# The unreasonable effectiveness of math vs evolution

A friend draws attention to an old paper, “The Unreasonable Effectiveness of Mathematics vs. Evolution” (The American Mathematical Monthly Volume 87 Number 2 February 1980) by R. W. Hamming:

If you recall that modern science is only about 400 years old, and that there have been from 3 to 5 generations per century, then there have been at most 20 generations since Newton and Galileo. If you pick 4,000 years for the age of science, generally, then you get an upper bound of 200 generations. Considering the effects of evolution we are looking for via selection of small chance variations, it does not seem to me that evolution can explain more than a small part of the unreasonable effectiveness of mathematics.

Conclusion. From all of this I am forced to conclude both that mathematics is unreasonably effective and that all of the explanations I have given when added together simply are not enough to explain what I set out to account for. I think that we-meaning you, mainly-must continue to try to explain why the logical side of science-meaning mathematics, mainly-is the proper tool for exploring the universe as we perceive it at present. I suspect that my explanations are hardly as good as those of the early Greeks, who said for the material side of the question that the nature of the universe is earth, fire, water, and air. The logical side of the nature of the universe requires further exploration. More.

One sign of Darwinism’s hold on the imagination is that these subjects are never honestly discussed. Rather, most of the academic herd is quieted and difficult animals are threatened.

We are told both that we did not evolve so as to understand reality and that we ought to regard science as a sort of candle in the dark. This won’t work and few dare to think beyond it.

Is celeb number pi “normal”? No. If it were, it wouldn’t be a celeb. It would be down there with 318.

and

Absolute zero proven mathematically impossible?

## 3 Replies to “The unreasonable effectiveness of math vs evolution”

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kairosfocus says:

News, I suspect this is the Richard Hamming of Hamming distance, digital signal processing, digital filters and more. A good name, well worth reading if that is so. I just put in, Mathematics is perhaps best understood as the logic of structure and quantity. That then refocuses: why is the world so utterly rational in its ways, especially as reduced to structure and quantity? And BTW, I am loving a PL-380 that uses a DSP chip to calculate the audio from radio signals. I esp. love how this little more than palm-sized wonder snatches faint signals out of the ether and by calculation reaps the audio. KF

PS: A great FFT clip:

Our main tool for carrying out the long chains of tight reasoning required by science is mathematics. Indeed, mathematics might be defined as being the mental tool designed for this purpose. Many people through the ages have asked the question I am effectively asking in the title, “Why is mathematics so unreasonably effective?” In asking this we are merely looking more at the logical side and less at the material side of what the universe is and how it works.

Mathematicians working in the foundations of mathematics are concerned mainly with the self-consistency and limitations of the system. They seem not to concern themselves with why the world apparently admits of a logical explanation. In a sense I am in the position of the early Greek philosophers who wondered about the material side, and my answers on the logical side are probably not much better than theirs were in their time. But we must begin somewhere and sometime to explain the phenomenon that the world seems to be organized in a logical pattern that parallels much of mathematics, that mathematics is the language of science and engineering.

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kairosfocus says:

PPS: Yep, it is him — I have a copy of his Digital filters sitting on my shelves. He has a food for thought provoker here:

Let us next consider Galileo. Not too long ago I was trying to put myself in Galileo’s shoes, as it were, so that I might feel how he came to discover the law of falling bodies. I try to do this kind of thing so that I can learn to think like the masters did-I deliberately try to think as they might have done.

Well, Galileo was a well-educated man and a master of scholastic arguments. He well knew how to argue the number of angels on the head of a pin, how to argue both sides of any question. He was trained in these arts far better than any of us these days. I picture him sitting one day with a light and a heavy ball, one in each hand, and tossing them gently. He says, hefting them, “It is obvious to anyone that heavy objects fall faster than light ones-and, anyway, Aristotle says so.” “But suppose,” he says to himself, having that kind of a mind, “that in falling the body broke into two pieces. Of course the two pieces would immediately slow down to their appropriate speeds. But suppose further that one piece happened to touch the other one. Would they now be one piece and both speed up? Suppose I tied the two pieces together. How tightly must I do it to make them one piece? A light string? A rope? Glue? When are two pieces one?”

The more he thought about it-and the more you think about it-the more unreasonable becomes the question of when two bodies are one. There is simply no reasonable answer to the question of how a body knows how heavy it is-if it is one piece, or two, or many. Since falling bodies do something, the only possible thing is that they all fall at the same speed-unless interfered with by other forces. There’s nothing else they can do. He may have later made some experiments, but I strongly suspect that something like what I imagined actually happened. I later found a similar story in a book by Polya [7. G. Polya, Mathematical Methods in Science, MAA, 1963, pp. 83-85.]. Galileo found his law not by experimenting but by simple, plain thinking, by scholastic reasoning.

I know that the textbooks often present the falling body law as an experimental observation; I am claiming that it is a logical law, a consequence of how we tend to think . . .

That points to the factual adequacy, coherence, explanatory power triple test . . .

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abdga64 says:

Good morning,
First time commenter – it appears that the title of Hamming’s paper is incorrectly named at the start of this article. Intentional to foster discussion or unintentional? Thanks.