Shape: The Hidden Geometry of Absolutely Everything

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there is no reason to know very many digits of π. There are real-world contexts where you’d want to know seven or eight digits, sure. But the hundredth digit? It’s hard to imagine what you’d need that for. Forty digits is already enough to compute the circumference of a circle the size of the Milky Way to within the size of a proton.

Ellenberg can ramble; there are a few times I felt the book was turning into a primer on COVID-19 modelling (which isn't bad, but didn't feel like the book I started reading). At times, the emphasis on geometry works (especially when discussing huge multi-dimensional spaces), but sometimes I felt he was pushing too hard to make something geometrical (e.g., the SIR model for epidemics). Overall, the theme is there to give Ellenberg a focus, but it's not carried out strongly. We want everyone to understand the importance of reading for pleasure and the benefits it brings not just for children but also for adults.The sections on gerrymandering are excellent. I learned a lot, and Ellenberg did a fantastic job explaining why proportional representation wasn't the ideal metric for dividing up districts and why random walks through the space of possible congressional districts can be a powerful tool.

This was just all over the place for me. At times, it was a two star read and somewhat boring (quite possibly because I know most of the math Ellenberg is describing); at times, it was a wonderful application of mathematical principles. I was sometimes jealous of how well Ellenberg described some ideas. (Yes, that's a problem I am ascribing to the book that really applies to me.) p. 205 An autonomous vehicle may be able to make the right choice 95% of the time, but that doesn’t mean it’s 95% of the way to making the right choice all the time; that last 5%, those outlier cases, might well be a problem our sloppy brains are better equipped to solve than any current or near future machine. The ultimate reason for teaching kids to write a proof is not that the world is full of proofs. It’s that the world is full of non-proofs, and grown-ups need to know the difference. It’s hard to settle for a non-proof once you’ve really familiarized yourself with the genuine article.

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Spoiler: this book is about math because everything is about math. And this is a former math-hater saying this. Shape is University of Wisconsin math professor and bestselling author Ellenberg’s far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.