I’m eager to summarize the (largely excellent) discussion of last week’s nightmares and to talk about what it all means. I’ll surely get to that in the next few days. But meanwhile, we have another loose end to tie up.
I recently asked what comes next in the following series:
The answer, of course, is
Please raise your hand if you found this intuitively obvious.
In case your hand didn’t go up, consider the following sequence:
I continue to be bowled over daily by the high quality of the discussion at MathOverflow, and the prominence of many of the frequent participants. But this one was special:
A newbie poster asked for a pointer to a proof of the “de Rham-Weil” theorem. There’s a bit of ambiguity about what theorem this might refer to, but I had a pretty good of what the poster meant, so I responded that the earliest reference I know of is in Grothendieck’s 1957 Tohoku paper — which led another poster to ask if this meant de Rham and Weil had had nothing to do with it.
This triggered an appearance from the legendary Roger Godement (had he been lurking all this time?), now aged 91 and one of the last survivors of the extraordinary circle of French mathematicians who rewrote the foundations of topology and geometry in the mid-20th century and changed the look, feel and content of mathematics forever. I tend to think of them as gods and demigods. Godement’s indispensable Theorie des Faisceaux was my constant companion in late graduate school. And now he has emerged from retirement for the express purpose of chastising me:
 |
 |
With a hat tip to our occasional commenter Ron….
Remember those faster-than-light neutrinos? The ones that threatened to overturn relativity, and along with it everything we think we know about how the universe works?
Well, it turns out that maybe they weren’t faster than light after all — they might have only appeared to be faster than light because their arrival time was mismeasured. The mismeasurement was (it seems) caused by the researchers’ failure to account for the effects of ….. relativity!
I hear an echo of the great ongoing debate between Einstein and Bohr on the foundations of quantum mechanics. Continue reading ‘Relatively Speaking’
Leonard Jimmie Savage was a pioneer in modern decision theory and a disciple of Frank Plumpton Ramsey, whose story occupies the final chapter of The Big Questions.
In 1954, Savage wrote a lovely and highly influential little book called The Foundations of Statistics, which starts with six simple axioms about human preferences — one of which says that if you prefer a dog to a cat, then you’ll prefer an 11% chance of a dog to an 11% chance of a cat (and likewise for any other percentage). From these axioms, he drew deep and surprising conclusions about human behavior. This work underlies much of modern game theory, decision theory and economics in general.
According to legend (and I have reason to suspect this legend is actually true), Professor Savage was giving a talk one day when he was interrupted by the French econometrician (and then-future Nobel Prize winner) Maurice Allais, who asked Savage if he’d be willing to answer two questions about his own preferences. Savage said sure. These were the questions:
A few years ago, billionaire David Koch donated $25 million to his alma mater, Deerfield Academy. From his presentation speech:
You might ask: How does David Koch happen to have the wealth to be so generous? Well, let me tell you a story. It all started when I was a little boy. One day, my father gave me an apple. I soon sold it for five dollars and bought two apples and sold them for ten. Then I bought four apples and sold them for twenty. Well, this went on day after day, week after week, month after month, year after year, until my father died and left me three hundred million dollars.
Now on the one hand I love this story. But wouldn’t it have been more plausible if he’d sold the first apple for, say, a nickel?
Well, maybe not much more plausible. Doubling your money every day, it takes just a little over a month to grow a nickel into three hundred million dollars.
I still like the story though.
