Wow. Rather amazing to hold the thing in my hand as an actual book, or almost-book. Duty compels me to remind you that you can pre-order, if you want, at Amazon.
How do you like my boombox, by the way?
Cathy blogs today about the enthusiasm for billionaires displayed at the AMS public face of math panel, and her misgivings about it. Cathy points out that, while gifts from big donors obviously accomplish real, useful, worthwhile goals for mathematics, they have a way of crowding out the public support we might otherwise have gotten, and sapping our will to fight for that support.
I think there’s an even deeper problem. When we’re talking about putting up buildings or paying people’s salaries, we’re talking about things that require many millions of dollars, and asking: who’s going to pay for them? It’s not crazy that the answer “a rich person” is one of the things that comes to mind.
But when we talk about improving the public image of mathematics, we are not talking about something that automatically costs lots of money. We’re talking about something that we can do on social media, something we can do in the newspaper, something we can — and frankly, should — do in the classroom. Cathy describes the conversation as centering on “How can we get someone to hire a high-priced PR agent for mathematics?” That means that the billionaire solution isn’t just crowding out other sources of money, it’s crowding out the very idea that there are ways to solve problems besides spending money.
The big news in combinatorics is this new preprint by Peter Keevash, which proves the existence of Steiner systems, or more generally combinatorial designs, for essentially every system of parameters where the existence of such a design isn’t ruled out on divisibility grounds. Remarkable!
I’m not going to say anything about this paper except to point out that it has even more in it than is contained in the top-billed theorem; the paper rests on the probabilistic method, which in this case means, more or less, that Keevash shows that you can choose a “partial combinatorial design” in an essentially random way, and with very high probability it will still be “close enough” that by very careful modifications (or, as Keevash says, “various applications of the nibble” — I love the names combinatorists give their techniques) you can get all the way to the desired combinatorial design.
This kind of argument is very robust! For instance, Keevash gets the following result, which in a way I find just as handsome as the result on designs. Take a random graph on n vertices — that is, each edge is present with probability 1/2, all edges independent. Does that graph have a decomposition into disjoint triangles? Well, probably not, right? Because a union of triangles has to have even degree at each vertex, while the random graph is going to have n/2 of its vertices with odd degree. (This is the kind of divisibility obstruction I mentioned in the first paragraph.) In fact, this divisibility argument shows that if the graph can be decomposed as a union of triangles with M extra edges, M has to be at least n/4 with high probability, since that’s how many edges you would need just to dispose of the odd-degree vertices. And what Keevash’s theorem shows is there really is (with high probability) a union of disjoint triangles that leaves only (1+o(1))(n/4) edges of the random graph uncovered!
Another entry in the series of “towering early 20th century thinkers were emo” (previously: B.F. Skinner was emo.) Bertrand Russell, age 31, writing to his friend Gilbert Murray:
I have been merely oppressed by the weariness and tedium and vanity of things lately: nothing stirs me, nothing seems worth doing or worth having done: the only thing that I strongly feel worth while would be to murder as many people as possible so as to diminish the amount of consciousness in the world. These times have to be lived through: there is nothing to be done with them.
This quote is pretty famous but glancing through his letters, holy cow, I had no idea how brutal Russell’s thoughts were. Here’s his take on math:
Abstract work, if one wishes to do it well, must be allowed to destroy one’s humanity: one raises a monument which is at the same time a tomb, in which, voluntarily, one slowly inters oneself.
And on marriage:
It is ghastly to watch, in most marriages, the competition as to which is to be torturer, which tortured; a few years, at most, settle it, and after it is settled, one has happiness and the other has virtue. And the torturer smirks and speaks of matrimonial bliss; and the victim, for fear of worse, smiles a ghastly assent.
All these letters are from the period when his first marriage was breaking up, so maybe he cheered up later?
A couple had a reservation at Alinea and their sitter cancelled at the last second and rather than absorb the $500 loss they decided to show up there with their 8-month-old baby. It didn’t work out, the baby cried, other customers were annoyed, chef Grant Achatz tweeted to his follows to ask how he should have handled it:
Tbl brings 8mo.Old. It cries. Diners mad. Tell ppl no kids? Subject diners 2crying? Ppl take infants 2 plays? Concerts? Hate saying no,but..—
Grant Achatz (@Gachatz) January 12, 2014
Then lots of people went ape about it, as is customary.
Emotions about this stuff run very high, for some reason. As for me, I wouldn’t bring a baby to Alinea. Then again, I also wouldn’t think someone who did so was some kind of war criminal.
But what this makes me think about is smoking in restaurants. Yes, younger readers, people used to do this! (And in France, even though it’s illegal, they still do, right? Help me out, French readers.) If a baby’s crying in a classy place, I’d find it annoying, but I would never say it ruined my experience. So I’m kind of rejecting the claim that a top-tier dinner is the same thing as a classical music performance or a play from this point of view. Though see here for further thoughts on the relationship between high-end Chicago dining and the legitimate theatre.
On the other hand, if somebody were smoking at a nearby table? That person is literally mixing a bad-smelling substance into the food I paid $500 for. It’s hard for me not to see that act as inherently more disruptive and dinner-ruining than a wailing baby.
Which is just to say that all these arguments about what rules should be “obvious to any thinking person” are kind of nuts. The rules don’t have justification — they are social norms, which are self-justifying. You shouldn’t bring a baby to Alinea because people, in this country, in this year have come to feel that their $500 buys them the right not to hear a baby. In some places and times, it didn’t buy you the right not to have cigarette smoke in your food. No one, back then, would have complained that the smokers in the room were ruining their special night — right? But now we would. Cigarettes haven’t changed, food hasn’t changed, noses haven’t changed: only the rules we make up for ourselves have changed.
In the comments, feel free to rant about how much you hate smokers, how much you hate breeders, how much you hate non-smokers, how much you hate non-breeders, or what rights you consider yourself to have purchased when you go out for a very expensive meal.
One good thing about flying LOT home from Israel (Chicago and Tel Aviv both have a lot of people of Polish descent, thus you can get from one to the other via Warsaw) is that you can learn a lot about rock in Polish from listening to the seatback audio. How had I gone my whole life without hearing Czerwone Gitary, the “Polish Beatles”?
Here’s “Nie zadzieraj nosa”
and “To Właśnie My”
My mother-in-law was toting around a book of short stories translated from the Hebrew and I saw a familiar name on the front: Aner Shalev. Not the same Aner Shalev as the group theorist I know, surely — but no, I checked, and it’s him! Good story, too, actually not a story but an excerpt from his 2004 novel Dark Matter (or I guess I should say Hachomer Haafel since it doesn’t seem to exist in English.) It was good!
Sometime last year I was in a coffee shop in Berkeley doing math with Tom Church and on the bookshelf there was an old issue of Story, and in the table of contents I found Vinayak Vatsal. Not the same Vinayak Vatsal as the number theorist I know, surely, but…. yep, it was him. I only got to read the beginning of Nike’s story because I was supposed to be doing math, but that one was good too, what I read.
How many mathematicians are secretly placing stories in literary magazines, I’d like to know?