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March 7, 2023

This Week’s Finds (101–150)

Posted by John Baez

Here’s another present for you!

I can’t keep cranking them out at this rate, since the next batch is 438 pages long and I need a break. Tim Hosgood has kindly LaTeXed all 300 issues of This Week’s Finds, but there are lots of little formatting glitches I need to fix — mostly coming from how my formatting when I initially wrote these was a bit sloppy. Also, I’m trying to add links to published versions of all the papers I talk about. So, it takes work — about two weeks of work for this batch.

So what did I talk about in Weeks 101–150, anyway?

In Weeks 101–150 I focused strongly on topics connected to particle physics, quantum gravity, topological quantum field theory, and nn-categories. However, I digressed into topics ranging from biology to the fiction of Greg Egan to the game of Go. I also explained some topics in homotopy theory in a series of mini-articles:

  • A. Presheaf categories.
  • B. The category of simplices, Δ\Delta.
  • C. Simplicial sets.
  • D. Simplicial objects.
  • E. Geometric realization.
  • F. Singular simplicial set.
  • G. Chain complexes.
  • H. The chain complex of a simplicial abelian group.
  • I. Singular homology.
  • J. The nerve of a category.
  • K. The classifying space of a category.
  • L. Δ\Delta as the free monoidal category on a monoid object.
  • M. Simplicial objects from adjunctions.
  • N. The loop space of a topological space.
  • O. The group completion of a topological monoid.

You can reach all these mini-articles from the introduction.

One annoying thing is that I now move in circles where it feels like all this stuff is considered obvious. When I was first learning it, I didn’t feel that everyone knew this stuff — so it was exciting to learn it and explain it on This Week’s Finds. Now I feel everyone knows it.

So, I have to force myself to remember that even among the mathematicians I know, not all of them know all this stuff… so it’s worth explaining clearly, even for them. And then there’s the larger world out there, which still exists.

I think what happens is that when scientists start discussing technical concepts like ‘group completion’ or ‘heterochromatin’, they scare away people who don’t know these terms — and attract people who do. So, without fully realizing it, they become encased in a social bubble of people who know these concepts. And then they feel ignorant because some of these people know more about these concepts than they do.

This phenomenon reminds me of the hedonic treadmill:

The process of hedonic adaptation is often conceptualized as a treadmill, since no matter how hard one tries to gain an increase in happiness, one will remain in the same place.

I think this phenomenon is especially strong for people like me, who roam from subject to subject rather than becoming an expert in any one thing. These days I feel ignorant about particle physics, homotopy theory, higher categories, algebraic geometry, and a large range of other topics. Whenever I blog about any of these things, some expert shows up and says something more intelligent! It tends to make me scared to talk about these subjects, especially when I know enough that I feel I should know more.

I fight this tendency — and I’m admitting it now to help myself realize how silly it is. But it’s funny to look back to my old writings, where I had the brash self-confidence of youth, and hadn’t yet attracted the attention of so many experts.

It’s also funny to think about how these scary ‘experts’, who I may picture as vultures sitting on nearby trees waiting to swoop down and catch any mistake I make, are actually people eager to be admired for their knowledge, just like me.

Posted at March 7, 2023 7:33 PM UTC

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Re: This Week’s Finds (101–150)

When you’ve finished this herculean effort, I think you should set up a place where folks can buy print-to-order bound copies. I’d certainly love to have the complete set of This Week’s Finds sitting on my shelf. I’d loan it to students, look things up…

These days I have some expertise in some areas (and not in others). TWF is a primary reason for that: it was my first introduction to most of the things I now study.

Posted by: Theo Johnson-Freyd on March 8, 2023 12:14 PM | Permalink | Reply to this

Re: This Week’s Finds (101–150)

Thanks! I’m glad This Week’s Finds has helped you. You are now a scary expert on a lot of things I like.

I’ll make a printed version available someday if I can find out a nice way. I’ve always thought a printed version of This Week’s Finds would be less useful since the links won’t work… but I still prefer reading explanations of math that are written on paper.

Posted by: John Baez on March 8, 2023 5:19 PM | Permalink | Reply to this

Re: This Week’s Finds (101–150)

yay for print versions

Posted by: a on March 9, 2023 4:18 AM | Permalink | Reply to this

Re: This Week’s Finds (101–150)

Duly added to the nLab page for 24.

Posted by: Blake Stacey on March 8, 2023 2:13 PM | Permalink | Reply to this


The greater someone’s intelligence or knowledge, the more likely they are to have imposter syndrome. The lower someone’s intelligence or knowledge, the more likely they are to have Dunning-Kruger syndrome. The more you know, the more you know you don’t know.

