Philip Davis on the Γ function

Brief description of some recent Brownian motion through books:

A little while ago I read Morris Kline’s Mathematics for the Nonmathematician, which I loved. Somewhere within it, he sang the praises of Philip Davis’s The Mathematical Experience; I think Kline said that Davis’s book was the greatest book ever written on the experience of doing mathematics. So I filed it away on ye olde wish list.

So we come to today, when I find myself bored with all the books available to me. This happens occasionally. The usual trick out of this is to read something by John McPhee. (I’d recommend The Curve of Binding Energy, about nuclear weapons manufacturing and the men who do it. I’d also recommend Uncommon Carriers, about the people who carry packages for us. I would also recommend almost everything else by McPhee, though I couldn’t get into his geology books. Perhaps I’ll give them another try because, outside of Annals of the Former World, he’s batted 1.000 with me.) Without any McPhee (that I hadn’t already read) to hand today, though, and having not found him in my wish list, I looked for something that a) would likely grab my interest and b) was available at the beautiful Cambridge Public Library. The Davis book satisfied both criteria (as did Lives of a Cell), so I went to pick it up.

My memory called forth a book called The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, which I thought might be by the same Davis. (Turns out it was Martin Davis.) This led me to ask the Wiki about Philip Davis. Turns out he won a prize for “an outstanding expository article on a mathematical topic”. Turns out that paper is a historical profile of the Γ function.

The paper is just so fun and engagingly written, and it makes me all the more excited to dive into The Mathematical Experience. Anyone with some college calculus under his or her belt, and some interest in the history of mathematics, will love Davis’s paper. I highly recommend it.

Daniel Imhoff, Food Fight: The Citizen’s Guide to the Next Food and Farm Bill

Green background, yellow-rimmed red letters, and a fist wrapped combatively around a fork

The annual farm bill, in one way or another, governs the most important thing a government could control: the health of its people. It controls matters all the way from the crop (via subsidies, conservation incentives, etc.) to the plate (the school lunch program and food stamps). So it impacts, directly or indirectly, the health of our waterways, soil erosion, and childhood obesity.

Unfortunately, the book is written in such a leaden fashion, while trying so hard not to be leaden, that your attention would best be directed elsewhere. As I read it, I kept thinking of how much better — how much more visceral — The Third Plate was. It’s hard to tell what Food Fight wants to be: it’s got the page layout of something that wants to be a coffee-table book, but the language of academics who’ve been reluctantly drafted into writing for newspapers.

There are many other books in this same field, if not ones that focus so specifically on the farm bill. The place to start, as I will never tire of telling people, is either Pollan’s Omnivore's Dilemma or Nestle’s Food Politics. And when you finish with Food Politics and find yourself depressed that lobbyists have captured the USDA and FDA, move on to Nestle’s What To Eat, which walks with you down the grocery aisle and helps you make decisions in the presence of this fallen world. Or read The Third Plate if you want a chef’s perspective on it — specifically the perspective of a chef who gets out in the world and buries his hands in the soil. Different angles on the same problem, all of them delightfully readable.

But I’d skip Food Fight. Either you don’t know the issues, in which case Food Fight is the last book that will help interest you in them; or you do know the issues, in which case it’s a particularly dreary recitation of facts that you’re already familiar with.

A thought prompted by the iPhone 6

…particularly this 240-fps video shot with the new camera: how long will it be until we have full Edgerton-quality videos? That’s thousands of frames per second. Is something like that achievable on mobile hardware? I have no idea what’s feasible. But I hope, given their basically infinite pile of cash, that Apple is investing money on projects like this that are just cool as hell.

Nancy Horan, Loving Frank

Sepia-toned background. Rectangles marked out on the wall, like the boundaries of corn fields. Shadows cast onto the rectangles. Something-something Frank Lloyd Wright.

Oh, how I hated this novel. It is truly one of the worst novels I have ever read. I am ecstatic upon having finished it. I hated it so much that I hardly want to write anything about it, so as to get the gross flavor out of my mouth as soon as possible. The Bookslut does the needful on this pile of garbage.

The basic gist of the book is:

Mamah: “Oh, Frank Lloyd Wright, you are such a genius, and so different from the drab conformity that I have come to know in my existence as a mother! My husband is actually a great guy. Too bad he’s not a genius on your level. Let us sex.”

