The Nine Point Circle

From my Jewish Post series: this one got published last fall. I think it's a really good article.

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You’d see him around campus, sometimes striding purposefully into the faculty building, sometimes just standing there in the student lounge, but always alone. He had those thick coke-bottle eyeglasses and a penchant for long black trenchcoats. He wasn’t a student and he wasn’t a exactly a professor either, but they still gave him his own office. He certainly earned his keep in terms of research and publications…but a faculty appointment? Not likely. Much as they respected or even were intimidated by his intellect, he somehow didn’t quite fit in. Not that he would have really fit in anywhere else…

Generations of former U of M student surely know who I’m talking about, even if they don’t know him by name, and didn’t know his story. Except…there are two of them…one in Law, and one in Mathematics. They are Eddy Lipsett and Barry Wolk, and they are Jewish Geniuses of a certain unmistakeable type. Perhaps on occasion the Christian world produces its own Eddys and Barrys, but if so, I haven’t met them yet. 

I hope both of them will forgive me for exaggerating the similarities between them, which I confess to having done for dramatic purposes. Of course they are really two very different people, with their own individual stories that I don’t really know much about, nor do I have their permission to tell, so I’m not going to say much more about them. But if it’s not too presumptuous of me, I’ve always felt a kind of cosmic connection to them, almost as though we three are part of what Lionel Boyd Johnson famously called a karass. Or perhaps I’m mistaken and I’ve simply identified a grandfalloon…who knows? (If you don’t know what I’m talking about, I suggest you google the religion of Bokonism.)

I’ve known Barry longer than I’ve known Eddy, because my involvement with math goes back a lot farther than my involvement with the Law. He once gave a lecture that I attended on something called the Nine Point Circle, a seemingly classical result of the ancient Greeks except for the surprising fact that it wasn’t actually discovered until 1822. Barry’s talk was a tour de force in which he proved the existence of the circle in three very different ways. It never occurred to me until this moment, but what a shame that I never invited him on my TV show, because then I could be posting him on YouTube. As they say, it’s the world’s loss.

I run into Barry nowadays at the downtown library, where I often go to meet my own private students. Last month we were trying to show that for any quadrilateral inscribed in a circle, the angles add up to 360 degrees. We started by putting four points around the circumference and connecting them with straight lines. It wasn’t too hard to show that the angles had to add up to 360. But Kyle (my student) wasn’t quite satisfied. “What if you just know that the four angles add up to 360…how do you prove that the points lie on a circle?” I told him it was the same proof…you just go through the steps in reverse order…”like so”, I began…but then I found it wasn’t so easy!

We sweated over this for at least 20 minutes before we got it right; and then we saw Barry passing by, on the way to the free Internet terminals. He was already online when we caught up with him, coke-bottle glasses on the table beside him and his face six inches from a screen covered in equations. “Barry”, I interrupted him, “have a look at this, will you?” I showed him what we had been working on, and Barry was like,”oh, it’s trivial…trivial”. “No”, I tried to explain,  “we got the “if” part right away…it’s the “only if” that gave us a hard time…”

“Of course you can’t just reverse the steps” he jumped in. “You have to do it differently…here, give me a piece of paper.” And in seconds he had drawn the proof. A vintage Barry Wolk moment.

I only got to know Eddy in the last year or so, since legal research has become a bit of a hobby with me. Eddy is a much more private person than Barry, and I don’t want to pretend to be on any level of intimacy with him, but I saw him just the other day. It was early in the morning and he was on his way to shakhris. I asked him how his research was going…did he have any interesting cases? Yes, he answered, in fact he had just published something on Whatcott v Saskatchewan, and he started to tell me where I could find the article.

I couldn’t believe my ears. “You’ve got to be kidding: I’m arguing Whatcott next week in Provincial Court!” It was true! I’m defending myself against trespassing charges brought against me by the U of W, and Whatcott is an anti-abortion activist who pleaded Freedom of Expression to successfully beat the rap for trespassing at the University of Calgary.

It turns out Eddy’s case was a little different. It was the same guy, different case. Whatcott had a number of cases in the past decade, all involving abortion protests, including trespassing at the U of Calgary, loitering at the U of Regina (he beat that one too), and something with the Saskatchewan Human Rights Commission. That last one was Eddy’s case.

