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Posina Venkata Rayudu (Jul 07 2023 at 15:49):Dear All,
I just thought of sharing with you my gratitude towards Professor F. William Lawvere and his inspirational seriousness of purpose:
https://conceptualmathematics.substack.com/p/professor-f-william-lawvere
Thanking you,
Yours truly,
posina
Notification Bot (Jul 07 2023 at 15:54):Posina Venkata Rayudu has marked this topic as resolved.
Notification Bot (Jul 09 2023 at 05:02):Posina Venkata Rayudu has marked this topic as unresolved.
Posina Venkata Rayudu (Jul 09 2023 at 05:02):History and Philosophy of Mathematic Reform
Posina Venkata Rayudu (Jul 09 2023 at 05:05):Posina Venkata Rayudu said:
Being the main contradictor that Professor F. William Lawvere is (according to Grothendieck ;) I am sure he would be happy to hear you contradicting his understanding of the history of mathematics education (as usual, it's just what I think ;)
Jencel Panic (Jul 12 2023 at 23:11):Conceptual Mathematics is one of the greatest books ever!
Josh Lalonde (Aug 01 2023 at 13:00):Hi everyone, apologies if this has been posted before but I was wondering if anyone has any links or references to biographical materials about F. William Lawvere. I'm particularly interested in his political engagement, but anything about his life would be helpful. Thanks in advance!
Notification Bot (Aug 01 2023 at 13:02):A message was moved here from #general > Lawvere bio materials? by Morgan Rogers (he/him).
Matt Earnshaw (Aug 01 2023 at 13:44):Here's a newspaper article covering his ousting from Dalhousie 19710122-DalhousieGazetteonWLawvere.pdf
Matt Earnshaw (Aug 01 2023 at 13:55):Unrelated, but just today I have scanned Introduction to Linear Categories and Applications which may be of interest to the pedagogues and philatelists out there. These are seemingly lecture notes for a course that would usually be called Linear Algebra. Some of the material later appeared in the books.
John Baez (Aug 01 2023 at 14:17):Philatelists are stamp collectors. Is this book of interest to them?
Matt Earnshaw (Aug 01 2023 at 14:22):Figuratively speaking.
Todd Trimble (Aug 01 2023 at 14:31):Matt Earnshaw said:
Figuratively speaking.
I still don't get it.
John Baez (Aug 01 2023 at 14:40):Maybe "bibliophiles"?
Matt Earnshaw (Aug 01 2023 at 14:48):Some years ago I received some lesser spotted Lawvere documents in an email entitled "among stamp collectors". I wasn't confused by the title. The psychological structures behind any form of collecting are surely at work in building this archive.
John Baez (Aug 01 2023 at 15:15):Okay, got it.
Kyle Wilkinson (Aug 01 2023 at 15:55):Josh Lalonde said:
Hi everyone, apologies if this has been posted before but I was wondering if anyone has any links or references to biographical materials about F. William Lawvere. I'm particularly interested in his political engagement, but anything about his life would be helpful. Thanks in advance!
I do recall an account in a book I have. Unfortunately, between attending this conference and drafting a prospectus, it'll be some time before I can track it down. But if I recall correctly, it's an account of getting him hired at Dalhousie. I speculate there's a connection with his eventual development of functorial semantics, too. I wish there were a "remind me" feature here.
Todd Trimble (Aug 01 2023 at 16:36):Matt Earnshaw said:
Some years ago I received some lesser spotted Lawvere documents in an email entitled "among stamp collectors". I wasn't confused by the title. The psychological structures behind any form of collecting are surely at work in building this archive.
To a degree, perhaps, but collectors may have very different motivations. For many, it's the pleasure of hunting down items because they are rare and for no other reason. Or because they are curiosities or just plain weird. Or because they belong in any well-rounded collection. Or because they have a particular special meaning or value for the individual.
Remember: "no question is dumb".
Jason Erbele (Aug 01 2023 at 16:50):Kyle Wilkinson said:
I wish there were a "remind me" feature here.
There is a "Starred messages" feature that could potentially be used for reminders.
Josh Lalonde (Aug 01 2023 at 17:26):Matt Earnshaw said:
Here's a newspaper article covering his ousting from Dalhousie 19710122-DalhousieGazetteonWLawvere.pdf
Thanks this is great!
Josh Lalonde (Aug 01 2023 at 17:27):Kyle Wilkinson said:
Josh Lalonde said:
Hi everyone, apologies if this has been posted before but I was wondering if anyone has any links or references to biographical materials about F. William Lawvere. I'm particularly interested in his political engagement, but anything about his life would be helpful. Thanks in advance!
I do recall an account in a book I have. Unfortunately, between attending this conference and drafting a prospectus, it'll be some time before I can track it down. But if I recall correctly, it's an account of getting him hired at Dalhousie. I speculate there's a connection with his eventual development of functorial semantics, too. I wish there were a "remind me" feature here.
No rush, but if you do find the book at some point and remember my question, please post it here.
Kyle Wilkinson (Aug 08 2023 at 21:50):@Josh Lalonde
So, I decided I needed a break and found the source I was thinking of. Let me start by saying I had my dates a little mixed up in my head. This was after Lawvere's time at Dalhousie. Also, I for some reason thought his Functorial Semantics was later work, when it was actually part of his dissertation. I think it was published later. In any case, this account is immaterial to that work, though both people were alike in spirit with respect to work on categories and syntax/semantics.
The other person was a biologist I know some here are familiar with given the relationship he had with category theory: Robert Rosen. If you haven't heard of him, I recommend at least doing a quick search. As far as I am able to discern from literature, he was the first to publish works on applications of category theory outside of mathematics itself. His first such seems to have been in 1958, so pretty early. He also studied the topic under both MacLane and Eilenberg, though transferred out of math to earn his doctorate in biology instead.
