Dear Ross,=0A= =0A= =0A= Thank you for your interesting message in this thread. I have two remarks = =3D=0A= to add relating your message. Concerning Saunders' 1968 "Geometrical Mechan= =3D=0A= ics" (2 parts), I just noticed that they are included in the references of = =3D=0A= "Foundations of Mechanics" by R. Abraham and J.E. Marsden, The Benjamin Cum= =3D=0A= mings Pub. Co., first edition 1978, second edition (with revisions) 1980, w= =3D=0A= hich means that they were actually useful and not just to his Chicago stude= =3D=0A= nts. This book was for a while one of my favourite textbooks on the subject= =3D=0A= . Somewhat surprisingly I found just now inside it a handwritten note that = =3D=0A= I must have put there myself, and which reads "SDG suggestions. Take equati= =3D=0A= ons of classical mechanics, do this synthetically, apply to function spaces= =3D=0A= , get equations of continuum mechanics, which are difficult". I can only th= =3D=0A= ink of Bill Lawvere having given such me (or everybody) such an advice.=0A= =0A= =0A= In connection with the calculus of variations, this is precisely what we di= =3D=0A= d in the paper by myself and my former student Murray Heggie, and which non= =3D=0A= e other than John W. Gray included in the Proceedings of the Special Sessio= =3D=0A= n on Mathematical Applications of Category Theory 89th Annual Meeeting of t= =3D=0A= he AMS, held in Denver, Colorado, January 5-9, 1983, where I gave a talk ab= =3D=0A= out it. Perusing that book after so many years, I just read (presumably for= =3D=0A= the second time, altough I have forgotten all about a first) John's introd= =3D=0A= uction to the volume which although short contains some interesting thought= =3D=0A= s. He writes there that the expression "mathematical applications" is a mis= =3D=0A= nomer as in is opinion there is (practically) no such thing as "pure" as di= =3D=0A= stinct from ":applied" category theory. He adds "Virtually all of category = =3D=0A= theory arises out of the attempt to understand some aspect of mathematics a= =3D=0A= nd place it in its appropriate context. Needless to say, this does not alwa= =3D=0A= ys work, but when it does it can lead not only to vast generalizations, but= =3D=0A= to vast clarifications and this is the purpose of category theory". I coul= =3D=0A= d not agree more.=0A= =0A= =0A= Best regards,=0A= =0A= Marta=0A= =0A= =0A= =0A= =0A= =0A= =0A= =0A= =0A= =0A= ________________________________=0A= From: Ross Street <ross.street@mq.edu.au>=0A= Sent: October 29, 2017 9:42:51 PM=0A= To: ptj@maths.cam.ac.uk=0A= Cc: Marta Bunge; Harry Dole; categories@mta.ca list; George Janelidze=0A= Subject: Re: categories: Re: Kinetic Energy Is A Riemann Metric On Configur= =3D=0A= ation Space=0A= =0A= Dear Harry, Marta, Peter and All,=0A= =0A= On my shelves is a slightly-under-A4-sized=0A= booklet of lectures on=0A= =0A= Algebraic Functions=0A= =0A= by Saunders Mac Lane (with the space, all three times typed!)=0A= delivered at Harvard in Spring 1939. The notes were taken=0A= by Edwin N. Nilson. The place and date on the booklet is=0A= Cambridge, Massachusetts 1947.=0A= The notes culminate in=0A= Section 25. Applications of Riemann-Roch theorem.=0A= At the time Weil had given ``an ingenious new proof''.=0A= =0A= Saunders' ``hobbies'' were many!=0A= =0A= I knew of Mac Lane's notes on mechanics and wrote to=0A= him asking for them but did not get a copy. So thank you=0A= Harry for making them available.=0A= =0A= Speaking of mechanics, I might mention that I believe=0A= Chapter 13 Classical Mechanics (last chapter)=0A= of ``Advanced Calculus'' by Loomis and Sternberg=0A= is based in large part on the PhD thesis of=0A= our colleague John W. Gray.=0A= =0A= Interesting you should mention Dr Pars, Peter.=0A= He was at the University of Sydney when I was in=0A= my final undergrad years. He taught us a course on=0A= the calculus of variations. It was very hands on with many=0A= nice examples: quite a good background for learning a=0A= more grown up approach later. So I met Pars before=0A= I met Saunders.=0A= =0A= Ross=0A= =0A= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]