Book review: Sleight of Mind (Matt Cook)
This book covers a range of science and mathematics topics by focusing on paradoxes — surprising results, or seeming contradictions. This is an effective way to quickly give a taste, and a few deeper results, across a range of areas. (Chapter list included below.)
Such a range of topics in a single book often means that some are fumbled, sometimes badly. Keeping each to a single chapter obviously mandates omissions and simplifications but, pleasingly, I didn’t notice any screw-ups. (Although perhaps that’s the bliss of ignorance since I’m not an expert in any of the subjects.)
(At the end one learns that the chapters on physics were written by other authors, who are experts in those areas. That’s probably a wise choice and it explained some stylistic discontinuities.)
Personally I was familiar with probably half of the paradoxes covered, which did make some of the chapters a little skippable. But I found that the unfamiliar ones were useful enough to justify hunting down. The chapter that left the strongest impression on me was actually the first one, on infinities. I think I’ve actually come across all of the paradoxes in that chapter — Hilbert’s hotel is pretty famous — but having them all laid out in series left me wondering whether infinity wasn’t a mistake:
Mathematics could have left the question of “how many natural numbers are there?” as undefined, like dividing by zero. There are as many as you want, but it’s not an expressible quantity. Instead we gave it a name and explored what followed from it. That’s not a bad idea in general: giving sqrt(-1) a name and seeing where that led turned out really well! But, as far as I know, the structure behind infinity is bereft, useless, and full of nonsense. Having the paradoxes written out, one after another, drove that home. Although perhaps I’m wrong, perhaps there’s a rich and useful study of infinities that I’m not aware of, but that chapter left me wondering that maybe we shouldn’t have bothered.
The chapter on voting (“Social Choice”) was the topic that I was least-well versed in, and was the one chapter that I went back and read again once finished. But voting systems are within the bailiwick of LessWrong so I’m not suggesting that most readers here would find it valuable. But, perhaps, it’s worth reading the chapters that one is very familiar with as an exploration of how paradoxes might work for explaining things to unfamiliar readers. It might be a useful explanatory tactic in one’s own writing.
One hiccup in the book that did distract me:
There are obvious names that you expect to appear in a book like this: Einstein in the physics chapters, Gödel on formal systems, and so on. But the name that comes up more than any other is … Ayn Rand? And for no very obvious reason? I suspected that the author lost a drunken bet to mention Ayn Rand in every chapter or something, and I think a sharper editor would have cut it out. But maybe objectivism has profound and useful things to say in this space and I’m too biased by having slogged through both The Fountainhead and Atlas Shrugged many years ago to try and find what people saw in them to see it.
But I wouldn’t want to end on that note. It’s an impressive book that I enjoyed. The format makes random access effective and the main downside is that you might already know a lot of it.
Zeno’s paradoxes of motion
Supertasks (paradoxes resulting in physically impossible systems)
Social choice (voting)
Induction (more worthwhile than it sounds)
Operations (basically “miscellaneous”)
A poem by 3Blue1Brown.