Friday, August 30, 2013

Rock gardens, Part 1

There is a shop in Cambridge, Mass., that specializes in clever ironic gifts for clever ironic people. You know what I mean: an Etch-a-Sketch key chain, a silver pin in the shape of Edward Gorey's Uninvited Guest, some interesting object that on second examination turns out to be a clock, a realistic imitation of a tipped-over wine-glass with a realistic imitation of a puddle of red wine attached, a wind-up toy for the connoisseur, campy stuff like a Diamond Jubilee Edition waving Solar Queen (and Corgi), a ceramic tile that proclaims "I am Woman. I am strong. I am so tired." (I shouldn't be so snide about it; I've shopped there myself, happily.)

You used to be able to go into this place and buy a miniature Japanese rock garden in a box. Maybe you still can.

I don't know about you, but when I see the words "rock garden" the first thing I think of is a place where decorative plants grow among rock outcroppings. There was a sunny little rock-studded embankment like that near my parents' house, covered (except for the rocks) with mosses and flowering this and that.

But that's not what I'm talking about. I mean the kind of rock garden with no plants at all, such as you might find at a Zen monastery in Japan. It consists of a bed of sand in a rectangular border or frame, in which rocks of various shapes and sizes have been arranged just so. The sand is raked regularly, to smooth it out and to remove any leaves and other debris that have come along. I imagine that from time to time the gardener or the abbot or some other very wise person might even rearrange the rocks, after careful deliberation.

The box in the gift shop contained everything you would need to set up a scale model of such a thing: a rectangular frame, enough sand, a handful of little dark rocks, and a teeny-tiny rake. The only thing that was missing was a wise person to arrange the rocks. The scale of the thing was maybe 1:50, so--I don't know--maybe you would only need some fraction of the full wisdom of a Zen rock-garden master. Would it be 1/50? 1/2500?

Well, I never had one of these, but I was aware of them, and I believe that for the most part I took their existence in the ironic or campy spirit in which it was meant. I also wondered whether there were any people who took these things seriously, people who actually thought that they could get some of the esthetic or philosophical or spiritual benefit of a Zen rock garden by acquiring the home version. Silly people: without the heft of the rocks, without the landscape, without the history, without the years of spiritual discipline, all you have is a box of toys from a toy store.

At least I'm pretty sure I wondered about that. And although this was a long ago I'm pretty sure that those speculations extended to questions/thoughts/confusions such as:

What in fact are the benefits of a Zen rock garden?

Is "benefit" even the right word, or am I falsely imposing some American utilitarianism here? What is a garden for?

Should I be less cynical about miniature Zen rock gardens? Who am I to say that someone with a toy rake and a box of sand and a few little rocks can't find a good Zen moment in their own way? What do I know about it?

Or, turning it around, should I be more cynical about full-size Zen rock gardens? Those carefully chosen but natural-looking arrangements of the stones: do I really believe that an observer with the right training, the right sort of highly refined sensibility, sees something that I don't see there? Is this like The Emperor's New Clothes? Zen can have a joking quality; is the joke on me for even trying to comprehend this practice of arranging rocks on a bed of sand?

In August of 1990 the big quadrennial event known as the International Congress of Mathematicians was held in Kyoto, and I had the honor of being one of the many invited speakers. At any math conference there is likely to be half a day set aside to take a break from lectures. At a small meeting there might be an organized outing for those who want it, but basically you are on your own. At the ICM the free afternoon was meticulously planned. In a packet that came to me before I left home there were descriptions of a dozen or more excursions, and a form for reserving a place in one of them. I don't think I was ever in doubt: as second and third choices I may have put down the boat trip on a river and the boat trip on a lake, but my first choice had to be the tour of the Zen monastery with its world-famous rock garden.

Friday, August 9, 2013

Watersheds, Waterways, and Penguins: Part 4

The Concord River arises from the confluence of the Sudbury and Assabet Rivers in Concord and goes on to pour itself (as I said before) into the Merrimack. That's the sort of thing I like to know.

Looking further afield, the Ohio River arises from the confluence of the Allegheny and the Monongahela in Pittsburgh. Try saying this aloud: "the confluence of the Allegheny and the Monongahela". Say it a few times.

Of course, not every confluence involves three river names: far from it. Very often the outgoing stream bears the same name as one of the two incoming streams and the other is considered a tributary. (Is it still called a confluence in that case? Sometimes it is, certainly: that's how the city of Koblenz, where the Moselle flows into the Rhine, got its name.)

