Dear Eckhard,
It seems each year you get better, and recall that I very much liked your essay last year.
I have glanced at many essays and have read yours twice, but it is so full of information I'm sure I have not digested all of your thoughts.
I would like to make a few observations. There many essays here that complain about the fact that a number of individuals have great wealth. While I am not a fan of bankers (who probably have the most wealth,) nor of children who inherit great wealth, Nobel illustrates a case where great wealth can be used very effectively to accomplish a purpose. As I noted in my essay, many billionaires are now supporting science, some are developing private space travel, some address health and education. What all have in common, in my opinion, is that they invest their own money much more effectively than governments spend tax monies. I would like to see more Nobels and fewer taxmen. If wealth is earned by solving problems or inventing solutions that people wish to buy I have no problem with it. Unfortunately corporations and governments "scratch each other's backs" and here corruption enters the picture. Anyway, I like your focus on Nobel.
Your insight into mathematics is applied well at analyzing Nobel's decision not to award a prize for math. In fact, as I was reading your essay, I realized that I really don't pay much attention to arguments about infinity as all infinities are mathematical objects, that is figments of imagination. There is no infinity in the physical world. There is continuity. Once the concept of infinity has been used to "justify" calculus and the limits of sequences, and used to derive Fourier theory, that pretty much satisfies my interest in infinity. I found your treatment of irrational numbers as only implicitly represented by an instruction interesting also.
My early math education followed the peak of Bourbaki power, and ruined much for me. I am naturally of the Heaviside or Feynman view of math, as a fluid, intuitive tool works to elucidate relations. But my teachers had been so heavily influenced by Bourbakis that I absorbed an attitude that perfect rigor was demanded. It is not! Certainly not for physicists.
I very much agree that speculative and formalist tenets are not directly relevant to reality. In fact, that is the problem with much (most?) of today's theoretical physics. Your remark on 'fans of Plato' is very apt. And your reminder that "abstraction is not a lossless process."
I also agree about Galilean transformations, and that relativity enters the picture with two observers in frames in relative motion connected only by a finite speed of light. And that "considering reality equal to that subjective perception denies the well confirmed causal coherence of the world."
I also appreciate "most basic entities don't change their sign"! Very nice. And "kinetic energy has nonarbitrary zero".
Eckhard, it was a joy to read your insight-filled essay. Thank you for writing it. I hope you find mine interesting.
Edwin Eugene Klingman
