Summer already. The spring seems to vanish before I have even caught up with my e-mail. Before I know it, the palm-tree-delivery truck is in the street behind us, winching a couple of big palm trees out to stand on the terrace at the Irish pub. (Dublin suburban gardens are full of palm trees, so an Irish pub has to have palm trees, almost as much it has to have Guinness and fish-and-chips.) The palm-tree-delivery truck means it is almost summer--and then it is summer, and we are tumbling toward the solstice, and the tremendous light pours into streets and rooms, filling them like water.
But--now hear this--I am recording a major achievement from the spring. When I was walking the Teltowkanal in February this year and passed along the edge of Bruno Taut's wonderful Hufeisensiedlung (Teltowkanal 7 post), I said that I wanted to come back in the spring to get a better look at it; and I also wanted to go back to the Britzer Garten, which is not so far away. I had very happy memories of sitting in a small library-cum-cafe there, reading math, on a beautiful summer day several years ago. I had always meant to go back and do more of the same, but never managed to do it.
But once in a while we manage to do the things we mean to do. Here is the edge of the Hufeisensiedllung on a fine spring day.
 |
| Cherries on Onkel-Bräsig-Straße, April 2015. My photo. |
And here am I, wandering around the streets gawping: Look at the cherry-blossom against the sky! Look at the tulips by people's doors! Look at the wisteria coming into flower against the red walls of the row houses!
 |
| Wisteria on Hüsung, April 2015. My photo. |
How wonderful all this is: the big old cherry trees in bloom against Taut's bright, solid, well-designed houses. Indigo-blue houses like the almost-last color at the edge of the rainbow. Red houses, yellow houses.
 |
| Cherry blossom, Hufeisensiedlung, April 2015. My photo. |
Ah, but I can't wander around in circles here all day with my mouth hanging open like a moron, I do want to get over to the gardens. So off I go, south and west through the neighborhood.
It's a perfect day, cool enough for walking, warm enough to toast in the sun and read in a sheltered place. What I
have with me today is not math, but it's at least a mathematician's book:
Descartes' Discours de la
Méthode.
It's nicely apropos, too: the Britzer Garten
has a tulip festival under way, and Descartes published the Discours in
the Netherlands in 1637, in the same year that Dutch tulip mania--the first recorded
asset-market bubble, I believe--peaked and crashed. (In the previous year,
tulip bulbs had been the fourth-highest-valued export of the country, following gin,
herring, and cheese. Is there any country nowadays whose biggest-money export is booze? I think not. World trade isn't what it used to be.)
Lucky Descartes. He had sold his inheritance
(French real estate) and invested the money in bonds that would give him an adequate
income and let him devote himself to mathematics and philosophy. If the tulip mania had been a modern bubble, large parts of the economy would have been swept up in it, and Descartes' bond investments might have been in
trouble. But it was a pre-modern bubble, which didn't make big waves in the economy at large. No mass unemployment when the tulip-futures market collapsed. (We don't
get the modern kind of asset-market crisis that sucks down a lot of relatively innocent bystanders,
until ... when? Later nineteenth century, I think.)
 |
| René Descartes, Portrait by Frans Hals. Photo, Wiki Commons. |
Descartes is one of those people you encounter in little canned summaries, but probably don't actually read, in introductory courses in college. --Though I remember being at some event at the U of Chicago decades ago (a lecture by some political bigwig of the time, I think) when a cluster of undergrads, loud and unsettled as a flock of starlings, came to roost next to me, arguing about Descartes. A tall dark young woman was holding some point against the united opposition of the rest, all of them convulsed with laughter. As this was the U of C, probably some of them had actually read the books they were talking about. The tall woman flung herself down near me, insisting to the rest of them with that luminous undergrad kind of intensity, "But I take Descartes seriously." And they swirled around her like starlings mobbing a bigger bird, screeching, "You can't take Descartes seriously!"
It's hard, actually. In canned-summary form, he seems unconvincing. In the summaries he says: I think, therefore I am ... and therefore [with just a couple of explanatory steps in between] a benevolent deity exists. And he says: I know that ideas are true when they are clear and distinct. Surely this does not make sense?