Still, I had hoped that this incredible coincidence would have been enough to pique Eddy’s interest in my case and get him to open up. But I had no such luck. As I said, Eddy’s a very private person and has a strict rule against getting involved in actual personal cases. In the meantime, I had unwittingly followed Eddy into shul, and our conversation was interrupted by the khazen’s intonation of the familiar words: piskhu-li shaarey tzedek…Eddy was already praying, and the shammes was handing me a tallis. Oh my god…was that Eddy harmonizing so beautifully? I turned my head to look in the direction of the sound. No, my mistake..it was Rabbi Green, singing into his microphone. Eddy was just standing right below the speaker… 

Yechts: The Gerund in Yiddish

I was playing Scrabble last week and I had a seven letter word sitting on my rack: hauling. But there was nowhere to play it…unless it could be pluralized. Is haulings a word? It’s tempting. Hauling is a noun…it’s an activity, and that’s a thing. To be sure, it’s also a verb, as in “I am hauling gravel”. But it’s also a noun: “Hauling gravel is hard work”. What else is the subject of that sentence if not hauling? I think that kind of noun is called a gerund.

But of course, not every noun can be pluralized by adding s. And the fact that it ends in ing is not necessarily the problem. You can have a number of undertakings going on at the same time, and that’s a perfectly good Scrabble word (except it might be too long to fit on the board). You can attend three different poetry readings in the same evening. And so on. But can you have multiple haulings?

To understand what’s going on here, we have to start by noting that there at least two different kind of ing words here. Undertaking and reading are not gerunds in the same sense as hauling. Well…reading is, if you say “Reading is fun”…that’s a gerund. But the “reading” in poetry readings is not the plural of the “reading” in reading is fun. If you see what I mean.

Because haulings actually looks like it might be a word, as in the following conversation: Tom says, “I was hauling garbage all day”…to which Dick replies: “What did you do with the haulings?” It’s a bit contrived, but it’s arguable. Was my Scrabble partner convinced? Well…

The thing is, this is a whole new kind of ing noun, different from the other two we’ve seen do far. It’s clearly different because it only takes the plural (or collective) form…no one takes away a single hauling of garbage. Or droppings. No one picks up a single dog dropping. They pick up droppings with an s. Yes, you can play dropping in Scrabble, if you’re dropping a ball. But it’s really a whole different word from dog droppings.

What about serving? Would you like one serving of Jello with your meal or two? I guess I’m not sure if servings  is more like undertakings or droppings. Maybe it’s somewhere inbetween…but that’s not my point. I want to talk about how these things work in Yiddish. Because in Yiddish, we have three different endings instead of one.

The first one is easy, because it is close to the English ending. Undertaking in Yiddish is unter-nehmung. In fact, in the Galitzianer pronunciation, the ung ending is actually just like the English ing. You can pluralize it with –en, so you have several unternehmungen. Another nice word that takes this type of ending is vorhandlen – to negotiate. “Peace negotiations” in Yiddish are sholem-vorhandlungen.

What about “reading and writing”? In Yiddish, we would have schreiben un lesen (or leyenen if you’re reading from the Torah…no one quite knows why!). The point is it’s a different ending…it’s just the infinitive form of the verb, without the ung. These are basically identical to the German constructions.

The third form is where it gets interesting. Have you ever heard of drippings? I had an English co-worker once from a very working-class background, and he once told me how his mother always used to save the “drippins” for his father, because animal protein in any form was at a premium. He was talking about the drippings from frying bacon…but of course, my readers wouldn’t know anything about that.

It’s funny that in the old country, we also had a culture of poverty, and there was a food item which arguably took the role of bacon for us: it was called grieven, and I don’t know what that word means, but it is sometimes translated as cracklings, and it was a special treat for the children when a goose was slaughtered…I think it was something about the way the skin got fried up in its own fat. So the English had their drippins, and we had our cracklings. But I digress…

I want to tell you about the third kind of ending…the one we use in Yiddish for words like drippings. It only shows up in a handful of words, but it’s very expressive: echts, and it lends a distinctly unsavory flavor to the word it attaches to. For example, the shell of a seed is a schâll; to remove the shell is schâllen; but if you have a big pile of sunflower seeds that you’ve been spitting in bowl (or on the floor), it’s called schâllechts – shellings, if you like.

Another one: saliva. To spit is speien, as in speien in die kasha (pissing in the soup, as we might say). But “saliva” in Yiddish is…yes, speiechts!..literally, “spittings”. Grease is schmierechts…you can see where that comes from. And there’s one I never figured out the story on, except that it’s a substance, presumably sticky and smelly, used in the process of bootmaking: dzhegechts. Maybe it’s a Slavic word. My favorite is ân-tuechts – from ân-tuen sich, to get dressed; and you use it to describe an embarrassing or inappropriate get-up that you find yourself forced to wear. Those are all the examples I can think of now.

Where does this suffix come from? You don’t see it in German…well, not normally. I sometimes visit a German Language discussion group online, and I posted the question: does the form exist in German? I got an interesting answer from one Takkat, a regular contributor, who offered the seldom-used term kehricht…meaning “sweepings”, from kehren, “to sweep”. It was the only example of this form in German that anyone could come up with, and it definitely jibes with the Yiddish pattern in terms of unsavoriness (except it’s missing the final s).

I wonder if any of our readers can think of any more echts words?