Sometimes the people who name the rivers get it wrong, in the sense that the bigger branch is called a tributary. A famous example is where the Missouri River meets the Mississippi at Saint Louis. The Mississippi upstream from Saint Louis is negligible in comparison with the Missouri. If anyone asks you what the longest river in North America is (and if they mean it to be a question about physical reality rather than about the names of things), the answer is not a river that has a single name for its whole length: it consists of the Missouri and part of the Mississippi. I believe this is widely known; I've known it since I was a child. (Actually--and I didn't know this until recently--there is more to say here. The Missouri arises from a confluence of not two but three rivers, not one of them called the Missouri, and the full list of names of segments of the continent's longest river seems to be "Mississippi River", "Missouri River", "Jefferson River", "Beaverhead River", "Red Rock River", "Hellroaring Creek".)

Anyway, by some kind of logic the upper portion of the Mississippi should have some other name, and the Missouri should be considered part of the Mississippi.

Don't get me wrong. I'm not here to complain, or to push one kind of logic at the expense of another. I can enjoy the names of rivers, and I can enjoy the reality of rivers, and I can also enjoy a little mismatch between the names and the reality.

After the Missouri the other main tributary of the Mississippi is the Ohio. This comes in further downstream, on the other side, the east. Imagine following the Ohio upstream from where it ends in the Mississippi at Cairo, Illinois. First you have Indiana on your left and Kentucky on your right. Later Ohio replaces Indiana, then West Virginia replaces Kentucky, then the river leads you into Pennsylvania and, as we know, ends (in name only) at Pittsburgh.

I like to think about the vast drainage basin of the Mississippi system, the huge middle portion of North America whose waters end up in the Mississippi Delta. You can see on a map that parts of it come very close to the Great Lakes. In Minnesota there is a divide, probably not very dramatic if you saw it up close, between the Mississippi and Lake Superior. It continues through Wisconsin and Illinois (where the relevant Great Lake is Lake Michigan) and into Indiana, possibly Michigan, and Ohio (now it's dividing the Ohio River from Lake Erie) and Pennsylvania, and even up into New York state, between Lake Ontario and the headwaters of the Allegheny.

The fairly vast drainage basin on the other side of this divide is that of the Saint Lawrence River, which is fed by the Great Lakes and opens into a wide bay or estuary called the Gulf of Saint Lawrence, in eastern Canada.

I have sometimes thought about the fact that there must be a point in New York where the basins of the Mississippi, the Saint Lawrence, and something else come together. I was pretty sure that the something else had to be Chesapeake Bay, because once, when I had occasion to drive from the Boston area to the State University of New York at Binghamton, somewhere on a lovely highway southwest of Albany, a sign told me that I was crossing the Susquehanna.

I like to imagine coloring in a map of North America in a certain way. First color the Mississippi basin. Then color the Saint Lawrence (or Great Lakes) basin. Look at the territory surrounded by these two basins and the Atlantic, and color in whatever drainage basin it is that touches both of the first two basins, namely that of Chesapeake Bay, which is fed by the Susquehanna, the Potomac, and some other rivers whose names I don't know. Now look at the remaining territory between the Saint Lawrence and Chesapeake basins and look for the basin that touches both; I suppose it is that of the Hudson. Now look between the Hudson and the Chesapeake and find the Delaware. Look between the Saint Lawrence and the Hudson and find, what? the Connecticut? And between the Saint Lawrence and the Connecticut the Merrimack? It's all about looking for those triple points. Between the Merrimack and the Connecticut is, I'm guessing, the Blackstone. And between the Blackstone and the Merrimack, finally the Charles?

Getting back to the Mississippi and the logic of river-naming, here's something I didn't know until recently, and it kind of blows my mind. Where the Ohio meets the Mississippi, the Ohio is in fact the bigger branch by flow rate (though not of course by length).

Imagine starting at the place in Louisiana where all that water flows into the Gulf of Mexico and, ignoring the names of things, going to see where the water is coming from. Travel up the stream, choosing at every confluence the branch that has the majority of the water. You would pass the mouths of the Red River, the Arkansas River*, and others, but at Cairo you would turn right and follow the Ohio. At Pittsburgh you would turn left and follow the Allegheny into western New York and then back into Pennsylvania, ending in some little creek in the woods.



* This is an impressively long river. And apparently outside of the state of Arkansas its name is pronounced with the stress on the second syllable. Think "Kansas". And apparently that's how some people used to pronounce the state of Arkansas, until the state legislature passed a resolution in 1881 to settle the matter.