But then, Descartes is not an
idiot. Being a brilliant mathematician doesn't guarantee that you're a brilliant anything else, but still--analytic geometry is an amazing invention, and I am curious to see what he really has to say about other matters.
So, off we go to the gardens, to sit in the sun and read. Past the Britz village church, one of those little medieval fieldstone churches that are dotted around the outer parts of Berlin. (The tower's much newer--you can tell, in part, because the stones in the tower have been cut so squarely and uniformly. In the main body of the church the stones just are what they are: big or small, square or round or blobby, more or less as they came out of the fields.)
 |
| Britzer Dorfkirche, April 2015. My photo. |
The church stands on a small height above the old village pond, and on the far side of the pond some spectacular mass of shrubbery is in bloom. (Good heavens, look at this, a whoosh of blossom coming up from the water like the flare of a welding torch. I come from a land of meager springs, I am amazed.)
 |
| Britzer Dorfteich, April 2015. My photo. |
On we go, looking for a bakery with sandwiches for lunch and not having much luck. Now that we're away from the Hufeisensiedlung and out near the ragged edges of the city, things are bleak and over-automobiled.
Ah, here's a bakery (not so appealing, but we'll take what we can get); and then here's the turn to the garden entrance. What is this going to be like, I wonder? My memory of the actual design, from the last time I was here, is fuzzy. There are so many ways of making parks and gardens.
A big German park or garden is often meant to be like a forest (here's the park we live next to in Berlin):
Ah, here's a bakery (not so appealing, but we'll take what we can get); and then here's the turn to the garden entrance. What is this going to be like, I wonder? My memory of the actual design, from the last time I was here, is fuzzy. There are so many ways of making parks and gardens.
A big German park or garden is often meant to be like a forest (here's the park we live next to in Berlin):
 |
| Großer Tiergarten, Berlin. Photo by Manfred Brückels, Wiki Commons. |
A French park or garden is often meant exactly not to be like a forest, not to look like nature in the raw: it is something more civilized and geometric.
I don't know quite what this means for the Britzer Garten, which is not supposed to be just forest: there is said to be a very fine spring-bulb display here, and a big dahlia show in the summer, and so on. So is there going to be something like the geometric but riotous flowerbeds that I saw in London earlier in the spring? (These pictures are both from Whitehall Gardens.)
As it turns out, there are some formal beds like these (mostly not as lush) at Britz. But it's not what the German flower-planter does best, at least not here. Here they just strew the landscape with flowers in a fine open-handed sort of way:
Ah, this is fine, this is great stuff. Let us perch on a bit of wall and eat our sandwich and make the acquaintance of René Descartes.
I hadn't realized how autobiographical the Discours is. I love autobiography (not the celebrity kind, but people actually trying to make some sense of their lives). To be sure, D.'s story of his life is programmatic, it's tendentious--he's trying to use it to explain and promote a set of works to which the Discours is the prologue. But still, it feels real.
At the risk of anachronism, I want to say: don't you just know people with the same take on the world as the young Descartes? He's dying to get out of school; it seems useless to him. Academics disagree with each other, so they're probably all wrong, he says, and anyway, what's the point? They're just sitting in their offices, without anything real at stake in their disputes, so there's nothing to stop them from spouting nonsense. Let me get out in the world, he thinks, where people are doing something that matters. Politics, trade, war. Let me get involved with people who are doing something real: they'll understand the world better than academics do, because they have to. They have to think clearly because the consequences of their decisions are so important and come home to them with such force.
So he leaves school and travels and meets real people and is a gentleman-volunteer with the Dutch army. Then he is in the Bavarian army, backing the Empire at the beginning of the Thirty Years' War. (A mathematically trained officer is useful for designing fortifications and calculating artillery ranges and so on. One of D's important later mathematical discoveries is based on his observations of the behavior of artillery shells as they head toward the people they are about to kill.)
Descartes is part of the Catholic Imperial army that wipes out the Czech Protestant forces early in the Thirty Years War. (A sizable Muslim contingent has been sent from Turkey to support Protestantism, but it gets entangled with the Poles and is no help.)
