During a holiday in Iceland some years ago it amused me to learn how the USA manages to have 1000 times the population of Iceland. Approximately speaking it’s 10 times as long, 10 times as wide, and 10 times as densely populated.
I’ve just arrived to live in Lyon after a stay in New York and noticed that these cities have something in common: their heart is a peninsula of land running north-south between two rivers. And how does Manhattan manage to have 27 times the population of Lyon’s Presqu-Île? You guessed it. Approximately speaking it’s 3 times as long, 3 times as wide, and — this time we can say it less abstractly — 3 times as tall!
[8 November 2017]
In the USA, roughly speaking, everybody has a gun. This big awful fact stares you in the face. Europeans find it inexplicable. It’s just so obvious, why don’t the Americans prohibit these killing machines?
In France, roughly speaking, everybody smokes. I’ve arrived for a year, and it’s strange how this fact feels similar. Americans find it incomprehensible. It’s just so obvious, why don’t the French just quit?
I feel oddly optimistic about these pathologies. Eventually, sloppily, rationality more or less prevails. The Americans will lose their guns one day, and the French will lose their cigarettes. But it will take generations, for habits steep into us, and we come to feel they are part of our identity. I’m sitting outside a bar right now in Vieux Lyon, smoke all around, and the very smokiness adds to that agreeable feeling of Frenchness.
[24 Oct 2017]
Classically, discrete molecular systems like the air in a bicycle tire have been modeled as continua. This would seem like the right thing to do for almost any application. We may know that the pressure in the tire ultimately results from 10^25 molecules bouncing around at random, but for most purposes it would seem crazy to try to follow those motions in any detail.
Lately, however, more and more mathematical scientists are trying to track statistics of individual particles. It seems everything nowadays is getting reformulated stochastically. I have been skeptical of this trend. Is it partly just a fad, a way of generating impressive new challenges for our latest computers?
But walking around New York has given me an illustration that sometimes, discreteness in our models really is indispensable. On the sidewalks there are hundreds of pedestrians flowing north, south, east, and west, and it is tempting to think of these flows as continua. You certainly feel like part of a wave when you are flowing along with the crowd! But at each crosswalk, something discrete happens. If the walk light is illuminated, a car wanting to turn right has to wait until the number of pedestrians crossing falls to exactly zero.
If pedestrians were a continuum rather than discrete, their density would always be positive, and no car in New York would ever be able to turn right.
[8 October 2017]
I just finished reading the wonderful book Hamilton by Ron Chernow. The fights among politicians were as awful then as now, but they were more capable and impressive people. Where are Hamilton, Jefferson, and Madison today?
The answer is that they are not in politics. Take a look at the Harvard Class of ’77, about to celebrate its 40th reunion. My 1600 classmates from Bill Gates on down include leaders of science, medicine, law, business, and the arts. Where are the senators, congressmen/women, governors, and mayors? Zero. Politics these days is a dim career choice, and the USA is paying the price.
[23 September 2017]
In Paris as in New York, on a nice evening, you’ll find people sitting at tables along the edges of restaurants, half indoors and half outdoors. Legally speaking, the tables in Paris are outdoors — because smoking indoors is against the law. By the same principle, the tables in New York are legally indoors — because drinking outdoors is against the law.
[23 September 2017]
Everybody seems to be wired these days, and yesterday I stood on Broadway and took a tally as 100 people walked by. 45 were using a phone or at least had wires in their ears, and 18 were holding a phone without apparently using it. Just 37 showed no sign of an electronic device.
My first thought was, how awful! How sad that we are so wrapped up in our wired worlds! My second thought was, just imagine twenty years from now. We’ll be more networked than ever, but the phones and the wires won’t be visible any more. Our hands will be free and our minds will be who knows where.
[22 September 2017]
Kate and I listened to Beethoven’s masterpiece today, the Ninth Symphony. This last of his symphonies explores one theme, then another, growing and growing, and finally giving us that amazing choral finale which everyone agrees is his greatest work.
Immersing myself in this magnificent music, I felt the parallel with the Beatles’ masterpiece, the second side of Abbey Road, their last album. So we listened to that next. Like Beethoven, the Beatles here go beyond their usual tracks, weaving a great work that explores one theme, then another, building and building to the big drum solo and the final catharsis.
Meanwhile I have just read Harari’s book Homo Deus. Harari shows us how for hundreds of years in the West we located meaning and morals externally, in an all-powerful God, but now we have moved to locating them in ourselves, in humanity and its needs and feelings.
And I realized that Harari’s point is perfectly reflected in the stirring final lyrics of Beethoven and the Beatles. Beethoven (Schiller) finishes with a triumph of religion: “Above the starry canopy must dwell a loving father” (Über’m Sternenzelt muß ein lieber Vater wohnen). The Beatles finish with a triumph of humanism: “And in the end, the love you take is equal to the love you make.”
[15 August 2017]