Weyl's take on symmetry and the continuum

[Fra]

Due to several threads, recent thinking and book readings, suggesting the the concept of "symmetry" itself, as well as the concept of "continuum" are somehow related to a key problem. I asked myself the question about the original line of reasoning of the introduction of symmetry historically.

While I am interested in many things, no one can read everything. And here I was lead to something where I have not read anything.

Woit seems to argue in his book, that Weyl's formalism was key to development of quantum theory, but also that some of the contemporary physicists, Dirac included, had a hard time understanding his reasoning.

Then I found that Weyl has written two books, that from the titles sound interesting. Touching not only the foundations of physical, but also mathematics.

The Continuum: A Critical Examination of the Foundation of Analysis
-- https://www.amazon.com/dp/0486679829/?tag=pfamazon01-20

and

Symmetry
-- https://www.amazon.com/dp/0691023743/?tag=pfamazon01-20

I have not (yet) read any of them.

I am just curious if anyone on here read this, and could give a short review, what Weyl original reasoning might suggest about the current state of physics?

Also are these books worth reading? I just found these today, and several interesting question popped up just from the apperance of the titles.

/Fredrik

 

[Fra]

The association I am after is the emergence of the symmetry in the brain of a "rational matematician" vs emergence of symmetry and spacetime during evolution of "rational matter". In in that context, what is the "problem" of the continuum idea?

/Fredrik

 

[Fra]

I located that supposed quotes from Weyl, giving a glimpse of his logic of reasoning and it's striking how his reasoning itself, reminds of how I picture emergent symmetry! I am probably going to order at least the symmetry book, not to learn the standard topic of symmetry groups, but hopefully to learn how Weyl's own reasoning towards it look like.

John L. Bell has written this note on Weyl
"HERMANN WEYL ON INTUITION AND THE CONTINUUM"

Some interesting quotes from Weyl

"In the Preface to Dedekind (1888) we read that “In science, whatever is provable must not be believed without proof.” This remark is certainly characteristic of the way most mathematicians think. Nevertheless, it is a preposterous principle. As if such an indirect concatenation of grounds, call it a proof though we may, can awaken any “belief” apart from assuring ourselves through immediate insight that each individual step is correct. In all cases, this process of confirmation—and not the proof—remains the ultimate source from which knowledge derives its authority; it is the “experience of truth”."

Encoded in this, is as far as I prefer to interpret it, an perpendicular view of progress of knowledge, relative to Popper. As E.T JAynes has pointed out, even a apparently hard and deductive discipline like mathematics, are in fact inductive. It's not what you see in the final paper, but the process whereby real mathematicans make progress do contain inductive reasoning.

"The beginning of all philosophical thought is the realization that the perceptual world is but an image, a vision, a phenomenon of our consciousness; our consciousness does not directly grasp a transcendental real world which is as it appears. The tension between subject and object is no doubt reflected in our conscious acts, for example, in sense
perceptions."

Now, this is to me very closely related to the paradoxal tension of the whole notion of symmetry. Acts here can be though of as action, subject and object can be though of as intrisic vs extrinsic.

In total I am tempted to GUESS that the reasoning from the two quotes suggests that the process of emergence of symmetry, is more fundamental than the symmetry itself.

If this is what Weyl meant, it seems his own reasoning is indeed key to his success in mathematics. Interesting indeed.

Would it not be remarkable if Weyl has pointed this out so long time ago, and still so little progress in this fundamental point?

Comment?

-- http://publish.uwo.ca/~jbell/Hermann Weyl.pdf

I am probably going to order at least his symmetry book, and see if he reveals any of his reasoning in there.

/Fredrik

 

[Fra]

Interestingly, it seems there is another book edited by Peter Pesic but containing material by Weyl, not yet released, schedueled for release 2009.

"Mind and Nature: Selected Writings on Philosophy, Mathematics, and Physics"

"...Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print..."

"...Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"..."

"...Also included are two book-length series of lectures, The Open World (1932) and Mind and Nature (1933), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics..."

-- http://press.princeton.edu/titles/8959.html

Frank Wilczek's comment on that page:
"Hermann Weyl ranks among the greatest mathematicians, and his deep contributions to physics were decades ahead of their time. But to know him only through his science is to miss the soul of a seeker. For Weyl, the experienced world in all its aspects was an inexhaustible source of wonder and inspiration. Here you can share in the life adventure of a beautiful mind."
--Frank Wilczek, Nobel Prize--winning physicist

/Fredrik