Frank Lloyd Wright: “Yes, I will do sex. Mamah, you are so intelligent. We have such conversations, you and I. I know that this will not be clear to anyone else, so I will explain that we have such conversations, you and I.”

Mamah: “Okay. I am glad you said that.

“Also, how do I, as a woman, live a full life with a career while still honoring my commitments as a mother? Maybe I should go work for famed feminist writer Ellen Key in Sweden.”

Frank Lloyd Wright: “Okay. This will be good for you, up to the point that it turns out she thinks your main responsibility is to your kids. I would think that would be upsetting to you.”

Mamah: “Probably! But no matter. I will continue writing for her, even though she lies to me and cheats me out of the money she owes me. Also, you lie to me a lot.”

Frank Lloyd Wright: “Yes! But this has something to do with the inner strivings of my soul.”

Mamah: “Okay. [Dies.]“

Seriously. Awful book. I advise you to read the Wikipedia entry on Mamah Borthwick, then pad out every event you read with a few dozen pages of “she probably thought” or “what must it have been like” or “she smelled the dogwoods, which reminded her of”s. You will have constructed something at most half as awful as the paint-by-numbers horrorshow that is Loving Frank.

P.S.: In some ways this novel reminds me of Umberto Eco’s essay on how to recognize a porn movie. “To put it simply, crudely, in porn movies, before you can see a healthy screw you have to put up with a documentary that could be sponsored by the Traffic Bureau.” Loving Frank really is that leaden.

John Lewis, Walking with the Wind: a Memoir of the Movement

The top 85% of the page or so is taken up with a picture of a young Lewis looking down and to the right, seemingly lost in a very serious thought. The bottom 15% has armed police officers on the left pointing their guns and truncheons at well-dressed black men on the right, while a crowd looks on from a parking lot behind.

Such a beautiful book: engagingly written, heartbreaking, frustrating, inspiring, and educational. You won’t find — or I, at least, haven’t found — a more ground-level view of the civil-rights movement from someone who actually lived it. When Lewis is out there on the ground, getting punched and kicked by citizens and police, you’re there with him. When his heart is broken by the death of his mentor, Dr. Martin Luther King, you feel it with him. When, mere weeks later, he’s in California with Robert Kennedy, and Kennedy in turn is assassinated, you feel a light inside yourself going out. And when a nation of black people runs out of hope and turns to violence, you, like Lewis, can understand why. Maybe you don’t agree with the turn to violence, but you understand that eventually something was going to have to change — and if the U.S. government wasn’t going to solve the problem, people were going to take matters into their own hands. And so they did. The dissolution of the SNCC, and its turn away from Gandhian methods, was tragic but probably inevitable.

The final chapter is about the world we live in now. Many people believe the civil-rights movement has run its course. Most everyone has lost faith in our leaders. Lewis’s answer is the same now as it’s ever been: organize. Get out there on the streets. Fight for what you know is right. Don’t back down. Realize that you’re in a long struggle, and be patient for results. It’s exhilarating. It’s overwhelming. And it often moved me to tears. This is a great book by a great man.

A question prompted by John Lewis’s Walking with the Wind: a Memoir of the Movement

The top 85% of the page or so is taken up with a picture of a young Lewis looking down and to the right, seemingly lost in a very serious thought. The bottom 15% has armed police officers on the left pointing their guns and truncheons at well-dressed black men on the right, while a crowd looks on from a parking lot behind.

I may write a full review of this amazing book when I’m done with it in a few days, or the following may do the trick. But for now I have a strategic question, which I’m sure labor unions and civil-rights organizers have answered many times in the past. At the risk of dramatically oversimplifying, the strength of the civil-rights movement and of labor unions comes from two sources: the power of groups rather than individuals, and attention from the media. Lewis inspiringly explains each of these sources of power throughout Walking with the Wind, but he doesn’t go into much depth, so far as I can tell, on the obvious question: if everyone is aware that these are its sources of power, then the obvious responses are to divide the movement and to cut out the media. So why didn’t this happen?

