Q&A: A Question About Human Mathematical Abilities
A Question About Human Mathematical Abilities
Question
In the book “Two Carts and a Hot-Air Balloon,” the Rabbi brings the parable of two synchronized clocks in the context of the fit between human beings and the world, and concludes that it is more reasonable to argue that there is a coordinating factor (=God) between the two clocks, as opposed to the accepted view that the mechanism of clock A (=the world) is what drives the mechanism of clock B (=the human being). In particular, the Rabbi refers to the human mathematical ability and argues that there is no reason for such an ability to exist, nor does it confer any survival advantage.
But is that really so? First, we do not have highly developed mathematical and physical intuitions. It is easy for us to think about only the most basic concepts, such as distance, shapes, speed, and acceleration, which we encounter in everyday life. With regard to such concepts, it is certainly understandable that there is a survival advantage. An animal that knows how to navigate in space, and knows how to decipher when various threats are approaching it, will survive better in the world, and this will continue to develop further through the process of natural selection.
The more advanced mathematical achievements, those farther removed from intuition, developed thanks to two factors: exceptional geniuses, whose brains can be seen as a kind of mutation that includes a refinement of the basic abilities mentioned above, and a collective effort—the contributions of many people (geniuses and simply wise people) accumulated over hundreds of years, step by step. Each step contains a bit of basic intuition, but taken together it is already very far from the basic intuitions.
Beyond that, we grasp (or succeed) only in areas where there truly is human potential to decipher the world. It may be that there are billions of other topics, or laws of nature, that we have no ability to perceive, and never will perceive them either.
Some claim that quantum mechanics lies exactly on that boundary. It is at the very edge of our intuitions, and indeed there there is almost no fit between the “clocks.” And there is no need for there to be, because that is already far removed from the basic concepts that provide a survival advantage.
So it turns out that evolution does indeed explain mathematical ability, and the simpler and more reasonable origin for the fit between the “clocks” lies in it—so what need is there for a coordinating factor?
Answer
Everything you said is a set of possible suggestions that, in my view, are no different from evolution itself. Basically, you just explained evolution in a nutshell. So I have nothing to say about them beyond what I said about evolution itself. For example, evolution itself became known to us as a result of our scientific abilities. Therefore it is hard to see it as a justification for our trust in those abilities. Moreover, evolution itself is a result of the laws of nature (without them it would not exist), and that itself proves the existence of the coordinating/planning factor (what I later called “the argument from the laws”).
Discussion on Answer
I explained all this both in the book and in the third booklet. I explained there why this is not ordinary skepticism. The claim that a random system produces a reliable result is difficult on its face, and doubting it is a reasonable conclusion. Exactly like Russell’s celestial teapot. Ordinary skepticism is casting doubt without any real basis, just from a generic “who told you so?” question.
Giving trust as a psychological phenomenon is clear. We were created in such a way that we have trust. And in general, facts do not require an essential explanation. That is the nature of the world, period. I’m not talking about that, but about granting trust on the cognitive level (that is, deciding that this trust is justified). I have a tendency to speak slander. Does that justify speaking it? The fact that I have some psychological tendency does not mean it is justified. Cognitively, it is supposed to pass through my filter.
Of course, someone who does not accept this, but is a determinist and a materialist, is not bothered by it, because he indeed does not grant trust and does not decide anything. He merely computes things. See also column 35 on intelligence.
Why isn’t it enough to say that we trust what proves itself? One can say (as I think you write) that this is a second-order induction question, but doesn’t the very raising of this question resemble excessive skepticism (which you attack in your “analytic” opponents)? Why does a cat trust its senses? Because of evolution / the laws of nature. Any further engagement beyond that does not lead to meaningful discussions or conclusions. I also don’t understand the question about the laws of nature. Things are the way they are because that’s how they are. The very question “why are they like this” already presupposes that there is an intelligent factor, so there is a logical fallacy here. If things developed randomly, then questions about trust in the senses and about a reason for the laws of nature have no meaning at all.