The Unreasonable Success of Physics (and Math(s))

What do people think of the “unreasonable success” arguments as prima facie evidence? I find them more compelling, on a relative scale, than cosmological fine tuning. Here is what I think, FWIW, taken from an old blog post of mine:

Interesting quote from Feynman:

What is it about nature that lets this happen, that it is possible to guess from one part what the rest is going to do? That is an unscientific question: I do not know how to answer it, and therefore I am going to give an unscientific answer. I think it is because nature has a simplicity and therefore a great beauty. Richard Feynman, “Seeking New Laws,” pp. 143-167, in Richard Feynman, The Character of Physical Law, New York: Modern Library, 1994. Quote is from p. 167.

At the risk of quote-mining, since I don’t have the book, this appears to be Feynman’s version of Wigner’s famous Unreasonable Effectiveness of Mathematics argument. Wigner wrote:

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. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

Both Feynmann and Wigner, in my reading, conclude that science can never answer the question as to why science and mathematics work as well as they do.

If you consider all the talking points in ID–irreducible complexity, privileged planet, cosmological fine-tuning–some of which I find useless (irreducible complexity) and some of which I find interesting (the apparent sensitivity of life to the values of constants) no one observation from the world of science or mathematics has ever struck me as a more powerful apologetic than Feynman’s and Wigner’s point.

The world is not only governed by orderly laws, but those laws are expressible in simple enough terms that we can make sense out of them and use them to make astonishingly accurate predictions. As Feynman suggested, if I read him correctly, science can never explain why this is so. It is, in fact, unreasonable that this happens.

I often think of it this way. The dawn of modern science arrives with Newton. Newton’s Second Law is a simple linear differential equation. (Probably trivial is a better word–speaking not of Newton’s insight–which was genius–but of the degree of difficulty of his equation.) One can only speculate in a What if Eleanor Roosevelt could fly? manner what would have happened if Newton’s Second Law had been a complicated nonlinear differential equation (or even a simple nonlinear differential equation)–but it is not far-fetched to argue that science would have been stillborn.

I appreciated this post very much. I would like to read what others think of it.

Frankly, I disagree that “science would have been stillborn”. But I do think that it would have been significantly delayed with a much different history.

It is an interesting thought experiment, but runs into difficulty before one can get too far. That acceleration is directly proportional to force and inversely proportional to mass seems very intuitive to us now, and if it wasn’t so then all of classical physics as we know it is radically different and probably in very complicated ways if the linear relationship even just became quadratic. Planetary orbits couldn’t even work as they now do (since all non-circular orbits involve changing accelerations).

But the strange thing is that in a sense this really happened. Relativity did overturn any “last word” status that Newtonian mechanics had, even if that doesn’t impinge directly on our daily experiences with object motion. So with relativity and QM the physical world really has taken bizarre turns in terms of ultimate understandings.

Yes! It is rather mind-bungling to consider the what-ifs.

Of course, your OP took me into immediate reflection on how the calculus got started and Newton’s (and Liebnitz’s) wrestling with the concept of mathematical limits. Thinking about thin rectangles was a brilliant way to approach it. I have often wondered if I would have ever thought of that solution had I lived in those days.

Your original post also brought to mind my second year economics course where I suddenly realized that the same differential calculus which I had applied to physics problems in high school suddenly provided answers to a demand-curve problem in microeconomics. I felt encouraged that my years of education had finally started to see a “cross-integration” of fields in fundamental ways. It seemed to link the entire universe together in my mind.