Specifically, imagine if civil-rights marchers hadn’t been taken off to the same prison, where they could coordinate their responses together, sing songs together, and provide each other moral support. Even imagine if they were taken to the same prison but held in separate cells. Yet time and again, that seems not to have happened: the marchers were kept together, and in their unity they found their strength. The police, at least thus far in the narrative, didn’t seem to realize that disunity was their ultimate weapon. Only one time thus far have they kind-of-sort-of figured it out, namely when the marchers demanded complete racial integration of lunch counters in Nashville, and the authorities countered with, essentially, partial integration. Some of the old guard took the bait, and there was a moment of ideological disunity within the movement. Splitting groups by ideas is useful, and I’m sure it’s part of a long historical tradition of dividing and conquering. What I’m wondering is why the authorities didn’t physically separate the movement.

Part of the answer might be that, in the presence of a modern media environment, such separation is impossible: if you drag protesters off to separate jails, the cameras will be following you the whole way.

Another answer might be that the authorities, along with the rest of white society, just could not — intellectually and emotionally would never be able to — respond to the movement in this sort of strategic, thoughtful, rational way. This answer seems right to me, actually: in its Gandhian way, the movement killed the authorities with love. Look your attacker in the eye while he’s smashing your skull. Try to talk with your assailant so that you can humanize him and, even while every fiber of your being screams out to treat him as the enemy, remember a newborn baby who at one time was innocent. Empathize with him and pity him: it’s not him whom you loathe, but rather the society that turned that innocent child into the monster who’s putting out a cigarette on your neck.

The movement knew the goals it was after and calmly pursued them; the authorities and the segregationists knew only rage. To ask the South to coolly reply to the movement’s unity by disuniting it is to expect calm rationality where none existed and where none could exist. Given time, perhaps the South could have formed a strategy to effectively combat the movement on its own terrain. But as it happened, the movement’s strategy had paid off before the South could stop it.

If I’m reading Lewis right, the movement’s strategy — the Gandhian strategy — explicitly foresaw this outcome. As the book unfolds, I suspect Lewis will tell us that the movement was working great until those untrained in Gandhian methods joined in. When calm is deliberately arrayed against rage, the rage can only increase and consume itself. When the movement understandably grows impatient with the slow pace of change and it starts to be rage against rage, then that is an entirely different battle with a very different end.

I’ve read books before, like Nixonland, that described the movement from a more synoptic historian’s perspective; Walking with the Wind is the first I’ve read from the perspective of a man whose actual head fell under the actual truncheon. It’s gripping and impossibly moving.

P.S.: Ah. Turns out that Lewis addresses exactly this strategic aspect in the chapter called “Raise Up The Rug”.

Margaret MacMillan, Paris 1919: Six Months That Changed the World

Three gentlemen walking down the street, with a crowd of lesser gentlemen behind them. The frontmost gentlemen are all wearing top hats and carrying canes. The front gentlemen, from left to right, are presumably Lloyd George, Georges Clemenceau, and Woodrow Wilson.

I’d like to make a meta point, first, about this book. As the years pass after some important historical event ends or some world-historical person dies, it often becomes irrelevant what the actual facts of the matter were. Thomas Jefferson is a great example of this, as Merrill Peterson made clear in his masterpiece The Jefferson Image in the American Mind: Jefferson-the-real-person matters much less than Jefferson-the-idea. Jefferson-the-idea changed with the times: depending upon the country’s mood, sometimes he was vilified as a Communist atheist, whereas at other times he was held aloft as the very father of liberty. Jefferson-the-idea had very little to do with Jefferson-the-real-person. Or rather, Jefferson-the-real-person had so many sides that people could choose the one they wanted to emphasize as attitudes shifted.

So it is with the end of World War I. I could argue — not sure if I would, but I could — that the widely believed story of the Versailles Treaty is more important than the actual facts of the matter. The standard story of Versailles would seem to track Keynes’s version pretty closely: Germany was never going to be able to pay the reparations imposed upon it, and the collapse of German democracy followed inextricably. The signing of the Versailles Treaty was a grievous error with world-historically catastrophic consequences.

