Geometric Irony

This morning on my drive to work, I was listening to an old (May 2018) episode of Conversations with Tyler, the second half of which was a discussion between Nassim Nicholas Taleb and Bryan Caplan on the problems with education. The recurrent examples of these problems are poetry and geometry, at least one of which probably scares you. Their issue wasn't that there's anything inherently wrong with poetry and geometry, in fact they think that both are perfectly good hobbies that everyone should have (Taleb, I should say, was a little more tolerant of your poetry classes, but not that much). But they worry about the practical problem that very few students will pursue a career in them, and students graduate from school at eighteen or twenty-two having forgotten approximately 100% of the poetry and geometry that they "learned"¹ in class and having no idea what kind of career will suit them. There aren't many poets in the world, and there are even fewer that have learned to convert verse into cash with ab efficacy sufficient to fill a refrigerator. And what fifteen year olds need to do is to sample the possibilities of how they can fit into the world, like plumbing and customer service.²

The liberal arts are best left to Sunday afternoons on the porch and autumn walks in the park.

I had finished the first half (where Tyler Cowen interviewed Taleb) and started on the part where Taleb talked with Caplan about his book The Case Against Education (both segments included a lot of talk about Taleb's books, especially Antifragile),⁴ when it was time to stop and get my cup of coffee.² I pulled out a paper on the history of the renormalization group and a pad of Bristol board, and started the day off by working on a cartoon for class and a bikini girl for Instagram while waiting for the caffine to get me attentive enough to read an academic paper. While I was drawing the cartoon, which is about integrating to find a volume, a local antique dealer, J., came by and we talked about finding volumes a little bit.

The cartoon, I hope you can see,⁵ shows the Riemannian process behind the integral for finding the volume of the pyramid. J. saw the point right away ("what about the steps?"), and pulled out a problem for his store. The way he'd have to solve the problem was, he said, to weigh a stick of butter, then to carve a scale model out of it, weigh again, and then do some ratios. This is a very good method.⁶

When he was in Versailles and saw a structure whose somewhat triangular shape he wanted to reproduce for his store, where he would put featured paintings at one point, antiquities on another, and books on the third. The shape was an equilateral triangle with the tips cut off (so, a hexagon), where the long edges had a slight inward curve. He'd add some walls and french doors as well, but what he wanted to know is that if the distance between next nearest points was 16' and the size of the cut was 4', what is the volume of concrete required to build the 1' thick base of the structure? I calculated it out with a little geometry, the quadratic formula, and a rather annoying bit of vector calculus (which was overkill).⁷ Then C., the old Airforce master sergeant, came by and we talked about history books and historical novels until the larger group started coming in. J. took the sketch and calculation, I went back to drawing, and some girls sat behind me watching me draw the leopard print on the pinup's bikini.

Then, when I got back into my car to get to work, I listened to the next fifteen minutes of the discussion, where Bryan Caplan and Nassim Nicholas Taleb continued their discussion on how unlikely it was that you'd end up using things like geometry or art in your day to day life, and thought about the wisdom of their words.

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¹ In fact, students lose the factoids they memorize for high school and undergraduate texts with a half life of about two weeks. So they'll always "remember" something from your class.

However, it might be the wrong thing. I remember talking to a high school friend just a year or two after graduation who was sure that Lamrkian evolution was correct, because he'd read it in the HS biology textbook. He even remembered the specific example: proto-giraffe mommies stretched their necks to reach higher leaves, and so their babies had longer necks. And then this repeated over generations until giraffes were the long necked freaks of nature we see in zoos today. This was in fact in the book (I remembered it, although I never studied in high school, so I don't know why), but it was there as a historical contrast to Darwinian evolution.

² And if you know me, especially if you knew me twenty years ago, you might remember my old rants against mindless education. And I still feel that way. I think, on the whole, Caplan and Taleb are correct. I'm not a fan of the pyramid schemes of psychology, but education kids love them, especially Maslow's heirarchy of needs. Poetry, art, and music are offerings to the sacraficial altar of self-actualization at the top of the pyramid. Caplan, and to a lesser extent Taleb, want the schools to focus more on the bottom steps of the pyramid, helping kids build the skills to keep themselves fed, housed, and safe. Those are the fertile soil for spiritual growth.

On the other hand, whenever I hear someone say "it would be better to teach kids EXCEL instead of calculus," I think, "You have to do the calculus before you use EXCEL."

^2½If you're cool, then you know Iggy Pop's feelings are also in tune with Caplan and Taleb from reading his liner notes on the reissue of Raw Power (which I did, of course).

...if you both like Iggy Pop and are literate (which I do and am, of course), which is not guaranteed (and that's the way he likes it; check out his liner notes).

³ I own a copy of Caplan's book and now I want a copy of Taleb's (I've read two others), but I'm about 40 books behind over the course of the pandemic. I usually read at least 50 books a year, but have gone down to a little over 30 each in 2020 and 2021.

⁴ I have a long commute which interacts with a complex morning routine, so this is a very simplified version. I've discussed the jalapeno boudin kolaches elsewhere.

⁵ Hopefully I'll get a way to put images up here.

I did! Ha! Although the screw ups on the cartoon make me nervous. I've spared you the pinup, which is beautiful, but you're not authorized for that kind of titillation. Bring a note to me during office hours from your psychiatrist saying that it's mentally safe for you to view such things, and I'll give you a link.

⁶ Before there was a lot of computer time available, and even when computers were reasonably slow, this was how experimentalists would do numerical integrations on their data. They'd plot out the spectrum on their plotter, very carefully cut out the shape of the specturm, and then weigh it. That weight would be compared with the weight of the paper and the untis on the axes to find the integral.

This is exactly J.'s butter technique.

⁷ If you are Nassim Nicholas Taleb and you really do enjoy doing geometry on your porch on Sunday afternoons, then this is a good little problem for you.