Re: Kinetic Energy Is A Riemann Metric On Configuration Space (fwd)
Dear All Last thursday I had sent a message to Harry Dole but wasn't sure whether it might interest others and did not send it to the list. Since the discussion continues, here is a copy of my message to Harry Dole. Johannes ---------- Forwarded message ---------- Date: Thu, 26 Oct 2017 10:20:42 +0200 (CEST) From: Johannes Huebschmann <huebschm@math.univ-lille1.fr> Reply-To: Johannes.Huebschmann@math.univ-lille1.fr To: Harry Dole <hfdole@gmail.com> Cc: johannes.huebschmann@math.univ-lille1.fr Subject: Re: categories: Kinetic Energy Is A Riemann Metric On Configuration Space Dear Harry This is great. Many thanks indeed. In 1977 (or so) Mac Lane gave a talk at Heidelberg and mentioned Max and Min, Lax and Lin, the principle of Courant-Weyl and other such issues.
From my recollections he did not say he had ever taught a course on mechanics.
If I had obtained a copy of these notes in my mathematical youth, that would have saved me a lot of trouble. Best wishes Johannes HUEBSCHMANN Johannes Professeur ?m?rite USTL, UFR de Math?matiques UMR 8524 Laboratoire Paul Painlev? 59 655 VILLENEUVE d'ASCQ Cedex/France http://math.univ-lille1.fr/~huebschm Johannes.Huebschmann@math.univ-lille1.fr On Tue, 24 Oct 2017, Harry Dole wrote:
Greetings,
As a student of Saunders Mac Lane, I took a course from him on Geometrical Mechanics. The subject line is from the introduction. I saved the course notes here:
https://harrydole.com/wp/2017/09/10/saunders-mac-lane-geometrical-mechanics/
While not necessarily categorical, it might have some interest to the general community.
cheers,
Harry Dole
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Dear Johannes et al, Well, let's give some thought to Rob Goldblatt. I met Rob in New Zealand at a sumptuous September dinner. I've been out of touch with the categorical community for a while so meeting Rob was a treat. I disclosed to him I had Saunders' old notes, and he advised they could be of interest to this list. I had no idea. Apologies for not posting sooner. cheers, harry On Mon, Oct 30, 2017 at 2:36 PM, Johannes Huebschmann < huebschm@math.univ-lille1.fr> wrote:
Dear All
Last thursday I had sent a message to Harry Dole but wasn't sure whether it might interest others and did not send it to the list. Since the discussion continues, here is a copy of my message to Harry Dole.
Johannes
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
I've guessed that MacLane mainly wanted to express "canonicity". He and Eilenberg rewrote canonical map in Bourbaki books by natural transformation. Then he attempted to rewrite "canonicity" of canonical equation in analytical mechanics on static system. Since your MacLane's notes open his powerful motivation for canonical equation, it amazed me. Thank you for your disclosing. However we have to admit lacks of "the principle of general relativity" in his mechanics. The general relativity without gravity theory is an extended analytical mechanics on moving system containing static system. In the old analytical mechanics, we cannot derive motion equations on moving coordinate system(reference frame) because energy is not an invariant variable under a relativistic transformation. In general relativity, energy is not a primary physical amount. Alternatively Minkowski's invariant variable, which contains energy concept, is a primary amount; however its physical interpretation is non-trivial. If we tried to get more complete system to derivate moving equation containing "canonicity" expressed by concepts of category theory, I think there are such barriers. I don't have any important key idea for realizing it yet. To tell the truth, it's too difficult to make such system. So, I want to create more workable system in any limited area. Thank you for your kindheartedness. IWAKI 2017-11-01 18:18 GMT+09:00 Harry Dole <hfdole@gmail.com>:
Dear Johannes et al,
Well, let's give some thought to Rob Goldblatt. I met Rob in New Zealand at a sumptuous September dinner.
I've been out of touch with the categorical community for a while so meeting Rob was a treat. I disclosed to him I had Saunders' old notes, and he advised they could be of interest to this list. I had no idea. Apologies for not posting sooner.
cheers,
harry
On Mon, Oct 30, 2017 at 2:36 PM, Johannes Huebschmann < huebschm@math.univ-lille1.fr> wrote:
Dear All
Last thursday I had sent a message to Harry Dole but wasn't sure whether it might interest others and did not send it to the list. Since the discussion continues, here is a copy of my message to Harry Dole.
Johannes
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
-- ---------------------------------------------- * 岩城 秀和（いわき ひでかず） * IWAKI Hidekazu * 住所：〒920-8217 石川県金沢市近岡町１２８−１シティハイムグランツ２０６号室 * Address: 128-1(206), Chikaoka-machi, Kanazawa-shi, Ishikawa, 920-8217, Japan * e-mail : i.hidekazu@gmail.com ---------------------------------------------- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (3)
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Harry Dole -
Hidekazu IWAKI -
Johannes Huebschmann