Shape

by Jordan Ellenberg

Ebook, 2021

Status

Available

Call number

516

Genres

Collection

ebooks

Publication

Penguin Publishing Group

Description

"Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. Geometry doesn't just measure the world-it explains it. Shape shows us how"--

User reviews

LibraryThing member neurodrew

I read Ellenberg's "How Not to be Wrong" about two years ago, and enjoyed his clear explanations of math problems. This was a little less satisfying, athough just as entertaining. In many of his examples I did not see much geometry, and Ellenberg did not always explain the connections. I read one

chapter on epidemic propagation twice without getting it down. His nuanced argument about voting districts and gerrymandering was very enlightening. It was also interesting to learn about the connections between statisticians, Poincare and Einstein in the early 1900's.

I marked several passages.
-Poincare was not a visualizer, and would draw a figure from memory by recalling how his eyes had moved along the figure.
-Bachelier, writing in 1900 after analyzing stock and option prices, concluded that mathematically, the expected gain of a speculator is zero
-Mathematicisn Hilda Hudson (working with Ronald Ross, who figured out that malaria was carried by mosquitos and was looking to perfect the mathematics of epidemics) came up with the following epigram in 1910: "The thoughts of pure mathematics are true, not approximate or doubtful; they may not be the most interesting or important of God's thoughts, but they are the only ones we know exactly)
- In English, there are four ways to put the stress on two syllables: unstressed/stresses - an iamb; stressed/unstressed - a trochee; both stressed - a spondee, and neither stressed, a pyrrhus.
- In the discussion of the Fibonacci series, the "golden ratio" appears as a ratio of later terms of the sequence. The golden ratio is exactly given as one plus the square route of 5, dived by 2. The ratio is an irrational number, and it digit order can be shown to be the most random order of all irrationals.

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LibraryThing member rivkat

Ellenberg’s paean to geometry. Sadly, I didn’t like it as much as his first popular book; he tells you that eigenvalues can do important things, but doesn’t quite explain what they are. Still, it’s amusingly written: “If you’re finding it hard to imagine what a fourteen-dimensional

landscape looks like, I recommend following the advice of Geoffrey Hinton, one of the founders of the modern theory of neural nets: ‘Visualize a 3-space and say “fourteen” to yourself very loudly. Everyone does it.’” Ellenberg loves geometry because it offers real answers—not necessarily important ones, but indisputable ones. Geometry can also offer insights for things like gerrymandering; he excoriates the Supreme Court’s willful misunderstanding of what anti-gerrymandering advocates seek (not equal representation—that would actually be weird—but representation that doesn’t reflect extreme partisan bias in drawing boundaries). As he explains about states like Wisconsin, “where Republicans get a majority of the statewide vote, the gerrymander doesn’t have much effect; those are elections where the GOP would get an assembly majority anyway. It’s only in Democratic-leaning environments that the gerrymander really kicks in, acting as a firewall.”

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LibraryThing member BraveKelso

A narrative of the role of geometry in underpinning other branches math and math applications including the random walk theory, which was developed by epidemiologists dealing with malaria and developed by Markov chains. In part, the book builds to an argument that math can help to identify

gerrymandered electoral boundaries. In part, sections seem to have been tailored to explain the statistics of epidemics and modelling. It has mathy parts which invite the reader to play with simple arithmetic, but these do not explain the higher math. It has some marginal relevant sections - for instance Abraham Lincoln's fascination with Euclid's theorems, but many stories about advances in math and the intuition of leading geometers - e.g. Henri Poincaré. Readable, relatable, relevant, recommended.

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LibraryThing member ehousewright

ok, i'll need to read this again and again if i want to follow it all, but I found it fascinating. He writes of how math education could be changed (back?) to a more hands-on, discovery basis and I do think he has a point there. Algebra startled me, geometry befuddled me, calculus -- well. But his

examples give you some confidence that with actual thinking time these tools might make sense.

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LibraryThing member steve02476

Good meandering explanation of geometry in our everyday lives. (Geometry being a much broader slice of math than I realized. ) I found the first few chapters a little too all-over-the-place but after a while I started enjoying the style and by the end of the book I was really appreciating it. The

penultimate chapter about congressional districting and gerrymandering was great - he shows some of the math aspects but also really explores the political and philosophical aspects as well - defining districts is a lot more interesting of a problem then I had realized.

There were a few pages here and there that I just skimmed. It wasn’t that he was doing complex math, he was just going over something relatively simple in a step-by-step way and it felt tedious so I skipped some of those. But that was just maybe a dozen or two pages out of 400.

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