Books: How to Not Be Wrong, 17 Equations That Changed the World
Movies: Lady Bird
How to Not Be Wrong by Jordan Ellenberg
This is a book about using math — and, more generally, mathematical thinking — to guard against fallacies and poor decision-making in real life.
This is like a lesser version of Algorithms to Live By, that impressive and eye-opening book about cleverly applying computer-science concepts (like stopping theory or packet control) to your everyday life. How to Not Be Wrong isn't at that level — it occasionally falls into very familiar territory (yes, book, I know what the Gambler's Fallacy is) — but it clearly presented some ideas here and there that I hadn't thought of.
One of my favorites: when you're using percentages, try to avoid dividing by things that can go negative. Say I have a fruit store. You are a fruit supplier. You show up one morning and give me five apples and five oranges. At that same moment, in a fit of pique, I throw five bananas in the trash. So: my net change in fruit has been (5+5-5=) +5 fruits.
At this point, we could do ill-informed division and say that the apples are responsible for (5÷5=) 100% of the net change in fruit. We could also say that the oranges are responsible for 100% of the net change in fruit. This is obviously insane and stupid, and it's what happens when your denominator ('net change in fruit') could theoretically go negative. (Imagine how the percentages would go if I'd thrown away *ten* bananas, and the denominator was *zero*.)
You think nobody would do that, but let me tell you about the time Wisconsin claimed to be responsible for 80% of America's annual job growth...
The book also has fun with "humans assume every function is linear", and an absolute *field day* with probability, where human beings just can't seem to come to a single non-stupid conclusion.
And he does a fascinating job of explaining that modern 'common sense' is built on centuries of math. An example: France had a form of government life insurance. It paid out, say, thirty francs when you died. And you paid into it, say, one franc a year. And the key bit: you paid in the same amount no matter what your age was. A weird thing: the government didn't realize that this made no damn sense. An even *weirder* thing: the French *population* didn't realize they could absolutely game the government. The math of it — adding things up and realizing that it's essentially free money for the elderly — wasn't common sense among the population. Not 'til we all understood probability a little better.
The prose is ably presented, a bit breezy, with amusing jokes popping up now and again. He presents the math well, and has the good sense to use formulas where they're appropriate, but sparingly. If you have a math background, How to Not Be Wrong is kind of hit-or-miss with respect to teaching you anything new. But it's still a fun, casual read.
17 Equations That Changed the World by Ian Stewart
This is exactly what it says on the tin: a listicle book about important mathematical equations.
But it is the very best version of that book that you can imagine. I do love that the title seems to tilt at the very nature of pop-science books — at the publishers, for example, who (allegedly) told Stephen Hawking that every formula he included in A Brief History of Time would halve its book sales. This book loves equations. It makes a rather poetic argument that equations are beautiful and important — that the equals sign itself is a way of drawing powerful equivalences between things that we never thought of as the same: the sides of triangles; error codes and orange-packing; matter and energy; and on and on.
And in that framework, the individual chapters really shine, each one telling one story of a discovery and a connection that radically shifted technology and common sense. (Apparently gambling was really interesting when nobody had a gut feeling for expectation values. And hell, *lots* of things were really interesting when nobody grokked fractions.)
Taken together, they serve best as the story of mathematics itself — which, viewed from one angle, is three thousand years of humanity grudgingly saying, "Okay, fine, we'll call that silly thing 'a number'" — first for whole numbers, then fractions, then zero, then irrationals, then transcendentals, then imaginaries and complexes, then infinity, then variously-sized infinities, and so on. (Who knows what they're dreaming up now.)
I was astonished to actually learn a few great things. The chapter on Euler's polyhedral equation (V-E+F=2) is astounding, with a gorgeous proof that finally, after forty-mumble years, made the penny drop for me w/r/t what topology is all about. And even the material I kinda knew already, the author presented very capably. It only really starts getting out of his hands with the latest chapters, like entropy and relativity. Once he's out of the wheelhouse of pure math, and trying to explain thermodynamics and cosmology, he's kind of out of his element. He understands it well enough to know it, but not well enough to explain it. (It winds up in similar territory in the Black-Scholes chapter about economics.)
It also fails a bit when it's discussing probability — the book handles the math itself well, including all the history and derivation and progress over time. But it ventures into "here's what popular perception keeps getting wrong about probability", which is not really the book's wheelhouse. (This is one of the few subtopics where How to Not Be Wrong is the far more interesting read.)
But when the book sticks to its core subject, it excels. It's great to read a pop-math book that isn't desperately saying, "Math isn't what you thought — it's something hip! and cool!" It's instead saying, "Math is what you think it is, and that possesses a deep and meaningful beauty."
This is the 2017 Greta Gerwig movie about a teenage girl growing up in Sacramento in 2002.
Something I always say: yes, you can make a movie without a plot, but if you do, then you'd better have something really engaging to take its place. Story arcs have been capturing our interest for thousands of years, after all, and abandoning that tool leaves you doing a lot of heavy lifting, capturing and holding the audience's interest in ways that require more labor and talent.
Lady Bird is one of the first movies I've seen in a long time that takes on that challenge and wins. There isn't much of an arc. It's episodic and meandering. Secondary characters come and go. The closest thing to a central question is "will Lady Bird get out of Sacramento?", and possibly "will she and her mother ever get along?" But those are questions you piece together after the fact — they don't drive us from one scene to the next to the next.
So, in lieu of a plot, what is it doing instead?
What it does instead is show us memories: raw, clear-eyed, uncomfortably honest memories. Many women who were teenagers in 2002 talk about how breathtakingly cathartic it is to see their own adolescence finally depicted for them. And even though I'm an old man, I'm still impressed with how real it feels. How many little details Sacramento has. How clearly the dialog echoes real speech. How bad everyone is allowed to be — seriously, I can think of only a couple of characters who are likeable throughout the film. How astoundingly, effortlessly good, across the board, the acting is. (Laurie Metcalf is a goddamn national treasure.)
I never needed to know what happened next, but I was always happy to be there.
And even if there isn't an overall story arc chugging along, individual scenes are plotted perfectly, full of conflict and discovery and reversals and daunting questions that you almost don't want to see resolved. Fairly quickly, abandoning any unity of plot becomes an advantage, because the meandering, scattershot approach lets the movie cover so much *ground*. You see so many characters, and so many places, and so many signpost events in the protagonist's life, that by the end of it you feel (in a good way) like you've watched a whole season of television.
For next week: watching season one of Brooklyn Nine-Nine. I finished listening to an audiocourse about the legal system, and I still need to write about it, plus do some quick writeups for the plays I'm reading.
 Another way to look at it: you're dividing one unit ("increase in apples") by another unit ("net change in fruit"), and pretending those units match when they don't.
 When teenagers who are new to adulting make agonizing noob mistakes, it's a little like watching a horror movie. "Noooo don't tell her she's ugly, you'll — welp, *that's* happening."
Mood: contemplative · Music: none