, thus let's not go there. Without that, we don't know - we can't know - whether mathematics is the only language free of human baggage. It remains possible there exists an even more fundamental language that relates to today's math in a way that today's math relates to narrative. And no, I can't tell you what that would be. But then, our brains didn't evolve to understand...

I actually think Tegmark isn't quite consistent on that point. One the one hand he is defending his hypothesis by saying fundamental reality should seem bizarre to our human brains that evolved to hunt bears, but then the idea that there's something more fundamental than math is too bizarre for him. Do you think 50000 years ago when humans had just begun to use spoken language and to scratch pictures into stones, many of them would have been sympathetic to the idea there's something more powerful than these ingenious achievements of the human mind that allowed them to communicate relations between things without actually pointing at them, and even talk about things that they might have entirely invented?

Now let's look at it from the completely other perspective. A lot of theoretical physicists like to talk about "naturalness," "elegance" or "beauty" of a theory or an equation. These are arguably human judgements and often perceptions that are considerd very important. It is also interesting that, given the required educational background, most people tend to agree on these terms (modulo a deliberate or opportunistic self-deception that financial or peer pressure can create). Whether it is reasonable or not, they do implicitly assume that the human brain has a sense about Nature's ways and that their intuitions will lead them a way to success.

I'm not sure why that would be except possibly that after all our brains are made of the same stuff as elementary matter and we are part of the universe we aim to describe and in constant interaction with it. What we are trying to do is to create an accurate image of the universe in our brains, an imperfect repetition of a structure within a structure of that system. Then the question we arrive at is why does the universe evolve to create subsystems that to increasing accuracy mirror the properties of the system? (And, can you continue this self-similarity both up- and downwards?)

Well, needless to say, I can't give you an answer for why the human brain is so unreasonably effective in understanding the laws of Nature. And indeed, spending most of my time between people who believe they have the key to understanding the universe, I sometimes wonder whether our ambitions will continue to deliver insights or whether we'll eventually reach the limits of what we can comprehend, endlessly fooling ourselves into believing we're getting closer to unraveling the fundamentals. But in any case, we're far from reaching that limit. Give it another 50000 years or so.