After the Czech army is wiped out, Ferdinand, the reactionary Catholic who has recently been elected Emperor, becomes the new King of Bohemia. The Protestant ex-king and queen and their children flee to the Netherlands, in the chaos almost forgetting to pack an infant son, who is tossed into a carriage by a member of the court at the last minute. (In later years, Descartes will be a friend of one of the other children; no hard feelings about who was on which side in Prague in 1620.)
After the defeat of the Czechs, Ferdinand goes in for forced reconversions to Catholicism, seizure of Protestant property, and increases in absolute imperial power. How else can there be order? he thinks. And order there must be. But unsurprisingly, there is a bad reaction to this. The war spreads, the imperial finances deteriorate, unpaid mercenary forces ravage the countryside, and order in Central Europe--everything in Central Europe--goes to hell in the proverbial hand-basket.
Descartes concludes, with regret, that real people spout nonsense also. High stakes don't guarantee good understanding. So what to do now? Or more precisely, what to think, how to be sure that what you believe is true? Descartes doesn't care so much what he does: his rule is to do what the people around him do. But he does care very much what he believes.
I am done with my sandwich and the wall is not a place to sit on for a long time. Let's wander on and look for somewhere more comfortable to continue.
The late narcissi are out in abundance here, more than I had expected:
Of course I have no clue where I am, or how the portion of garden I am wandering through now relates to the portion of garden that I was in the last time I was here. I can't find the cafe with the little library in it; perhaps it's gone, or perhaps I'm in the wrong part of this rather large (200-acre-plus) establishment. I probably came in from the other side before.
I think I remember the small hill I have just come to, which I climbed the last time time I was here, because how can you see a hill without wanting to climb it? It was rather sweaty and boring on a hot summer day, but it's wonderful now, covered thick with daffodils from top to bottom. Not suitable for photography, however: the wind is blowing so hard, the flowers are just a blur.
Here's a lower, more sheltered spot where the breeze is not so wild.
And of course there are tulips, scattered through the grass as if we were on a hillside in Anatolia.
I don't see any of the streaky-stripey kind of tulips that were so prized in the seventeenth century. In early 1637, when the Discours was in press, one of these might cost as much as a rich man's house in Amsterdam. (Eighty cents a pop at Walmart for the modern version.)
Scholars still disagree--typical! the young Descartes would have said--about whether the peak tulip prices were really irrational or instead were somehow efficient and tied to fundamental values, at least insofar as this was possible under the circumstances. (It's complicated: part of the 1636-37 problem was that the people who ran the tulip markets changed all the futures contracts to options contracts temporarily, which was bound to muddle up the pricing. And maybe it mattered that short-selling in tulip futures had been made illegal.)
In any case, the market peaked and crashed, and development of new tulip varieties slowed way down. I think this early-double or peony type of tulip is a Victorian creation. (And don't the flowers just look like it? A little loud, a little overconfident and Albert-Memorial.)
 |
| Grape hyacinth and cherry blossom, Britzer Garten, April 2015. My photo. |
Ah, this is fine, this is great stuff. Let us perch on a bit of wall and eat our sandwich and make the acquaintance of René Descartes.
I hadn't realized how autobiographical the Discours is. I love autobiography (not the celebrity kind, but people actually trying to make some sense of their lives). To be sure, D.'s story of his life is programmatic, it's tendentious--he's trying to use it to explain and promote a set of works to which the Discours is the prologue. But still, it feels real.
At the risk of anachronism, I want to say: don't you just know people with the same take on the world as the young Descartes? He's dying to get out of school; it seems useless to him. Academics disagree with each other, so they're probably all wrong, he says, and anyway, what's the point? They're just sitting in their offices, without anything real at stake in their disputes, so there's nothing to stop them from spouting nonsense. Let me get out in the world, he thinks, where people are doing something that matters. Politics, trade, war. Let me get involved with people who are doing something real: they'll understand the world better than academics do, because they have to. They have to think clearly because the consequences of their decisions are so important and come home to them with such force.
