• David Richeson, Euler’s Gem: The Polyhedron Formula and the Birth of Topology

Pretty cool book, much of which was lost on me; it’s a popular-ish math book, and I think I placed too much emphasis on “popular” and not enough on “math”. The secret of reading math books is that you don’t read them like you’d read a novel. You need to sit down, do proofs, write code, come up with counterexamples, try to visualize things, etc. I couldn’t do this when I was lying on the beach.

Regardless, even at the fairly shallow level at which I approached this book, there’s a lot of interesting stuff. The book centers on the Euler characteristic, the very beautiful observation that any convex polyhedron (think cube or pyramid) which has V vertices, E edges, and F faces satisfies V-E+F=2. This is the earliest example of what we now call a topological invariant — a property of a mathematical object that remains unchanged even if you distort the object in various approved ways, like stretching. Other topological invariants include the genus of a shape, i.e., the number of “holes” it has, which is how we end up with the notion that a coffee cup and a doughnut are topologically identical: you can deform the one into the other without tearing, and the number of holes remains the same.

Topology is, in this way, a “global” view of a shape, but the global view can be used to prove theorems about local attributes of that shape. The book contains some elegant proofs that use the Euler characteristic, for instance, to prove theorems about the interior angles of a polygon, or to prove that there exist only five Platonic solids.

The book contains applications, too, not just examples from the domain of pure mathematics. Here it samples from graph theory, which is a branch of mathematics you touch every time you use Google Maps, and from differential equations, which are the lifeblood of physics. One of the more famous topological results proves that every continuous function on a space that’s topologically equivalent to a sphere has a fixed point — a consequence of which is, for instance, that at any moment there is always at least one spot on the earth at which the wind is not blowing.

I need to reread this, and reread it better. The author’s appreciation for the beauty of his subject is palpable. I saw him speak recently at an MAA event in D.C., where he went over some of the classic mathematical impossibility results; a book is apparently forthcoming. If it’s anything like the other work I’ve seen from Richeson, it’ll be a must-read.

• Rachel Kranson, Ambivalent Embrace: Jewish Upward Mobility in Postwar America

This is a fascinating look at American Jews’ discomfort with their increasing affluence after World War II. The shtetl looms large in American Jewish ideology: when they were poor, goes the mythology, they had more character, built a stronger community, and paid more attention to religious studies; American affluence made them lazy and weak. At the same time, American Jewish identity drew heavily on Lower East Side socialism — another identity that had a hard time surviving as American Jews grew wealthy and moved out to the suburbs. And the part of Jewish self-identity that centered around Jewish intellectualism suffered as Jews headed into “the professions” and became grubby company men.

One of the allures of the new state of Israel, then, was that Jews could return to a tougher, more authentic version of Judaism. The stereotype of American Jews as weak and nerdy could be replaced by the stereotype of the Israeli soldier. Hence the allure of the Birthright trip to Israel, and of the kibbutz.

The idea of the shtetl’s being baked deeply into Jews’ self-image is fascinating to me. I wonder whether similar “life was better when we were poor” ideas exist in other religions. Does the Irish-American self-image, for instance, contain a belief that they were more authentically Irish when they were suffering during the potato famine or traveling to the United States in steerage?

Kranson embeds this Jewish conversation in a broader conversation, happening at the same time, about postwar conformity and suburban homogenization. Outside of Jews, did any other ethnicities address this conformity by venerating the poverty and suffering from their recent pasts?

Overall, this book is a fascinating look at what happened to Jews as consumerist 20th-century America closed in on all sides.

(Full disclosure: Professor Kranson is a friend of mine. I would have found her book delightful even if she weren’t.)

• George Saunders, Lincoln in the Bardo

I don’t get what the fuss was about. This was the It Book of 2017. In it, we see Lincoln visiting his dead son’s body as it awaits burial, the ‘bardo’ being a waiting room for souls on their way from this world to the next. The souls arrayed around him flit about, discussing what will become of little Willie Lincoln. Eventually … without giving anything away, the souls decide that something must be done to ensure that Willie leaves the bardo and enters his permanent afterlife, and A Man Learns To Move On.