Sunday, August 4, 2013

Waterways, Watersheds, and Penguins: Part 3

In the nearby city of Newton there is a road that I have been noticing for years. I like to roll its name around in my mouth: Albemarle Road. It's not a major route, but it has some striking qualities (apart from its name). It wanders along, crossing more important streets at sometimes funny angles, and wherever it goes it sports a broad green median strip. You can see why it wanders: it's following a waterway: in the middle of the green strip is what looks like an elegant drainage ditch, its sides lined with stone. The elegance is spoiled somewhat by the fact that there's usually not much more than a slimy trickle of water in it. At least that's my impression. Maybe I'm being unfair. I should really get out of the car and take a closer look.

At the northern end of all of this the road comes to a dead end (or rather two dead ends, one on each side of the water) and the stream disappears into the woods, casts aside its artificial stone walls, and after about 100 yards debouches into the Charles. Moving in the other direction, upstream, you come to a residential block of Albemarle Road (two one-way roads joined by a footbridge) followed by a longer block in which one side is residential but the other is a big public park with a playground, athletic fields, and a swimming pool. Through the middle of all of this runs the stream in its stony ditch, with grassy banks sloping down to it from the roadway. At Watertown Street the grassy banks suddenly give way to a stretch of impenetrable-looking jungliness, a fenced-off block in which weeds and vines have been allowed free rein on both sides of the water; and then suddenly the jungle gives way to an attractive little neighborhood park with benches and paved walks and plantings. Here Albemarle Road ends and the brook, still with squared off stone-lined sides, can be seen running between back yards. To spot any more of it from a public place you have to zig-zag around the neighborhood looking for all the spots where the stream ducks under yet another road. After about five of those I lose the trail. It emerges from under a street, but across the street is no sign of it.

Of course I have looked at a map. The Newton page of my Street Atlas of Metro Boston and Eastern Massachusetts shows that there is quite a bit more to this waterway: its headwaters are shown as being about a mile to the southwest of where I lose it (quite close to another part of the Charles, in fact--there is a ridge of high ground by the river in that part of Newton, so that rain falling quite near the river will initially flow away from it, not finding its way in until much further downriver). This supposed upper portion of the brook is on the other side of the Turnpike from the lower part that I have described. But I've gone over there and looked, and I can't find it.

Oh, the map told me its name, too: Cheesecake Brook.

Now, I have lots of questions about all of this, such as: How did Cheesecake Brook and the area around it get chosen for this special treatment, with stone walls and parks and footbridges and all? Was that jungly bit once meant to be a public park, too? What is the history of Albemarle Road? Why can't I find the upper part of the brook? And why "Cheesecake"?

I have not been in a hurry to answer these questions. (The answers might not be as enjoyable as the questions, you know.) I do in fact have tentative answers to some of them, based on some internet searching. But before I go into that I might have to tell some stories about family life, the Mystic/Charles divide, and the mighty Mississippi.

Waterways, Watersheds, and Penguins: Part 2

Rivers

One source of my current obsession with rivers is that I cross the Charles River a lot. I've been noticing this for some time. Every time I drive to Providence I cross the Charles five times, and every time I drive back I cross it seven times. I enjoy understanding this, and I want to share my knowledge. Of course the general explanation is that I'm not going in a straight line and that the river is not going in a straight line, either, but there are interesting details. For example, you can see high places here and there that account for bends in the river. And there is the coincidence that the river runs right through the area where Route 128 connects with the Turnpike, where there are looping, branching ramps (different ones for different directions of travel), and that just at that spot the river is as wiggly as it ever gets. I could go on, but maybe I'll spare you.

Of course, when I'm making those drives alone I don't spend the whole time talking to myself about crossing the Charles. That would be boring. If I am in a geographical mood, I can find other things to think about. For example, between the last crossing of the Charles and the first crossing of the Neponset, where exactly does the highway cross the watershed? There used to be a sign: "Entering Neponset River Watershed", but it must have disappeared when they widened the highway. Where was it? Common sense says that the divide must be either at this one high point in the town of Dedham or at this other high point in the town of -- well, I think that that other high point is also in Dedham, but I can't be sure: somewhere between the "Entering Dedham" sign near Exit 17 and the "Entering Dedham" sign near Exit 15 the road must have left Dedham. There ought to be another sign: "Entering [town]". Westwood, maybe? I wonder if there was a sign before they widened the highway ... But I see that I am digressing. Let's get back to rivers.