So he leaves school and travels and meets real people and is a gentleman-volunteer with the Dutch army. Then he is in the Bavarian army, backing the Empire at the beginning of the Thirty Years' War. (A mathematically trained officer is useful for designing fortifications and calculating artillery ranges and so on. One of D's important later mathematical discoveries is based on his observations of the behavior of artillery shells as they head toward the people they are about to kill.)
 |
| White narcissi and grape hyacinths, Britzer Garten, April 2015. My photo. |
Descartes is part of the Catholic Imperial army that wipes out the Czech Protestant forces early in the Thirty Years War. (A sizable Muslim contingent has been sent from Turkey to support Protestantism, but it gets entangled with the Poles and is no help.)
After the Czech army is wiped out, Ferdinand, the reactionary Catholic who has recently been elected Emperor, becomes the new King of Bohemia. The Protestant ex-king and queen and their children flee to the Netherlands, in the chaos almost forgetting to pack an infant son, who is tossed into a carriage by a member of the court at the last minute. (In later years, Descartes will be a friend of one of the other children; no hard feelings about who was on which side in Prague in 1620.)
After the defeat of the Czechs, Ferdinand goes in for forced reconversions to Catholicism, seizure of Protestant property, and increases in absolute imperial power. How else can there be order? he thinks. And order there must be. But unsurprisingly, there is a bad reaction to this. The war spreads, the imperial finances deteriorate, unpaid mercenary forces ravage the countryside, and order in Central Europe--everything in Central Europe--goes to hell in the proverbial hand-basket.
Descartes concludes, with regret, that real people spout nonsense also. High stakes don't guarantee good understanding. So what to do now? Or more precisely, what to think, how to be sure that what you believe is true? Descartes doesn't care so much what he does: his rule is to do what the people around him do. But he does care very much what he believes.
I am done with my sandwich and the wall is not a place to sit on for a long time. Let's wander on and look for somewhere more comfortable to continue.
The late narcissi are out in abundance here, more than I had expected:
 |
| Narcissi, Britzer Garten, April 2015. My photo. |
Of course I have no clue where I am, or how the portion of garden I am wandering through now relates to the portion of garden that I was in the last time I was here. I can't find the cafe with the little library in it; perhaps it's gone, or perhaps I'm in the wrong part of this rather large (200-acre-plus) establishment. I probably came in from the other side before.
I think I remember the small hill I have just come to, which I climbed the last time time I was here, because how can you see a hill without wanting to climb it? It was rather sweaty and boring on a hot summer day, but it's wonderful now, covered thick with daffodils from top to bottom. Not suitable for photography, however: the wind is blowing so hard, the flowers are just a blur.
Here's a lower, more sheltered spot where the breeze is not so wild.
 |
| Daffodils, Britzer Garten. April 2015. My photo. |
And of course there are tulips, scattered through the grass as if we were on a hillside in Anatolia.
 |
| Britzer Garten, April 2015. My photo. |
I don't see any of the streaky-stripey kind of tulips that were so prized in the seventeenth century. In early 1637, when the Discours was in press, one of these might cost as much as a rich man's house in Amsterdam. (Eighty cents a pop at Walmart for the modern version.)
Scholars still disagree--typical! the young Descartes would have said--about whether the peak tulip prices were really irrational or instead were somehow efficient and tied to fundamental values, at least insofar as this was possible under the circumstances. (It's complicated: part of the 1636-37 problem was that the people who ran the tulip markets changed all the futures contracts to options contracts temporarily, which was bound to muddle up the pricing. And maybe it mattered that short-selling in tulip futures had been made illegal.)
In any case, the market peaked and crashed, and development of new tulip varieties slowed way down. I think this early-double or peony type of tulip is a Victorian creation. (And don't the flowers just look like it? A little loud, a little overconfident and Albert-Memorial.)
 |
| Double tulips, Britzer Garten, April 2015. My photo. |
At the moment I have a very clear and distinct idea that it's time for the first Eiscaffee of the season. This is cold strong coffee over vanilla ice cream with whipped cream on top. I don't indulge in too many of these in the course of the summer (really not), but now might be the time. A sunny park-bench among the flowers, a little strong coffee, and we will get through the rest of the Discours.