Margaret MacMillan’s main response to this in Paris 1919 is to widen the lens a bit from just Versailles, to include everything else that was happening a few kilometers away. Practically the entire world was being reborn in Paris that year: Japan wanted the bit of China that Germany had had its hands on; the Austro-Hungarian Empire needed to be divided up; the Ottoman Empire was teetering and finally allowed to fall; Poland had spent centuries being torn between Russia and Prussia and wanted its chance at becoming a living, breathing, independent state; speaking of Russia, the Empire had just ended and been replaced by Lenin and friends; there was this new thing called Czechoslovakia in the making; and of course the West was just learning that the Middle East might have some important resources. The question that year wasn’t just how to punish Germany; it was how to shape a whole new world.

Petitioners of all sorts showed up in France to plead their cases. Germany’s overrunning Belgium had started the Great War, so Belgium believed that it had a special need for security. France had lost well over a million of its citizens, and it demanded a buffer between itself and Germany; this demand was, of course, perfectly reasonable given the centuries of animosity between the nations. And then one ethnic group after another took Wilson’s principle of “self-determination” to heart and believed that it deserved its own nation. Before considering Versailles, consider the unavoidably conflicting demands from each of these groups. Consider, behind each of them, the constituencies back at home: the French citizens understandably thirsty for blood, the British eyeing the French with suspicion and unease dating back at least to Napoleon, or for that matter the Americans who for centuries had taken George Washington’s words to heart:

Our detached and distant situation invites and enables us to pursue a different course. If we remain one people under an efficient government, the period is not far off when we may defy material injury from external annoyance; when we may take such an attitude as will cause the neutrality we may at any time resolve upon to be scrupulously respected; when belligerent nations, under the impossibility of making acquisitions upon us, will not lightly hazard the giving us provocation; when we may choose peace or war, as our interest, guided by justice, shall counsel.

Why forego the advantages of so peculiar a situation? Why quit our own to stand upon foreign ground? Why, by interweaving our destiny with that of any part of Europe, entangle our peace and prosperity in the toils of European ambition, rivalship, interest, humor or caprice?

It is our true policy to steer clear of permanent alliances with any portion of the foreign world…

Americans wished very much to return to this tranquility.

Finally, consider the time-sensitivity on resolving all of these conflicts and settling the German question once and for all. The Allies had not occupied Germany, as they were to do after World War II. And the soldiers were already demobilizing, heading home by the thousands every month. The longer the negotiations took, the weaker the Allies’ bargaining position would become and the less willing the folks back home would be to send their children back to Europe. Time was of the essence.

Bear all of this in mind, says MacMillan, when you read Keynes’s description of the negotiations. You’ll recall Keynes’s vivid portrayals of Clemenceau, Lloyd George, and Wilson: Clemenceau the Bismarckian French patriot, eager to destroy Germany in repayment for the Franco-Prussian War by which Bismarck birthed the modern German state (Clemenceau was 30 when Paris was under siege and Napoleon III fell); Wilson the naïve, moralizing Calvinist preacher, walking into the negotiations with his principles under his arm, absolutely outgunned at every turn by the wily Frenchman; Lloyd George the unprincipled schemer.

Were the Paris negotiations a failure? You can imagine any number of ways to answer that question. Did people believe at the time that they were a failure? Well, some did and some didn’t. Let’s even suppose that everyone did; even then, maybe you want to be asking a counterfactual, namely: was any other better outcome from the negotiation even possible? That counterfactual (like all counterfactuals) is probably unanswerable.

MacMillan gives answering that counterfactual her best shot, I’d say, and convinces me that probably nothing better was possible. There were too many moving parts, and too many petitioners with too many conflicting demands; there was just no way to make anyone else happy.

But again, to an extent it doesn’t matter whether the outcome was “actually” satisfactory. Consider just the issue of German reparations payments, which totaled 132 billion marks in 1919 (somewhat less, MacMillan notes, than what France paid Germany at the end of the Franco-Prussian War, when the French economy was quite a lot smaller than the post-Great-War German one). MacMillan says that historians have reconsidered whether German reparations were really as crippling as Keynes, and the Germans themselves, made them out to be at the time, but then MacMillan is also quick to note that the Germans certainly believed the reparations were crippling, and Hitler exploited this belief when he campaigned on nullifying the Versailles Treaty. (As of 1950, Meinecke was still calling out the reparations payments, along with the Jews’ rapacity, as a cause of German woe.)