This book is trying and failing to do something. It’s some combination of sci-fi/fantasy, an attempt at being affecting, and a bit of silliness (the souls sometimes engage in frenetic group copulation). I found it deeply pointless.

• R.R. Palmer, Twelve Who Ruled: The Year of the Terror in the French Revolution

This is certainly the best book I’ve read thus far on the (low point of the) French Revolution, namely what we today call the Great Terror. On the one hand, it doesn’t skimp on moral censure against the Committee of Public Safety, which famously made such liberal use of the guillotine. On the other, Palmer takes care to note the very real threats that the Republic was under from all its neighbors, who thought France’s chaos and weakness gave them a lovely opportunity to invade. At the same time, the country was by no means internally unified: the famously Catholic French did not all support nationalizing church property and building a new currency on the stolen lands. Much of western France was in an armed uprising against the Revolution. So the twelve members of the CPS were trying to re-establish a government in the Weberian sense: a monopoly over legitimate violence in a defined area. Under the circumstances, I can understand why they’d see no difference between ideological disagreement and treason. It’s a short jump from there to the revolution’s devouring its children.

My historical imagination runs into a bit of a wall right there. Because identifying ideological disagreement with treason is interlaced with some ideas of Rousseau’s, which were thick on the ground at the time. As any number of authors have mentioned (I think here of Russell’s History of Western Philosophy), Rousseau believed in something called the “general will,” which was not to be confused (I gather) with anything so earth-bound as a poll of the real people’s opinions. Instead, the general will seems to be some spiritual, almost Platonic, aspect of an idealized people. By definition, the will of the people was indivisible. Says Palmer: “It was a cardinal principle of the Mountaineers (and of the Girondists, too, who in their time had been Jacobins and were still Rousseauists) that the people, the real people, could not be divided in its will.”

I have a very hard time understanding what that could possibly mean, or why — if I attach a reasonable meaning to it — anyone could believe it. If “the people” means … well … the people, then anyone who has ever interacted with other human beings will recognize that disagreement happens (even within one person!); wills are divided. If, on the other hand, “the people” means something more idealized, then why does it matter what this idealized people believes? That way lies Cartesian parody.

You can see how this notion of The People (capitalized) could lead to a lot of people (lowercase) losing their heads. Again to quote Palmer, “Robespierre easily identified with foreign conspirators anyone who deviated from the program of the Mountain.” If the French People is, by definition, as one, then disagreement with the French People is, by definition, anti-French.

I need to get inside the heads of these people. I need to get inside the head of Robespierre, in particular. How does this sort of ideology begin? How do others become part of his movement? They can’t all be insane. They can’t all be power-mad.

In any case, Palmer tackles the twelve in the CPS as well as you could hope for: a single chapter for each of the twelve, each of which is a vigorous character study. And the characters—the haughty, incorruptible Robespierre, whom I can only imagine with his lantern jaw raised heavenward; the fiery ideologue Saint-Just; the great orator Danton; Carnot, the engineer of the revolution—are all worthy of these sketches. The French Revolution, if nothing else, is a gripping story. And the CPS, in particular, needs a sympathetic reading, which Palmer provides.

Finally, Palmer’s attitude reminds me a lot of E.P. Thompson—specifically Thompson’s refusal to reduce all human action to the mechanical, ineluctable movement of the dialectic. Thompson and Palmer are both humanistic, in the sense that they believe the goals of people and of movements matter. This might be the ultimate source of their historical imagination, their sympathy, their attention to detail, and their eye for storytelling. It makes their books a pure delight to read.

• Karl Marx and Friedrich Engels, The Communist Manifesto

Hard to think of anything to say here that you don’t already know. Maybe the only point worth emphasizing is how much Marx and Engels admired what the English bourgeoisie had accomplished in such a short time.

