Abi Gopal and I have a new idea we want to announce to the world, a new method for solving the Laplace and Helmholtz equations. We sent a Letter to Nature, which was rejected in five days. Then we sent a Brief Report to Science, and it was rejected in 23 hours. Neither journal sent our contribution to referees.
But we want to put our names on this! So what did we do? We posted the announcement online as an e-print at arXiv. Now we can move on and develop our idea at leisure.
Here is what tickles me about this story. You might think journals are the classic medium and arXiv is the new kid on the block. But in a sense, it’s just the reverse. In the old days, a scientist could send an idea to a journal and get it published quickly. A classic example was Gibbs’ announcement of what is now called the Gibbs phenomenon, which he sent as a letter to Nature back in 1899. These days, however, journals have evolved into armored tanks. Nature of 1899 is arXiv of 2019.
[6 February 2019]
During my career so far, I’ve given around 800 talks on 150 subjects in 31 US states and 32 countries on 6 continents.
If an average audience is 30, it would seem around 25000 people have seen me speak, or maybe 10000 if you weed out repeats. Such numbers are huge by an ordinary standard, but infinitesimal on the scale of politicians or celebrities.
[12 February 2019]
In the old days the idea was that if A annoyed B, they sorted it out among themselves. Now, it is increasingly likely that B will accuse A of being a homophobe or a racist or some other kind of oppressor. Yesterday a woman I’d met only sixty seconds earlier accused me of talking like a man, adding that at her age, she didn’t have to put up with that any more. It hurt.
I may have been guilty as charged, but still, I think her response was inappropriate. The issue is what lawyers call the principle of proportionality. When B brings identity groups into the discussion, a tussle of one against another becomes a battle of millions against millions. In cases of genuine oppression, the big battle may be needed, but most of the time, day to day, that scale of response is disproportionate. It’s like sentencing Jean Valjean to five years for stealing a loaf of bread. It’s like pulling out a gun to settle a fistfight.
[7 February 2019]
You’d think knowing mathematics would help me understand things, but there’s an article in this week’s Economist for which it was just the reverse.
It seems that women tend to give birth in the wee hours of the morning, for reasons of natural selection. The article describes two groups of women studied and then says that “the average time of birth” was 6.34am for one group and 4.18am for the other.
The average time of birth??!! To a mathematician this is patently a meaningless notion. How can you talk about the average time of something when the time variable is periodic?
After some thought, you realize that they must be measuring time by a 24-hour clock starting at midnight, and then, well, maybe it’s arbitrary, but at least the average is well defined. After a little more thought you realize that to anyone without mathematical training, this would be perfectly obvious.
[27 April 2017]
At Harvard I took both math and physics courses all the way through, but I knew which was my subject. In mathematics, any principle you learned was simply true: you could apply it anywhere you liked and you’d never reach a falsehood. In physics, that wasn’t enough. You had to have some kind of deeper understanding to see that this principle was appropriate here and that one could be applied there. It made me uneasy.
Forty years on, what kind of mathematician have I become? One whose pride is that he doesn’t apply principles blindly but guided by deeper understanding! Indeed, not long ago I published an essay on “Inverse Yogiisms” all about mathematicians’ habit of following rigorous logic to misleading, though mathematically valid, conclusions.
Which brings me to two thoughts. One is that maybe I could have been a pretty good physicist after all. The other is that as a physicist, maybe I would have been a little less distinctive.
[3 February 2019]
We were listening to Christmas carols today and they reminded me disturbingly that the Christ child was a baby boy, not a girl, destined to grow up to be a man, not a woman.
All my life I have marveled that no amount of absurdity in religious doctrine seems to dent people’s faith. But listening to these carols, for the first time, I had a glimmering of what might finally bring Christianity down. Cathedrals of nonsense and impossibility? — no problem. Traditional sex roles? This is a problem.
[20 December 2018]
The great discovery of computer science in the 1970s was the distinction between P and NP. All problems in P were equivalently tractable, and all problems in NP (assuming P≠NP) were equivalently intractable. And this came with a prediction seemingly beyond doubt: as computers grew faster in the future, the gulf between the two classes would widen.
What ever happened? Forty years on, P vs. NP is famous as a mathematical challenge, a million-dollar Clay problem, and it’s a reference point for all kinds of theoretical analyses; but though computers got millions of times faster, the gulf seems to have narrowed! Nowadays a long list of NP-complete problems are largely tractable in practice, including traveling salesman, maximum cut, edge coloring, frequency assignment, maximum clique, 3SAT, set cover, vertex coloring, knapsack, and integer programming. And only theorists nowadays regard all problems in NP as equivalent.
The explanation seems to have two parts. One is that NP-completeness is defined by worst-case analysis, and many problems turn out to be rarely in that zone, especially if softened up with good heuristics or randomization. 3SAT is one example, now a workhorse of practical computing, and even more striking is that the simplex algorithm is used all the time for linear programming even though it’s an exponential algorithm for a polynomial problem. The other is that NP-completeness is defined by exact optima, whereas if one relaxes the goal by a fraction, what used to be exponential may become polynomial. By such means a discrete problem can often be approximately solved, even in the worst case, via continuous algorithms such as linear or semidefinite programming. An example is max cut.
Nobody seems to talk much about this great surprise at the epicenter of computer science. This puzzles me.
[9 December 2018]