Ultimately, he would develop a model of life (to be distinguished in kind from non-life) using some basic category theory, in addition to lots of writing on abstract "modeling relations" (formal syntax-semantics maps), measurement, and feedforward systems which he called "anticipatory". There have been mixed reviews on his use of math, since he did not always write it in a rigorous manner, especially when using it to develop his more philosophical ideas. The really interesting part to me IS the philosophy of science work he did, though. In many ways, he (in spirit) anticipated some of the work I see happening recently in this community, especially as relates to questions of compositionality and emergent/generative features, though he used different terms. It's exciting to see math really making formal headway into some of these old questions.
Anyway, this does relate back to Lawvere! It is possible they knew of each other due to both having been at Columbia with Eilenberg (at different times, though. Rosen left in 1957 and Lawvere arrived in 1960). Rosen would start at SUNY-Buffalo and move to Dalhousie in 1975. Lawvere, of course, was at Dalhousie first and in 1974 moved to SUNY-Buffalo. But they did in fact know each other when Rosen by his account went to bat for the "eminent category theorist" whom he helped get hired at SUNY, just before he left. He doesn't name Lawvere, but I can't imagine any other conclusion.
So, I don't know if that is helpful to you. I just happen to have been interested in Rosen's work, and recalled that passage. I guess I recalled it being more relevant than it turned out to be once I found the source again. The source, by the way, is "Old Trends and New Trends in General System Research," a memorial lecture he gave for von Bertalanffy. https://doi.org/10.1080/03081077908960904
Here is the excerpt, which follows a brief historical account of the development of category theory. One of his points in the talk was that category theory is a natural language for formally describing Bertalanffy's general system theory (for instance like Mesarovic has tried to do):
"It is interesting to note that Category Theory has elicited exactly the same reaction within the community of pure mathematicians that system-theoretic approaches have generated in the community of experimental or empirical scientists. Initially, category theory was dismissed out of hand by many mathematicians as at best a cumbersome language for stating well-known facts about algebraic topology. Later, when it became clear that category theory could answer important open questions in a variety of areas, it was conceded to be of some limited usefulness for specific applications, but still of no significance as an independent branch of mathematics. This attitude is still prevalent; indeed, just a few years ago, I served on the Executive Committee of the Department of Mathematics at SUNY Buffalo, when that department was in the process of hiring an eminent category theorist. A substantial group of senior faculty tried to block this appointment on the grounds that category theory was not real mathematics; they were dissuaded only with difficulty from writing to other departments to collect opinions on whether category theory was mathematics or not."
At the very least, it is interesting to piece together these random connections from the past! Also, there is much to be gleaned by digging through the old texts, finding forgotten threads of research.
Josh Lalonde (Aug 11 2023 at 21:03):@Kyle Wilkinson thanks, this is very interesting. Rosen is someone I've had on my radar for a while but never looked into in any detail.
Posina Venkata Rayudu (Aug 22 2023 at 11:51):Speaking of Rosen, I thought you might find my corrections (of some related misunderstandings published in Neuron) grandiously entitled:
On making sense of science
https://disqus.com/home/discussion/cell-press/dialogue_across_chasm_are_psychology_and_neurophysiology_incompatible_neuron/
of some interest. I look forward to your critique (unvarnished ;)
Posina Venkata Rayudu (Aug 22 2023 at 12:18):Josh Lalonde said:
Hi everyone, apologies if this has been posted before but I was wondering if anyone has any links or references to biographical materials about F. William Lawvere. I'm particularly interested in his political engagement, but anything about his life would be helpful. Thanks in advance!
I just thought you might find:
F. William Lawvere (1937–2023): A lifelong struggle for the unity of mathematics
https://euromathsoc.org/magazine/articles/143
of some interest.
The above slide (due to Professor Peter Johnstone, unless I'm mistaken) is within couple of days of the publication of Professor F. William Lawvere's 2007 Axiomatic Cohesion (http://www.tac.mta.ca/tac/volumes/19/3/19-03.pdf), which can be traced to his 1991 Future of Category Theory (cf. categories of Being and Becoming; https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1991-some-thoughts-on-the-future-of-category-theory.pdf). I can't readily recollect any earlier discussion of Being/unity/cohesion vs. Becoming/change/variation. Please correct me if I'm mistaken (which is more often the case than not ;) Thank you!
Josh Lalonde (Aug 30 2023 at 13:00):Posina Venkata Rayudu said:
Josh Lalonde said:
Hi everyone, apologies if this has been posted before but I was wondering if anyone has any links or references to biographical materials about F. William Lawvere. I'm particularly interested in his political engagement, but anything about his life would be helpful. Thanks in advance!
I just thought you might find:
F. William Lawvere (1937–2023): A lifelong struggle for the unity of mathematics
https://euromathsoc.org/magazine/articles/143of some interest.
The above slide (due to Professor Peter Johnstone, unless I'm mistaken) is within couple of days of the publication of Professor F. William Lawvere's 2007 Axiomatic Cohesion (http://www.tac.mta.ca/tac/volumes/19/3/19-03.pdf), which can be traced to his 1991 Future of Category Theory (cf. categories of Being and Becoming; https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1991-some-thoughts-on-the-future-of-category-theory.pdf). I can't readily recollect any earlier discussion of Being/unity/cohesion vs. Becoming/change/variation. Please correct me if I'm mistaken (which is more often the case than not ;) Thank you!
Thank you very much, I'll check these out.