archived as
(also …Pitkanen_85.pdf) =>doc pdf URL-doc URL-pdf
more from Matti Pitkänen is on the /Pitkanen.htm page at doc pdf URL
note: because important websites are frequently "here today but gone tomorrow", the following was archived from private emails onMay 17, 2012.
In Search Of A New Mathematics To Describe TGD Physics
by Dr. Matti Pitkänen
Postal address:
Köydenpunojankatu 2 D 11
10940, Hanko, Finland
E-mail:
URL-address:
(former address:)
"Blog" forum:
From: Matti Pitkänen [
To:
Sent: Wednesday, May 16, 2012 10:23 AM
Subject: re. the search for the 'correct' formula
> From your response to Hamed in "A Universe From Nothing" blog:
> "I believe that the correct guideline is that the mathematics that one learns or perhaps even creates must naturally emerge from applications to real world problems (in my case, Physics). When I was younger, I used to make visits to math library and walk between bookshelves with the idea that I might find some miraculous cure to my mathematical problems with TGD. I left the library in a rather depressed mood!;-)."
> Didn't Einstein struggle with a mathematical description of General Relativity? If I recall, it was his mathematician friend Grossman who searched the libraries (for 2 years?) before stumbling upon Riemann's forgotten "Foundations of Geometry" lecture (1854?) that gave the correct formula for GR.
> And wasn't string theory discovered by physicist Gabriele Veneziano who searched for a year for a formula that could describe the strong nuclear force when he came upon an almost obsolete Euler formula that was the answer?
> Apparently you tried the same thing by searching libraries. But how did these guys know when they had the "correct" formula? Do you try to match up experimental data with each-and-every formula that you come across? Or do you build hypothetical mathematical models and then try to see if a more robust theorem already exists? Maybe it doesn't; maybe the hypothetical model will come before the more formal theorem.
Yes. Einstein had to learn a lot of mathematics in the technical sense and in this process lost his ability for great visions.
It took more than 5 years to accept that path integral formalism then and still in fashion simply does not make sense in TGD. Same about canonical quantization. Finally I realized that Einstein's geometrization program must be generalized. Geometrize quantum physics by geometrizing the World of Classical Worlds (WCW) and obtain quantum physics as physics for classical spinor fields in this space. "No quantization" as Wheeler would say. The next question was how to identify this geometry.
After this, it took 5 years to end up with the realization that the geometry defines what is usually called "classical physics" as Bohr orbitology.
The idea of p-adic physics emerged without any rational motivation and it took a long time to realize that real and p-adic physics must be fused together by generalizing the notion of geometry.
I did not fit any formulas simply because it was impossible (and is still to a high degree impossible). All breakthroughs in TGD have been discoveries of principles just as Einstein's key discoveries were principles rather than formulas.
-- Matti
From: Edward Halerewicz, Jr. [
To: McWilliams, Mark L
Sent: Thursday, May 17, 2012 3:39 AM
For the case with Einstein, the fundamental postulates about Nature come first. This is a rare thing to do. Most discover laws or mathematics from observation. But people like Einstein do it with their mind. Einstein thought up the Equivalence Principle (acceleration ~ gravitation) since acceleration can appear to bend light, so gravitation can bend "space".
When Einstein tried to describe such a space, it differed wildly from rigid classical Euclidean space due to curvature and so he was left without a valid mathematical model to describe bent space and make predictions until Grossman pointed out that Riemann had already done so. The dilemma that Einstein faced was that his bet was the space was bent. But at the time he did not have the vocabulary to describe bent space, what does bent space look like, and how does it behave. No easy task to answer without a prior background and that's why mathematicians have a special place in history. My guess is that Matti means that he has the first principles in mind for his model but lacks the proper math to describe it in full and make proper testable predictions.
I am not sure how to make a computer-engineering analogy. But without the right mathematics, there are just some things you can't describe. It would be like using algebra to solve a differential equation without knowing anything about calculus, a process that could take decades or centuries and that's without getting into the physics. You know you have the right formula when it satisfies rigorous mathematical proofs and you are able to apply those proofs to known problems and spit out the correct solutions. I think you have to keep in mind that chemistry makes uses of known numbers systems, natural numbers, engineering makes use of known physics.
It's a bit like expecting to derive the Periodic Table of elements in say N-dimensional space. Can't do that with standard chemistry because there is no language for it. You need to create a new language to describe N-dimensional chemistry. You could probably do it eventually but it's a time-consuming process and by default it would force you to become a mathematician and likely years of study to obtain any tangible results. But the task becomes trivial if you can find somebody who has already written about N-dimensional space in a library.
Edward Halerewicz, Jr.
Independent Researcher
BSc Geography & Env Res, ASc Physics
From: Matti Pitkänen [
To: McWilliams, Mark L
Sent: Thursday, May 17, 2012 7:27 AM
Much of the new mathematics exists potentially. Some examples:
A. The notion of Super Kac-Moody algebra generalizes since instead of 2-D complex space one has 3-D light-like surface. Algebra extends dramatically. Kac-Moody algebras are based on finite Lie algebras. Now finite Lie algebra is replaced with certain infinite-D symplectic algebra. A further generalization is extension to multilocal algebra generalizing the notion of Yangian. All this would require a legionofmathematicians to work out the formulas.
B. Geometry of WCW as a union of symmetric spaces would require precise mathematical formulation and again mathematicians would be needed. The basic structure is understood and even formulas for the metric tensor are known to high degree. But this is far from enough.
C. The fusion of p-adic and real mathematics to larger coherent whole would require a lot of work by mathematicians. Typically both physicists and mathematicians work with models limited to single prime p. I learned only recently that top mathematicians (including Grothendieck) have been working the last decades with various mathematical problems related to p-adic physics (p-adic integration is one example).
D.Hyper-finite factors of type II1 represent existing mathematics developing all the time. But there is a huge communication gulf between mathematicians and physicists (including me). Bourbaki should be translated to the language of physicists.
E. The formulation for the hierarchy of Planck constants would also require a lot of mathematical work.
These are just some examples. Big ideas require a newmathematicallanguage.
-- Matti
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