Actually, with the benefit of coffee and cream, I think I understand how it could be that, as Descartes says, clearness and distinctness are criteria for the truth of ideas. (How satisfactory it is to one's sense of order to get this straight. It's as good as cleaning out the broom closet.) The criteria do not make sense if the ideas we are talking about are what would now be called ontologically objective propositions--that is, if they are about external, material, measurable things. The proposition, "I am ten feet tall" might be very clear and distinct to me if I am a loony, but that doesn't make it true: the criteria don't apply to statements like this.
The criteria do make sense, however, if the ideas we are talking about are ontologically subjective propositions--propositions like "I am in pain," which are essentially about subjective states. When it is very clear and distinct to me that I am in pain, then it is certainly true that I am. If it's not so clear to me that I am in pain, then maybe it's not so true that I am. (When people have pains in phantom limbs, the subjective pain is real, even though the material, objectively measurable limb isn't.)
The kind of propositions Descartes is interested in are about cognition more than about feeling, but clarity is not irrelevant here either. If it's quite clear and distinct to you that you believe such-and-such, then it's quite true that you believe it (even if such-and-such in itself is not true). If it's not clear in your own mind what you believe, then perhaps it's not true that you believe anything. (And could a mathematical proposition that was not clear be satisfactorily provable and therefore established as true? Not.)
Descartes takes subjective states seriously as a separate reality: mind is one thing, measurable material is quite another, and each of these is as real and important as the other. He's probably more interested in mind--that's where the math is, after all. We don't prove the Pythagorean theorem by objectively measuring a lot of triangles. But Descartes does admire empiricists: the part of the Discours that I am reading now goes rocketing off-topic into extravagant praise of William Harvey, who discovered how the blood circulates through the body.
In fact, D says he is going to devote the rest of his life to what we would now call biomedical research. This, he says, is the activity that would benefit the human race the most--because the mind is, although separate and different, so intimately dependent on the condition of the body that our best hope of making people wiser is to improve their health.
So often we don't do what we mean to do, however. Descartes does not in fact devote the rest of his life to biomedical research. It's not so surprising that he doesn't, perhaps: he is a spectacularly good mathematician, but I think he is not by nature an empirical, data-drudge type like William Harvey. It's hard to imagine him spending a lifetime dissecting corpses and experimenting with fish hearts (over and over and over) as Harvey did.
Part of the attraction of medical research may have been the hope that it would explain mind-body, subjective-objective connections, which D. knew were were a weak point in his theories. If mind, as he believed, is absolutely not material--if subjective reality is not part of the measurable material world--how could it be so intimately involved with the body?
One of D's scientific correspondents, Elizabeth of Bohemia, pushes him hard on this point. (The daughter of the Protestant ex-King thrown out of Prague by Descartes' comrades-in-arms in 1620, she is now grown up and a competent mathematician and philosopher and behind-the-scenes mover in practical affairs.) Think of this and that sort of behavior, she says, giving examples. Wouldn't it be easier to account for these things by allowing the mind to be material? Why don't we go for the more economical explanation?
Descartes, in response, bobs and weaves and evades. She pushes, again: Think about the passions, she says (the emotions, we would say now, not meaning quite the same thing). If we really understood what they are and what role they play in our lives, maybe some of these problems about human nature could be better addressed. He responds by writing a new book on this subject, but it is his last. (It doesn't look that interesting in the canned summaries, but who knows?) The next year he will be dead.
This is just after the Thirty Years' War ends, at last. Elizabeth is busy with correspondence nudging her connections this way and that in the negotiations for the peace treaty. She is always in correspondence: advising the University of Leiden about hiring a mathematics professor, nudging the negotiators after the English Civil War and Commonwealth, when the Stuart monarchy is restored. (She and her siblings are the closest relatives the new English king has, after his regrettable brother.) Eventually she becomes Abbess of a Protestant convent in northern Germany, runs the surrounding territory, nurses it back to modest prosperity after the ravages of the war, and shelters a variety of radical religious refugees (heretic Calvinists who don't believe in private property, Quakers who don't believe in violence).