I would rather have broad knowledge of many subjects than specialized expertise of one subjects. You can see connections that would specialized expert would miss. It is possible that your articles, noting subtle but profound hidden connections, inspired the experts to consider things they would never have otherwise considered.

Posted by: Jeffery Winkler on March 9, 2023 4:17 AM | Permalink | Reply to this

Re: Jeffery

The greater someone’s intelligence or knowledge, the more likely they are to have imposter syndrome.

That’s very flattering to people with imposter syndrome, so it’s a good way to cheer them up, but now I’m wondering if there’s some evidence for this.

By the way, the term ‘imposter syndrome’ seems to be locked in, but I don’t usually feel like I’m an imposter: I just sometimes feel like I’m not good enough. But I guess ‘feeling not good enough syndrome’ is not very catchy.

Posted by: John Baez on March 9, 2023 9:53 PM | Permalink | Reply to this

Re: Jeffery

I think “imposter syndrome” is a very good term for its original use, as described for example in this Wikipedia article, to refer to one not only doubting one’s skills or accomplishments despite external evidence of those skills, but also fearing being exposed as a fraud. But, as happens with many technical terms that pass into common usage, it has come to be applied ever more broadly, and now people frequently talk of “imposter syndrome” anytime someone simply doesn’t feel like they’re good enough. Which is really a broader phenomenon — if you don’t think you’re as good as you should be but also don’t think you’ve tricked people into believing that you are, then there’s no question of fraud.

Which is of course not to say that feeling not good enough is a pleasant feeling. But it’s not what the term “imposter syndrome” was coined to describe.

Posted by: Mark Meckes on March 10, 2023 3:28 AM | Permalink | Reply to this


I’m slowly working through the earliest weeks. It’s interesting seeing what people were grappling with at the time. This note especially tickled me:

C. The 64,000 dollar question: how does all this generalize to 4 dimensions? What sort of algebraic structure corresponds to a 4d topological lattice field theory? It is becoming increasingly clear that 4d field theories will involve some kind of “higher algebra” that we are only beginning to understand.

I have to assume since the mid nineties we know a lot more about these boutique algebras and have made all sorts of progress modeling quantum gravity or at least topological field theories these days? As someone with not much physics background it’s exciting to hope so!

Posted by: Tim Haloun on March 10, 2023 6:50 PM | Permalink | Reply to this

Re: Curious

People have made a vast amount of progress understanding the algebraic structure of topological quantum field theories in 4 dimensions. For starters, see the final entry of this chronology, the 1999 entry:

(and also the earlier stuff if you’re not fully up on the background material, much of which was discussed somewhere or other in This Week’s Finds.)

But that was 1999 — then came 24 more years of work! People did manage to categorify a bunch of quantum groups, as I was already hoping in “Week 2” — here’s a random reference relating different approaches:

And people have used these ideas to study topology in 4 dimensions! It’s a sprawling subject with lots of people doing lots of cool things; I wish people would unify everything and clean it up in a magnificently written textbook, but I guess it’s not time for that yet.

Quantum gravity, on the other hand, is a deeply confused subject. A lot of people are excited about a lot of things, but these things keep changing in a way that does not convince me real progress is happening… and some events, like the wormhole publicity stunt, make me feel it’s what Kuhn called a “degenerating research program”. I try to not think about it: there is a lot of other good stuff happening these days.

Posted by: John Baez on March 10, 2023 8:13 PM | Permalink | Reply to this

Re: Curious

I think “degenerating research program” was Lakatos, not Kuhn.

(Not to be confused with a “degenerate research program”, which is a research program that resists a collapse into irrelevance because of Pauli exclusion.)

Posted by: Blake Stacey on March 11, 2023 5:23 AM | Permalink | Reply to this

Re: Curious

I think “degenerating research program” was Lakatos, not Kuhn.

Whoops! Now I’ll be in trouble with David.

(Not to be confused with a “degenerate research program”, which is a research program that resists a collapse into irrelevance because of Pauli exclusion.)

So you’re saying at least degenerate matter still matters.

Posted by: John Baez on March 12, 2023 12:07 AM | Permalink | Reply to this

Re: Curious

Whoops! Now I’ll be in trouble with David.

Absolutely! This was from Lakatos’s attempt to say that Kuhn was wrong to think there’s no way to appraise the relative success of rival programs/paradigms, that we can assess through “honest score-keeping” how things are going.

Kuhn had warned that the criteria of success are to a degree embodied in the paradigm, so there’s no paradigm-neutral way to compare rivals.

Posted by: David Corfield on March 12, 2023 10:06 AM | Permalink | Reply to this

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