Kinetic Energy Is A Riemann Metric On Configuration Space

Kinetic Energy Is A Riemann Metric On Configuration Space

[Harry Dole]

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


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Re: Kinetic Energy Is A Riemann Metric On Configuration Space

[George Janelidze]

Dear Mr. Dole,

I am one of many who is (or will be) very grateful to you for these
beautiful notes. I have never seen them before. Do you know how accurate
they are? Had Mac Lane seen them?

While making a copy of them I read on your webpage:

"...Below are the lecture notes dating back to 1968. Interestingly, there’s
no space in “MacLane”...

As a comment to that here is what Mac Lane says in his book "A Mathematical
Autobiography" (Page 6):

"...The space in Mac Lane was added years later by me, when my first wife,
Dorothy, found it difficult to type our name without a space".

Best regards,
George Janelidze

--------------------------------------------------
From: "Harry Dole" <hfdole@gmail.com>
Sent: Wednesday, October 25, 2017 4:03 AM
To: <categories@mta.ca>
Subject: categories: Kinetic Energy Is A Riemann Metric On Configuration
Space

> 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/ ]

Re: Kinetic Energy Is A Riemann Metric On Configuration Space

[Marta Bunge]

Dear George,


Although I have yet to read the Saunders MacLane's notes on "Geometrical Mechanics"  for a course given in Chicago in 1968 in some more detail, just perusing them seems to me that the notes in question are based on several sources which are explicitly mentioned in them and that are well known in the  subject matter. I doubt therefore that Saunders himself may have thought of them as original in any way. Doubtless they must have been useful to his students as well as to himself, for instance when writing Chapter VIII (Forms of Space) and Chapter IX (Mechanics) of his very nice book "Mathematics Form and Function", Springer-Verlag, 1968.


I am still not sure myself whether to write "Mac Lane" or "MacLane", and I certainly did not know the story behind his opting for the latter. I am sure that these notes will be useful to anybody not familiar with the material  exposed on them, and that we should certainly thank Harry Dole for his having provided us with them.


Sincerely,

Marta


************************************************
Marta Bunge
Professor Emerita
Dept of Mathematics and Statistics
McGill University
Montreal, QC, Canada H3A 2K6
bunge@math.mcgill.ca
************************************************


________________________________
From: George Janelidze <George.Janelidze@uct.ac.za>
Sent: October 25, 2017 6:23 PM
To: Harry Dole; categories@mta.ca
Subject: categories: Re: Kinetic Energy Is A Riemann Metric On Configuration Space

Dear Mr. Dole,

I am one of many who is (or will be) very grateful to you for these
beautiful notes. I have never seen them before. Do you know how accurate
they are? Had Mac Lane seen them?

While making a copy of them I read on your webpage:

"...Below are the lecture notes dating back to 1968. Interestingly, there’s
no space in “MacLane”...

As a comment to that here is what Mac Lane says in his book "A Mathematical
Autobiography" (Page 6):

"...The space in Mac Lane was added years later by me, when my first wife,
Dorothy, found it difficult to type our name without a space".

Best regards,
George Janelidze


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Kinetic Energy Is A Riemann Metric On Configuration Space

[ptj]

Dear Marta,

Yes, I am sure Saunders saw his excursions into geometrical mechanics
as a `hobby', and wasn't seeking to make original contributions (other
than, perhaps, a new way of looking at established results). I remember,
when I was in Chicago in 1975--76, he asked me whether I knew L.A. (Alan)
Pars, a Cambridge mathematician whose book on dynamics was one of his
favoured sources. (At the time I didn't know him -- he had retired long
before I first went to Cambridge -- but I did meet him subsequently.
He was then in his nineties, and was delighted to learn that Saunders
was a fan of his work.)

Regarding the spelling of Saunders's surname: my recollection is that,
once he had decided to adopt the space in `Mac Lane', he was quite
insistent that everyone should use it. Since that happened well before
1968, it's surprising that he allowed `MacLane' to stand on the title
page of those 1968 notes.

Best regards,
Peter

On Oct 27 2017, Marta Bunge wrote:

>Dear George,
>
>
> Although I have yet to read the Saunders MacLane's notes on "Geometrical
> Mechanics" for a course given in Chicago in 1968 in some more detail,
> just perusing them seems to me that the notes in question are based on
> several sources which are explicitly mentioned in them and that are well
> known in the subject matter. I doubt therefore that Saunders himself may
> have thought of them as original in any way. Doubtless they must have
> been useful to his students as well as to himself, for instance when
> writing Chapter VIII (Forms of Space) and Chapter IX (Mechanics) of his
> very nice book "Mathematics Form and Function", Springer-Verlag, 1968.
>
>
> I am still not sure myself whether to write "Mac Lane" or "MacLane", and
> I certainly did not know the story behind his opting for the latter. I am
> sure that these notes will be useful to anybody not familiar with the
> material exposed on them, and that we should certainly thank Harry Dole
> for his having provided us with them.
>
>
>Sincerely,
>
>Marta
>
>
>************************************************
>Marta Bunge
>Professor Emerita
>Dept of Mathematics and Statistics
>McGill University
>Montreal, QC, Canada H3A 2K6
>bunge@math.mcgill.ca
>************************************************
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Kinetic Energy Is A Riemann Metric On Configuration Space

[Harry Dole]

Dear Marta,

It's been a while since we've talked.  Hope all is well.

I agree with you that Saunders might not thought of this as original
work.  As it happens in my experience with him it was in how he
approached any topic that was illuminating.  He's why I wanted
category theory.

With regards to George's question, yes, he saw them as he personally
gave me the now scanned copy.

For whatever reason, this course in the latter 70's gave him great
joy, of all the courses and seminars I had the pleasure to attend with
him.  Perhaps, in his mind, this is a form of practical mathematics to
share with all (especially the spinning ball part).  As far as I know,
this may have been the last actual course he taught.

cheers,

harry


On Thu, Oct 26, 2017 at 8:23 PM, Marta Bunge <martabunge@hotmail.com> wrote:
> Dear George,
>
>
> Although I have yet to read the Saunders MacLane's notes on "Geometrical
> Mechanics"  for a course given in Chicago in 1968 in some more detail, just
> perusing them seems to me that the notes in question are based on several
> sources which are explicitly mentioned in them and that are well known in
> the subject matter. I doubt therefore that Saunders himself may have thought
> of them as original in any way. Doubtless they must have been useful to his
> students as well as to himself, for instance when writing Chapter VIII
> (Forms of Space) and Chapter IX (Mechanics) of his very nice book
> "Mathematics Form and Function", Springer-Verlag, 1968.
>
>
> I am still not sure myself whether to write "Mac Lane" or "MacLane", and I
> certainly did not know the story behind his opting for the latter. I am sure
> that these notes will be useful to anybody not familiar with the material
> exposed on them, and that we should certainly thank Harry Dole for his
> having provided us with them.
>
>
> Sincerely,
>
> Marta
>
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]