• E.P. Thompson, The Poverty of Theory and Other Essays

The title essay is a sustained attack on the Marxism of Louis Althusser, about whom I knew nothing when I started the essay. It’s more sarcastic and vitriolic than some of the other Thompson I’ve read, but the heart is the same: a belief that humans matter, and that anyone who tries to reduce social movements to mere abstract social forces is doing violence to the movements. Here Thompson goes a step further, denouncing Althusser as a barely closeted Stalinist, when the Soviet invasion of Hungary in 1956 and Khrushchev’s “cult of personality” speech of the same year should have permanently emptied the world of Stalinists. Thompson ties the evils of Stalinism, in part, to the mechanistic view of history, which turns individuals into mere cogs in a machine. If people don’t matter, and if history is going to move according to its own logic, then the blood drains out of the movement and it hardly matters whether we liquidate the kulaks.

At the base of Thompson’s alternative view is his understanding of class, about which he writes in The Making of the English Working Class:

I do not see class as a “structure”, nor even as a “category”, but as something which in fact happens (and can be shown to have happened) in human relationships. … class happens when some men, as a result of common experiences (inherited or shared), feel and articulate the identity of their interests as between themselves, and as against other men whose interests are different from (and usually opposed to) theirs.

You can see how this understanding of class would shape his understanding of everything that rides on top of it. If classes aren’t immutable or predefined, then the movements of people into and out of classes, and their understanding of who stands against them, are also not immutable or predefined. To my eye, understanding class in this way leads to a much more supple and rich eye for history. Indeed, The Making of the English Working Class itself wouldn’t have had much at all to say if it had flattened the English working class along Althusserian lines.

The other essays in the collection are bound by a similar humanism. “Outside The Whale” begins with someone else’s sarcastic description of a speech by Bertrand Russell, in which the 83-year-old Nobel laureate pleaded with the public to vote Labour in order to prevent nuclear annihilation. It continues into George Orwell’s scorn for anyone, it seems, who feels that anything in this world matters. Thompson is on the side of those whose conscience still burns.

In “The Peculiarities of the English”, Thompson defends his countrymen against those orthodox Marxists who fault the country for ideological impurity. Again, this is of a piece with the book’s general iciness toward continental-European Communists, whose theory didn’t account for the humanitarian disasters of actually existing Communism. French Marxism, in Thompson’s eyes, was intellectually corrupt and had managed, besides, to weaken real labor movements.

It’s a beautiful, engaging book, though I admit that a lot of it was taking place on topics about which I know nothing (beyond what Thompson educated me on). The only Marx I’ve read is the Communist Manifesto (see supra), and dribs and drabs here and there (e.g., “The 18th Brumaire of Louis Bonaparte”). I’ve not read Marx enough to know which ideas were his, and which were inventions from later on.

Though I’m not sure whether it matters who invented what; as a general matter in my life, I’m inclined to think it doesn’t matter. To take a totally unrelated topic: it doesn’t really matter whether Jesus’s teachings were a misreading of Judaism, or whether modern Christian practice was a misreading of the New Testament, or whatever. At one level, sure, it matters intellectually that someone misread a book and built a movement from that misreading, but by this point the movement is more important than the “true” meaning underlying the text. Fussing over true original meanings is both fundamentalist and utterly beside the point.

So I’d like to read Marx, not to understand what “true Marxism” is, but just to understand the conversation. Then maybe I’d read Althusser, though Thompson certainly suggests that leaden philosophical French prose is not for the faint of heart. Or maybe I’d read others for whom Thompson has more respect. The point is just to get into the conversation; outside of that conversation, Thompson doesn’t make much sense. I suspect he’d want me to engage with the texts and then get back to him, and so I shall.

• Thomas Paine, The Rights of Man

I read this as a followup to Burke’s Reflections on the Revolution in France, as indeed it was; I read it also as the foundation (so E.P. Thompson tells me) for a good century of British labor-movement mobilization. It’s hardly a close call: Paine got the better of this argument with Burke.

When he’s not defending tradition for its own sake, recall, Burke is telling the French that their king isn’t such a bad guy. Paine begins by demolishing that point, like so:

Every place has its Bastille, and every Bastille its despot. The original hereditary despotism resident in the person of the king, divides and sub-divides itself into a thousand shapes and forms, till at last the whole of it is acted by deputation.

