November 26, 2008

Mathematics, Physics and Philosophy

Posted by Urs Schreiber

For some purpose I was asked to formulate what motivates for me interdisciplinary research at the border of mathematics, physics and philosophy. Here is something that I have come up with today:

Motivation für interdisziplinäre Arbei im Grenzbereich von
Mathematik, Physik und Philosophie
(pdf, 5 pages)

Sorry that it’s in German. After I have slept over this and become more convinced by the form of the text I might produce a translation.

Posted at November 26, 2008 4:57 PM UTC

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Re: Mathematics, Physics and Philosophy

A translation would be very much appreciated if possible.

Posted by: Daniel da Silva on November 29, 2008 9:26 AM | Permalink | Reply to this

Re: Mathematics, Physics and Philosophy

I would be interested in reading the English version as well. Please take your time and let us know when it is available.

Posted by: st on December 4, 2008 6:53 PM | Permalink | Reply to this

Re: Mathematics, Physics and Philosophy

Thanks for your messages.

I don’t find the time for making a translation right now, but I will consider doing it later, maybe over the Christmas holidays.

Posted by: Urs Schreiber on December 4, 2008 11:44 PM | Permalink | Reply to this

Re: Mathematics, Physics and Philosophy

While we’re waiting we can try Google’s best effort.

Posted by: David Corfield on December 5, 2008 1:08 PM | Permalink | Reply to this

Re: Mathematics, Physics and Philosophy

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!

Posted by: Urs Schreiber on December 5, 2008 3:08 PM | Permalink | Reply to this

Re: Mathematics, Physics and Philosophy

Have you read Shahn Majid’s philosophy of physics - On the nature of physics?

Posted by: David Corfield on December 11, 2008 1:10 PM | Permalink | Reply to this

Magid, Zwicky, Discover; Re: Mathematics, Physics and Philosophy

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?

Posted by: Jonathan Vos Post on December 13, 2008 5:30 PM | Permalink | Reply to this

Re: Magid, Zwicky, Discover; Re: Mathematics, Physics and Philosophy

The culprit is known as the establishment’ but also as perceived wisdom’ or the prevailing paradigm’.

A biologist friend told me of an example where the problem was not witht he master but with the disciples: the master gave 5 alternative hypotheses for a certain biological phenom. #1 became the perceived wisdom’ without any further experiments

cf. biochemistry explains all

Posted by: jim stasheff on December 14, 2008 1:34 PM | Permalink | Reply to this

Biochem and Humanity At The Edge of Chaos; Re: Magid, Zwicky, Discover; Re: Mathematics, Physics and Philosophy

Jim Stasheff puts forth a fascinating metaphysical position with: “biochemistry explains all.”

To be sure, we humans think mostly with our brains (though 1% as many neurons are in our gut, hence my current research on 8 types of dynamics in robustly modeled peristalsis), which (microneuroanatomically) in turn function by biochemical processes whose physiology we are more deeply understanding. Hence our view of the Platonic universe of pure Mathematics, and of the physical cosmos, is influenced by the laws of Biochemistry.

The argument can be made, as Jim hints, that there is a hierarchy of sciences, with Biochem as the root.

Since my PhD research was on the dynamics of the metabolism, and used some cute Math, such as the Krohn-Rhodes decomposition of the semigroup of differential operators of the Michalis-Menten equations, I made these related arguments starting in 1975 (the terminology slightly updated to contemporary usage):

(1) We evolved by what is modeled as The Genetic Algorithm, and an equivalent algorithm determines the changes over time of the population of thoughts in our brains; hence there is a multi-level (hence n-Category!) model of the dynamics of thought, organism, population of humans, ecosystem.

(2) We evolved At The Edge of Chaos; our metabolism operates At The Edge of Chaos; our brains operate At The Edge of Chaos; and hence we are able to perceive and manipulate the chaotic cosmos.

Posted by: Jonathan Vos Post on December 14, 2008 5:06 PM | Permalink | Reply to this

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