What a general disaster Descartes' lifetime is. Climate change, famine, plague, civil and foreign war. The world loses something like 25% of its population. (I am speechless with amazement when I look at official estimates of twenty-first century climate-change costs that include only things like storm damage, reductions in agricultural output, and increased energy costs. They don't include the costs of people's increased desire to kill each other and smash institutions when they are under economic stress. Surely these costs are quite high?)
Descartes' disastrous lifetime is also a time of astonishing creativity in math and science--and in part, people are working so hard at these things because they are working on the basis of ill-founded hopes. They think that if we knew how to reason properly (math) and knew our facts (how do hearts work?), then things like the Thirty Years' War and the English Civil War wouldn't happen again.
Thomas Hobbes, whom one does not usually think of as naive, believed that if we just pulled up our socks and tried, we could develop propositions about the optimal organization of society that would be as clearly true as theorems in geometry. So then, Hobbes thought, given this extension of geometry to politics, everyone would agree on political matters instead of trying to cut each other's throats because they disagreed. (But no, poor Hobbes. Better geometry has only given us more accurate artillery ranges.)
Elizabeth's brother Rupert--the one who was almost left behind as an infant in the flight from Prague--grows up to be a noted military commander, occasional African explorer and developer of the slave trade, English government official, inventor, scientist, and sometime artist (printmaker). (He was also said to be the fourth best tennis player in England. Where do people find the time for all this?) The subject of his best-known print is taken from a painting (probably) by the Spanish artist Ribera, supposed to represent the execution of John the Baptist. The John-the-Baptist iconography in the picture is about nil, however; at least in Rupert's version, the subject looks more like the sadness of generalized official killing.
 |
| Prince Rupert of the Rhine, mezzotint (after Ribera): The Great Executioner. Photo, Wiki Commons. |
Rupert had considerably broader experience of cutting off heads than the Spanish painter did. The executioners in Ribera's paintings tend to be warty and grotesque; this one is a serious man, a realist. A soldier in hard times, perhaps.
Rupert signs his own name on the length of the executioner's sword blade. If he can identify with anyone in the picture, it is not necessarily the saint. Though it is also noticeable that the saint's and the executioner's faces do not look as different here as they often do in the iconography. Rupert, who has been there, knows that the two are sometimes harder to tell apart--and maybe less different at bottom--than we sometimes imagine.
**
Time to wrap it up and go home. One more stroll through the flower-fields. ..
This is Narcissus poeticus, I believe: the pheasant's-eye or poet's narcissus.
 |
| Narcissi, Britzer Garten, April 2015. My photo. |
The really nasty parts of the seventeenth century produce a lot of poetry addressed to flowers. In civil-war England it's delicate formal verse, in elevated language: Fair daffodils, we weep to see you haste away so soon. In Germany, which is worse devastated, the poetry is rougher stuff.
There's a seventeenth century verse, apparently written in 1637 (the year of the tulip crash and the Discours) that describes the grim reaper Death with a sort of ferocious humor: He's whetting his knife today! It already cuts better! (Heut wetzt er das Messer, Es schneidt schon viel besser.) One by one it lists the flowers that will fall: The noble narcissus, the jewel of the meadows; the lovely hyacinth, the Turkish lily, ... the sky-colored speedwell, the yellow and white tulips.
The refrain is: Take care, little flower!
**
A relatively recent contribution to the debate about whether the tulip market was efficient is Earl Thompson (2007), "The tulipmania: Fact or artifact?" Public Choice 130 (1-2): 99-114.
Some information on the history of tulip varieties: http://www.hortmag.com/plants/collectors-choice/tulips
The Stanford Encyclopedia of Philosophy has a useful entry on Elizabeth of Bohemia:
http://plato.stanford.edu/entries/elisabeth-bohemia/
The poem that begins Fair daffodils ... is by Richard Lovelace. The first version of the German verse, Es ist ein Schnitter, heisst der Tod, appeared in an anonymous broadsheet printed in 1638. (There are numerous versions.)
