Tackling John Baez Head-On

>>From Osher Doctorow mdoctorow@xxxxxxxxxxx

Since John Baez didn't put my criticism of his last post into
sci.physics.research where his post originated, I'm going to tackle his
posts head on here. You can find my criticism of his last post other
than the one(s) mentioned below somewhere in the sci.physics backlog.
Basically, I attacked his usual algebraic orientation. In my view,
algebra has too much "data" ("facts") and too little theory for
mathematics intuition to use as guides, unlike geometry,
probability-statistics, analysis, differential equations, etc. Algebra
is also a poor guide to reality, not making equal contact with the
concrete physical world and the abstract world, unlike even Arithmetic
(which algebra of course claims as its own, as it does logic and so on)
which is closer to our daily counting and measuring numbers. It
combines with geometry and topology admittedly - but the intuition
comes from outside algebra, as Pierre De Fermat illustrates in his
discovery of Cartesian/Analytic Geometry (algebra + geometry) and
Probability with Pascal and modern Number Theory and parts of Calculus
before Sir Isaac Newton and Leibniz and his work on optics.

His "This Week's Finds in Mathematical Physics - Week 213, continues
his "glorification" of algebra, or I suppose that he would say that he
is merely reflecting the truth. It is good to have competition, it
stimulates Creativity, so I am glad to have this opportunity to argue
in the other direction without however urging anybody to abandon
algebra (just de-emphasize it from the runaway train that it has become
in algebraic topology and algebraic geometry that are now dominant in
Superstring Theory, Loop Quantum Gravity, etc.

John Baez argues, in agreement with James Dolan, that the bridge
between algebra and topology in algebraic topology is about the unity
of mathematics, topology being about "space" while group theory is
about "symmetry", the idea going back to Galois's idea of classifying
embedding (in different language) by the Galois group of all symmetries
of the "big thing that map the little thing to itself."

This is the open and hopeful John Baez, but as in my criticism of one
of his recent postings of similar type, I notice his tendency to
eventually wander away from openness and hopefulness to episodic
detail-orientation which is where algebraists tend to go -if there's an
Algebraic Heaven, it's full of mathematicians and scientists and
philosophers and others counting the number of Angels on the head of a
pin or the number of grains of sand in a desert. Last time he made a
grand introduction perfect to page 5 or something like that, after
which we were "swept away" to endless details of classifying the usual
algebraic objects which would make a taxonomist classifying types of
fur jealous.

Emmy Noether didn't come before Einstein - Einstein came before Emmy
Noether. She was inspired by him, not vice versa. Her symmetries and
conservation laws came from physics intuition, not algebraic intuition.
And the same with Hermann Weyl in his own algebra. And Einstein's
intuition came from the real physical world but also from geometry, and
if you don't know the story of how Einstein asked his geometry
Professor Friend Marcel Grossman and was directed toward Ricci and
Levi-Civita's Absolute Differential Calculus (later called Tensor
Analysis), then now's a good time to learn it. He also was motivated
by his Chair Minkowski in geometry in both Special and General
Relativity, and by Lorentz and Fitzgerald, and on and on.

Still on page 1 of his "This Week's Finds...Week 213" we find him
talking about Felix Klein's "Erlangen program" plan for reducing
"geometry" to group theory and the Klein bottle. I have some terrible
news for John Baez. People don't go around discovering Special and
General Relativity and Quantum Theory or even how the universe expands
and accelerates by converting Klein bottles and Mobius strips to
algebra. People do the latter partly to systematize and organize, but
the degree of "organizing" and "systematizing" that Germanic
Civilization gave us via its Algebraists is more like that of the ants
than that of Beethoven, Mozart, Vivaldi, Rossini. Rossini of the "Four
Seasons" was played on KMZT (K-Mozart) tonight in Los Angeles County.
A Man For All Seasons has to have the real world to know what a season
is. And Vivaldi, who began for the Priesthood, had quite a few seasons
himself.

Osher Doctorow

.

Relevant Pages