The French system of government wasn’t just corrupt at its head; corruption had worked its way into the remotest tendrils of the empire. Hereditary monarchy was the original sin that led to all the others. Hereditary power bore no connection with merit:

the idea of hereditary legislators is as inconsistent as that of hereditary judges, or hereditary juries; and as absurd as an hereditary mathematician, or an hereditary wise man; and as ridiculous as an hereditary poet laureate.

Hereditary monarchy, in England as well, had become a device for impoverishing the people in order to fatten Walpole and his cronies:

In reviewing the history of the English Government, its wars and its taxes, a bystander, not blinded by prejudice nor warped by interest, would declare that taxes were not raised to carry on wars, but that wars were raised to carry on taxes.

So Paine’s book wasn’t just a defense of his brethren across the Channel; it was a sustained attack on the wisdom of any inherited monarchy at all. And pace Burke, this wasn’t a matter of airy theory overturning a system that had generally worked well for centuries; it was a matter of unaided human reason, available to everyone, finally realizing that the emperor wore no clothes:

certain am I, that when the people of England come to reflect upon them they will, like France, annihilate those badges of ancient oppression, those traces of a conquered nation.

No wonder Burke was terrified. According to Thompson, the entire English ruling class shook at the earthquake Burke initiated.

Stylistically, too, Paine is running circles around Burke:

How dry, barren, and obscure is the source from which Mr. Burke labors! and how ineffectual, though gay with flowers, are all his declamation and his arguments compared with these clear, concise, and soul-animating sentiments! Few and short as they are, they lead on to a vast field of generous and manly thinking, and do not finish, like Mr. Burke’s periods, with music in the ear, and nothing in the heart.

I’m genuinely curious if anyone found himself or herself convinced, in the late 18th century, by Burke as against Paine. From this vantage, a couple hundred years on, that would be hard to believe.

I wonder, finally, whether Paine’s book initiates a particularly “American” style of writing, as against Burke’s late-18th-century British style. The Burkean style is one I’ve always had a hard time stomaching: rather than go from fact to fact and then jump to an abstraction, it basically starts and ends in abstractions. I’m sure there’s empirical Hume out there, for instance, but the habit of dealing in pure abstractions—about the nature of man or what have you—drives me a little mad. I’m much happier with the Paines of the world.

• Isabel Wilkerson, The Warmth of Other Suns: The Epic Story of America’s Great Migration

Absolutely gripping, and indeed “epic”, story of African-Americans’ Great Migration from the South to the industrial cities of the North, stretching from World War I through the mid-1960s. Wilkerson tells this story through four specific people—selected from among hundreds of people whom Wilkerson interviewed—who made the journey from the South to Los Angeles, to Chicago, and to New York. Through Wilkerson’s storytelling, I was there with them as they told only one or two people about their plans to leave their homes—keeping the story quiet so that they wouldn’t be lynched on the way out of town. It made for almost unbearably tense reading.

There are some ground-level details that I never would have thought about, had I not read Wilkerson’s book. For instance, trains traveling south to north would eventually reach a point where segregation ended. Going north to south, blacks who had been sitting comfortably among whites would now need to move into segregated passenger cars; the switch would happen right around Washington, D.C., the unofficial boundary of Jim Crow. This is just an impossibly odd transition, and it’s hard to imagine decades of American life during which it was treated as a frustrating but regrettable necessity.

The book’s strength is in the personal stories, though it also takes some time in each chapter to scale out and examine what was happening nationwide. I could have appreciated some more on, say, redlining in the north, or white flight, but those would have made this a much different book. As it is, Wilkerson’s ability to keep the macro and the micro in focus at the same time is a great feat—as when she describes a black man’s creation on a small scale of a labor union within a single orange grove, which he can do because so many blacks have left the South that few are left behind who are willing to do agricultural work.

There may be other books that cover other aspects of the Great Migration, but it’s hard to imagine Wilkerson’s book ever being surpassed in its storytelling ability. And as those who were alive during the Migration slowly disappear, her book may turn out to be the last great oral history of the era.

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