What we really need is a Jefferson Image in the American Mind for World War I: a study of how the war has been perceived, and how that perception has affected subsequent reality. MacMillan’s book is probably as close as we’ll come to that goal in my lifetime: it’s a stunning combination of the facts as they were understood while the negotiations were ongoing, of how the reality was perceived later on, and of how the history played out in the decades that followed. There’s basically one chapter per involved nation (Japan, China, Turkey, etc.), each of which ends with a couple paragraphs noting how the 20th century worked out for Yugoslavia, Czechoslovakia, Syria, and the rest. Spoiler alert: it often didn’t work out very well.

Whether Europe, the Middle East, and Asia could have been carved any better at the joints to avoid the nightmarish century that followed is an inherently impossible question, but MacMillan’s attempt at answering it is magisterial.

Friedrich Meinecke, The German Catastrophe

A Reichsadler on a flaming red background -- essentially as though the German Reich is being torched.

I picked this book up because Pflanze mentioned it in his biography of Bismarck. The question that anyone had to ask after World War II was whether Bismarck planted the seeds for Hitler’s later rise to power, and apparently Friedrich Meinecke — an esteemed German historian whose life stretched from the creation of Germany under Bismarck to its downfall under Hitler — had asked this very question. I assumed that a historian (of all people) in the immediate aftermath of the collapse (of all times) would have some morally and intellectually probing thoughts on the matter.

It’s really sad that he doesn’t; I hate to say it, but The German Catastrophe is nothing so much as a work of moral cowardice. Germany — no, Germans — had just thrown the full power of the modern industrial state at the task of destroying human beings; this calls for an exhaustive moral accounting, which Meinecke is simply not willing to provide. The German people, he tells us, were fundamentally good, and he knew all along that they would emerge from the Hitler disaster. To the extent that he seeks out answers, he finds those answers in chance and historical contingency. If Hindenburg had not named Hitler chancellor, the Nazi movement might have faded out on its own. If Hindenburg’s mental faculties had not been on the decline, he might have been a stronger leader. And so forth.

I’m not denying the importance of chance in history. But if you’re going to pin the 20th century’s most important event on chance, you had better convincingly argue that you’ve excluded all other avenues first, and Meinecke doesn’t do this. He certainly doesn’t take the time to explain why Bismarck’s state is not at fault; he’d rather venerate the man and the Prussian state than study its failings in any depth. To the extent that he mentions Jews at all, it is to hint — none too subtly — that their own greed after World War I may have drawn the German people’s ire.

I’m also not singling out Germans as history’s most barbarous people, nor am I singling out the Holocaust as the only historical event that requires deep soul-searching. The United States still doesn’t appreciate the effects that slavery, Jim Crow, redlining, restrictive covenants, and the rest of the arsenal of racism have on the everyday lives of black people. We still don’t appreciate how deeply the legacy of slavery is baked into the very basic structure of our society, and we live in a land where actual legal slavery is nearly a century and a half behind us; you’d think we’d have the appropriate objectivity at this remove. So I can certainly understand why a German historian within five years of the end of the war would be unable to study his homeland’s destruction with probing detachment.

Which is why Meinecke’s book, written in 1950, is better viewed as a balm to wounded German souls while their country was still under Allied occupation than as a serious work of history. He meant to tell the German people that they were fundamentally good and that they would soon recover. Viewed as a homily, it may have had the intended effect. Viewed as a work of moral discovery, it is appalling.

Tiny, ever-so-brief note on Ferguson, by way of George Orwell

The issue was clear enough. On one side the C.N.T., on the other side the police. I have no particular love for the idealized ‘worker’ as he appears in the bourgeois Communist’s mind, but when I see an actual flesh-and-blood worker in conflict with his natural enemy, the policeman, I do not have to ask myself which side I am on.

– George Orwell, Homage to Catalonia

Dan Barber, The Third Plate: Field Notes on the Future of Food

Title in white, overlaid on a photo of soil and clover.

Did you read The Omnivore's Dilemma? If not, why not? If you didn’t, go read it now. I’ll wait.

Okay, great. Now that everyone reading this post has read Pollan, I think we can all agree that the bit about Joel Salatin — the Virginia farmer whose farm is “beyond organic” — is the best. Not only is Salatin pesticide-free; his cows wander the fields eating grass and leave poop behind, which yields fertilizer for future grass; the chickens follow behind the cows and peck at their poop. Salatin has created a closed ecological loop.

