The n-Category Café

we can try Google’s best effort.

Now I really have to hurry up, lest I’ll leave you all wondering about the guy “Rigo Roser” that appears on the second page…

He used to approach me and say:

Hey, I am Rigo Roser than you are!

Yes. Three points on my initial reaction to Magid’s paper.

(1) Mathematics, a sort of shorthand, is rich in ambiguity because of its brevity.
Mathematics is both a language (signs, rules for combining signs, rules for precedence of one sign over another, etcetera), and part of the content of that language (the mathematical ideas that can be expressed in the symbolism). What Chemists are interested in are the
Chemical concepts that can be expressed in Mathematics. What Biologists are interested in are the Biological concepts that can be expressed in Mathematics. What Experimental Physicists are interested in are the structures and patterns and changes in the experimental
data that can be expressed in Mathematics.
And, as S. Magid put it: “the goal of theoretical physics, at least in my opinion, is to arrive at our best understanding of the fundamental processes of nature. We use of course the language of mathematics, and most physicists (including me) would ideally like to find a single elegant theory powerful enough in principle to explain
all known phenomena. In practice it means our existing domains of understanding should be recovered as special limits.”

(2) The ‘=’ sign has at least four mutually exclusive meanings; identity,
equality, implication and correlation.” I’ve seen different shades of these meaning used in Geometry, where bad textbooks and bad teachers confuse equality and congruence. I’ve seen the sign used in Mathematical Logic and in the Electronic Engineering that embodies
Boolean Algebra to mean a specific relationship between input and output.
Failure to specify which means the equation is meaningless. Or at least depends on interpretation, and thus can lead to useless argument.

(3) Mathematics which has taken over a physical subject, such as Electromagnetic Theory, and gone where the Math is pretty but the experiments not in line with prediction, is deeply flawed.”
Magid: “The starting point is that Nature after all does not know or care what mathematics is already in textbooks. Therefore the quest for the ultimate theory may well entail, probably does entail, inventing entirely new mathematics in the process.” [hello, n-Category theorists!]
Americans can find on the newsstand right now the so-called January 2009 “Discover” magazine, a special issue on “100 Top Science Stories of 2008.” Interesting summaries and pictures of paradigms collapsing in some cases, and consolidating in others. There is also a spirited defense by his daughter of the late great Fritz Zwicky, inventor of
Dark Matter, gravitational lensing, neutron stars (partly), supernovas
(partly), carpooling (sort of). What’s of extra interest to me, who’d met and spoken with him, is how he was defamed, censored, marginalized by the Establishment figures he ridiculed. Including the late Jesse Greenstein, who was my Astronomy Mentor.
I’ve commented in this blog a number of times about Fritz Zwicky’s theory of the Ideocosm, the space of all possible ideas. Magid makes an interesting
philosophical question about the Mathematical portion of the Ideocosm:
“‘in the tableau of all mathematical concepts past present and future, is there some constrained surface or subset which is called physics?’ Is there an equation for physics itself as a subset of
mathematics?”
Experts can differ on this. Is Math part of Physics? Is Physics part of Math? Are they two different approaches, practiced by two different communities? These are what I’ve called differing
metaphysical stances.
In an ideal world of rational people, which does not exist, special attention would be paid to iconoclasts who make many correct predictions: Alfven, Tommy Gold, Zwicky. But the world is very very far from ideal, and these folks are mercilessly attacked. It takes decades for anyone in the Establishment to ask: was there something correct in what these people said and did?