Watersheds 

And let's get this "watershed" business out of the way. Many of us know that the good old sense of that word is the sense that I used it in in the paragraph above, as opposed to the sense of the highway sign. As Henry Fowler puts it in Modern English Usage, a watershed is "the line of high land dividing the waters that flow in one direction from those that flow in the other, called in America a divide." He goes on, "The older of us were taught that that was its meaning, and the senses sometimes given to it of river-basin and catchment area and drainage-slope were mere ignorant guesses due to confusion with the familiar word shed." He laments, but he also concedes that the battle has been lost, that it has been lost for some time--and he is writing all of this in 1926. Of course the battle was lost: battles like that are nearly always futile.

Where does that leave us? The new sense is thriving and the old sense is not dead. In context it is usually easy to distinguish the two senses. No problem, right?

Well, I have no problem when other people use the word, but I have a little problem every time I use it. I feel the need to make it clear that I know the history of the word, and even to show that there is some part of me that disapproves (like Fowler) of the upstart modern sense, however convenient it may be. For the rest of this series of posts I will try to set those feelings aside and freely use "watershed" interchangeably in both senses.

The Charles, the principal river in these parts, flows into Boston Harbor. The Concord River, not so many miles west of here, is a tributary not of the Charles but of the Merrimack, which it joins at the old mill town of Lowell, well to the north. The Merrimack has a lot more water flowing through it than the Charles does, and most of its water comes from the White Mountains of New Hampshire, still further north. I have sometimes wondered what a map of these watersheds would look like--I mean, a map showing the outlines of these drainage-basins, catchment areas, valleys--these watersheds. And there must be what I would call a triple point, a place where three watersheds come together: those of the Charles, the Concord/Merrimack,  and the Mystic (what a great name!), this last being a smaller river that enters Boston harbor just north of the Charles. Where's the triple point, I wonder? I've worked out that it is somewhere in Lexington, but I'd like to know more. And where does the Charles-Mystic divide run from there? It has to go through parts of Belmont,  Cambridge, Medford?, certainly Somerville. That pond in front of Belmont High School--it receives water from a brook running down from Belmont Hill, but where does the water go from there? I suppose either to the Charles by way of Fresh Pond or to the Mystic by way of Alewife Brook (another fine name). Come to think of it, the space between Fresh Pond and the railroad tracks near Alewife Station is so flat that the question of locating that divide has got be a subtle one. Besides, whatever divide existed there in a state of nature must be long gone: that flat space is largely paved over now. I mean, there is a shopping center with a big parking lot on each side of you as you drive away from Fresh Pond on Alewife Brook Parkway, a.k.a Route 2 westbound, a.k.a. Route 3 northbound, a.k.a Route 16 eastbound. (Routes 2 and 16 are state highways; Route 3 is part of the old Federal Highway System.) But I see that I have wandered off the subject again.

Penguins

When Tesi was a child, her family used the word "penguins" as a private signal meaning something like "That's quite enough, dear. I think you can stop talking about that specific topic now." It was a reference to the following true story (I found this version at the website Futility Closet):

In 1944 a children’s book club sent a volume about penguins to a 10-year-old girl, enclosing a card seeking her opinion. She wrote, 'This book gives me more information about penguins than I care to have.' American diplomat Hugh Gibson called it the finest piece of literary criticism he had ever read."

Imagine that you have guests for dinner. One of your children starts giving an account of something that happened to them, or something they did, or something they have been learning about, and it is an excruciatingly detailed account, and the end is nowhere in sight. The time has come for drastic action, but you don't want to embarrass the speaker, so you casually work the word "penguins" into a sentence, something like, "Was there anything about penguins in it?"

If all goes well, the child quietly gets the message and cedes the floor. He or she probably flashes the signaler a quick irritated look, guests may raise a few eyebrows as they try to work out what just happened, and life goes on. (Occasionally the child will go beyond flashing looks and loudly reply, "It is not penguins!")

I have been saying "child", but theoretically it could just as well be an adult who requires this treatment. Some families probably have more need of such a private signal than others; we certainly find use for it around here.

I'll get to Cheesecake Brook next time. I have a lot to say about it.


About Me

I am a professor of mathematics. (I began calling myself "Empty" or Ø when hanging around at blogs, because I am somewhat fixated on the empty set. Students and colleagues know that I can be a bit of an ancient mariner about it.)