One bit of trouble is that farmers only produce what the market tells them to produce. If all the market wants is chicken breast, then chicken thighs and gizzards are going to go to waste. What to do?

Dan Barber’s answer in The Third Plate is that we need to widen our lens: sustainability has to include the farmer, the cook, the eater, the land … every part of the food system. If farmers will only produce what the market wants, then we need to change the market. And Barber, as a chef, knows that his people are vital to the shape of that market. We’re all about “farm to table” now, and we’re all about organic, and much of the impetus for these changes came from restaurant food movements — the nouvelle cuisines and Chez Panisses of the world. If we’re going to make the food system truly sustainable, chefs will probably be on the front lines, shaping what we eaters think the word “sustainable” means.

Barber travels around the world and meets a delightful cast of farmers who are trying to change how we think about sustainability. There’s Eduardo Sousa, who’s already famous (can’t remember where I read about him; maybe The New Yorker?) for producing foie gras without force-feeding his geese ("gavage"). There’s the farmer who shows Barber — and for my money, this is the most fascinating and disturbing part of The Third Plate — what the roots underneath modern industrial wheat and pre-industrial wheat look like. The modern roots are much shorter than the pre-industrial ones, meaning at least a few things: the roots are giving back less to the soil, they’re protecting less against the sort of soil devastation that led to the Dust Bowl, and they’re catching less rainwater than long, deep roots would. Since they catch less rainwater, they require more irrigation.

Modern wheat is inseparable from modern bread production. Since bread is now largely made at industrial scale, it requires huge quantities of flour. Whole-wheat flour turns rancid within a matter of hours after grinding, so industrial production requires some method of getting it shelf-stable. Hence: white flour.

All of this might be, at best, the sort of liberal more-sustainable-than-thou trolling that everyone knows and loves. But that’s where Barber turns this from Pollan++ into something that we can all appreciate: cuisine produced with an eye toward overall food-system sustainability just tastes better. Geese produced without gavage, who are allowed to forage for their own food, know where to look to get the nutrients they need, and those nutrients show up in what we taste. Cows allowed to wander on grassland seek out — in fact, have the anatomical equipment to seek out — very select grasses to get what they need at that exact moment. Wheat with deep roots can capture and yield up more minerals from the land. We can taste these subtleties; they taste better than fruits, vegetables, and meats that have been force-fed an industrially selected diet in order to rush them out the door as fast as possible.

One metaphor that makes this make intuitive sense to me is alcohol versus Sprite. A beautiful Scotch or bourbon tastes subtle and complex and transcendent in a way that a soft drink simply never will. In principle, industrial chemistry could build a drink that features the boundless flavor profile of a delightful spirit; but if nothing else, we can expect the constant push for higher profits to push Coca-Cola Brand Highland Scotch Whiskey ™ into something simple that’s reproducible at scale. Scotch is delicious for at least two reasons: first, that yeast produce countless chemicals that (I’m given to understand) we still haven’t entirely mapped out; and second, that there’s a patient human being tending to the process, tasting each small batch to confirm that it features all the notes expected from a good Islay malt. The patience, and the biology, just seem impossible to get at industrial scale. A world of industrial wheat is a world of Sprite rather than a world of Scotch.

Exactly because industrial wheat is built for industrial scale, it’s not clear that the world Barber envisions can supply the volume of food that our current industrial world does. There are plenty of counterarguments to this point. For one, the current system tries to shove more food into the same size mouths over time, with predictably rising obesity; a food system like Barber envisions wouldn’t require unsustainably rising output. The current system also turns a vast swath of the Gulf of Mexico into a dead zone every year as fertilizer empties out of the Mississippi River; Barber’s world wouldn’t borrow from tomorrow to pay off today. “Unsustainable” doesn’t mean anything hippie-dippie. It really means nothing more than Stein’s Law: If something can’t go on forever, it will stop. A sane food system would guarantee that our children have healthy, tasty food available to them.

Barber’s book is an attempt to understand what this means, literally from ground level. He meets the farmers, he meets the chefs, he foments arguments between them, and he eats their food. Anyone who read Michael Pollan and felt angry or inspired will need to pick up and devour The Third Plate.