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February 21, 2023

This Week’s Finds (51–100)

Posted by John Baez

Grab a copy of this:

These are the second fifty issues of my column, from April 23, 1995 to March 23, 1997. They discuss quantum gravity, topological quantum field theory and other topics in mathematics and physics. They were typeset in 2020 by Tim Hosgood. Since then I’ve edited them more and changed most references to preprints into references to published papers and/or the arXiv. If you see typos or other problems please report them. (I already know the cover page looks weird).

By the way, I’ve also done a lot more editing of the first 50 issues, with help from Fridrich Valach, so please grab a new copy of this even if you already have it:

But let me say a bit more about what’s in issues 51–100.

Weeks 50–100 contain two long expository threads. One is on “ADE classifications”:

  • Week 62 — The ubiquity of ADE classifications. The classification of finite reflection groups using Coxeter diagrams.

  • Week 63 — The classification of crystallographic finite reflection groups and semisimple Lie algebras.

  • Week 64 — Semisimple Lie algebras. Affine Lie algebras, Wess–Zumino–Witten models and quantum groups.

  • Week 65 — The A, D, and E lattices. The McKay correspondence and the classification of minimal models.

The other, called the “The Tale of nn-Categories”, was an introduction to categories and higher categories — mainly just 2-categories. It can be found in these issues:

  • Week 73 — The category of sets and the 2-category of categories.

  • Week 74 — Kinds of categories: monoids, groups, and groupoids. The periodic table of nn-categories.

  • Week 75 — The fundamental groupoid of a topological space. The classifying space of a groupoid.

  • Week 76 — Equations, isomorphisms, and equivalences. Adjoint functors.

  • Week 77 — Adjoint functors.

  • Week 78 — Adjoint functors and adjoint linear operators.

  • Week 79 — The unit and counit of an adjunction.

  • Week 80 — The definition of 2-category.

  • Week 83 — Adjunctions in 2-categories and dual objects in monoidal categories.

  • Week 84 — Review. Monads and monoids.

  • Week 89 — Monads in 2-categories. Monoids and monoidal categories as monads.

  • Week 92 — Monads from adjunctions.

  • Week 99 — 2-Hilbert spaces. Coproducts.

  • Week 100 — Definitions of nn-category.

I am now editing issues 101–150, which total 347 pages. In old age I am paying penance for the loquacity of youth.

Posted at February 21, 2023 9:41 PM UTC

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Re: This Week’s Finds (51–100)

Wow, do those take me back. Around week 62 or so is when I started college and first had an internet connection. I’m not sure exactly when after that I discovered sci.math and sci.physics and started reading This Week’s Finds regularly, but it was probably within the first year. There was obviously a lot in there that I wasn’t prepared to understand (and there still is!), but I fondly remember TWF as giving me my first glimpse into just how big mathematics is.

Posted by: Mark Meckes on February 22, 2023 2:44 PM | Permalink | Reply to this

Re: This Week’s Finds (51–100)

Great! It’s fun to think back on those old days. I’ve seen you here and there for quite a while now.

I think part of why people liked This Week’s Finds, besides the fact that I explained things clearly, is that I had a youthful, jocular, cut-through-the-bullshit persona where I admitted I didn’t understand all the math and physics I was explaining — but was optimistic about the prospect of figuring it all out.

I don’t think I could write This Week’s Finds now. If I did, it would be very different. For example, I could no longer show off about flying here and there for conferences, oblivious to the climate crisis. I’ve also become more cynical about many trends in modern math and physics. And the internet, which was brand new when I started writing This Week’s Finds, is a very different place.

There are still lots of things I’m eager to talk about, though! For the kids out there, here are some:

These are from my column in the AMS Notices. They’re more about specific ‘things’ than broad ‘theories’. And the writing has a different tone.

Posted by: John Baez on February 22, 2023 9:23 PM | Permalink | Reply to this

Re: This Week’s Finds (51–100)

Another aspect of your persona back then, which I think hasn’t changed, was your approachability. You may not remember, but in addition to some Usenet interactions, I emailed you out of the blue a couple times while I was still an undergrad, partly to ask math questions and partly about trying to decide between going into math or physics, since I knew you’d once struggled with a similar choice yourself.

Part of the advice you gave me is that you can do a lot of math as a physicist, and a lot of physics as a mathematician. I’ve passed that advice on to a lot of students myself.

(I actually eventually became a mathematician who doesn’t do a lot of physics. But your advice was part of what helped me get on what turned out to be the right track for me.)

Posted by: Mark Meckes on February 23, 2023 7:42 PM | Permalink | Reply to this


Have you updated them with discoveries and developments since they were written?

Posted by: Jeffery Winkler on February 22, 2023 6:32 PM | Permalink | Reply to this

Re: Jeffery

Hell no, that would be a full-time job! Luckily the mathematics is still correct and interesting. As for the physics… well, we all know how sad the situation is with quantum gravity and string theory, but my descriptions of these theories are still worth reading if you care about such theories.

Posted by: John Baez on February 22, 2023 8:20 PM | Permalink | Reply to this

Re: This Week’s Finds (51–100)

The links to “Week 20” in Week 65 are broken, referring to the current document instead of the previous collection.

Posted by: Blake Stacey on February 24, 2023 2:44 AM | Permalink | Reply to this

Re: This Week’s Finds (51–100)

In Week 63, without dependence on arbitrary choices is missing a closing quotation mark and has the opening mark pointing the wrong way.

Posted by: Blake Stacey on February 24, 2023 2:52 AM | Permalink | Reply to this

Re: This Week’s Finds (51–100)

I don’t know if I have the energy to fix links between weeks that point out of a given document to previous documents, especially since there will be more and more of these as I go on, I’m too lazy to write software that does this automatically, and ultimately I may combine all the documents into a single latex-crashing document containing all the issues.

In short, I know about this problem, but I haven’t yet figured out what I want to do about it.

I will definitely make your easier corrections, though — thanks!

Posted by: John Baez on February 24, 2023 5:39 PM | Permalink | Reply to this

Re: This Week’s Finds (51–100)

I think it was at some point early in this batch that I began to tune in, maybe Autumn 1995. I don’t think I had regular access to the internet before then.

I remember the thrilling sense the posts gave that I could access ideas in mathematics and physics at the research frontier. And nn-categories were going to lead the way.

Posted by: David Corfield on February 28, 2023 10:50 AM | Permalink | Reply to this

Re: This Week’s Finds (51–100)

Those were exciting days… leading to the formation of this blog!

Posted by: John Baez on March 3, 2023 10:16 PM | Permalink | Reply to this

Re: This Week’s Finds (51–100)

I’m very much in reminiscence mode preparing my talk to the Topos Institute next week.

Posted by: David Corfield on March 4, 2023 11:37 AM | Permalink | Reply to this

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