[Morris Berman, Pittsburgh Post-Gazette]
In my previous post, I described an annoying error of fact in the book I am now reading, Jim Baggott’s The Quantum Story: A History in 40 Moments. Baggott’s error was to describe the great Norwegian mathematician Sophus Lie as having lived in the eighteenth century when, in fact, Lie lived entirely in the nineteenth. Baggott may make other errors in the book, but in this case he erred on a subject I know something about. I don’t know much. I do know Lie theory.
If I were to list my areas of expertise, included would also be the New York Giants professional football team of the late 1950s and early 1960s. Imagine my dismay, then, when I stumbled on an error about the Giants just minutes after the Lie biographical error.
No, not in The Quantum Story. The Lie error had so bugged me that I had put the book aside. Moments later, the mailman dropped testerday’s mail in our slot. I got up, brought it in, was delighted to find the new issue of The New York Review of Books, and began reading Nicholas Lemann’s review of Howard Cosell: The Man, The Myth, and the Transformation of American Sports, a new book by Mark Ribowsky. (If you follow the link to Lemann’s review, you’ll discover that it’s behind a paywall. Sorry.) The following passage stopped me dead.
Big-time sports is deeply woven into the texture of American society. They evolve in tandem. Can anybody name the heavyweight boxing champion of the world? Boxing still exists, but it has begun to feel like a cultural artifact from the vanished heyday of the American working class. Football is much more distinctively American than boxing—attempts to export it have mainly failed—and its triumph in popularity and commerce over all other sports is a little mysterious. The heavily armored players are hard to see, it’s violent, the action is highly sporadic, and the teams play fewer games than in any other major professional sport. Whatever the reason for its success, to maintain its position football has to absorb all the main currents of the culture as they present themselves.
David Halberstam was killed in an auto accident while on his way to interview Y.A. Tittle, the New York Giants quarterback in the 1958 National Football League` championship game against the Baltimore Colts, a muddy cliffhanger known as “The Greatest Game Ever Played.” Halberstam’s book on the game, had he lived to write it, would surely have noted that the great majority of the players were white, grimly determined, and not very well paid (their number included Howard Cosell’s future broadcasting partner Frank Gifford).
Today fewer than a third of NFL players are white, though whites still dominate some positions, like quarterback and kicker. Star quarterbacks can make more than $10 million a year. Linemen are enormous three-hundred-pounders, receivers have sculpted, tattooed bodies and do flashy little dances in the end zone when they score touchdowns, and stadiums are filled with luxurious touches like indoor box seats for high rollers. The exciting pass, not the dutiful run, dominates the game. Coaches use the latest information and communications devices to decide which plays to run and to get them to the players on the field. Everything that happens in American popular culture, marketing, ethnicity, and technology seems to manifest itself on the field.
Did you catch the error? Geez. I mean, we’re talking about one of the four or five most famous games in the history of professional football. Maybe no longer considered the greatest, but among them. I might put Super Bowl III up there with it in terms of impact on the sport’s history. Even if one wasn’t there, even if one didn’t watch it or a tape of it, even if one doesn’t even care, it wouldn’t take a lot of effort to check whether Y.A. Tittle was actually the Giants’ quarterback that day.
I can assure you that he wasn’t. In fact, he wasn’t even on the team. He played for the San Francisco 49ers through the 1960 season, joining the Giants for the 1961 season and then leading them to three consecutive championship games, losing to the Packers in 1961 and 1962, the Bears in 1963.
I don’t need to look this up. I lived it, following every moment of every Giant game in those days, glued to the radio as Marty Glickman* called them, most memorably Tittle’s seven touchdown pass game. But one doesn’t need to live it. One can look it up. Given the ordinarily reliable Lemann’s apparent ignorance of football history, he should have.
*I knew nothing then of Glickman’s own story, as a member of the US 4×100 relay team in the 1936 Berlin Olympics who the US team decided to keep out of the race to avoid offending Hitler, Glickman being Jewish.
I mentioned last week that I had begun reading Jim Baggott’s The Quantum Story: A History in 40 Moments, inspired by Jeremy Bernstein’s WSJ review just short of a year ago. I’m on moment #25 now, having made it from Max Planck’s introduction of quantized energy in Berlin in 1900 to Sheldon Glashow’s introduction of the charm quark at Harvard in February 1970.*
*Speaking of which, I was there! February 1970 would have been the start of spring semester of my freshman year. I was taking the honors freshman physics course. No one bothered to tell me that exciting developments were going on right around me. From where I sat, physics was pretty darn boring.
The Quantum Story has been interesting, but it’s a puzzle what Baggott assumes of his readers. He doesn’t explain much. I suppose you’re actually supposed to know the physics already. It helps, for instance, to know about the strong and weak forces, which appear on the scene quite suddenly, as the book shifts from the oft-repeated history of the early days of quantum theory through World War II to quantum electrodynamics, electro-weak theory, and high energy experimental physics. I was happily reading about the good old days of Franck, Einstein, Bohr, Heisenberg, and Schrödinger, then the war comes and suddenly they have left the stage, supplanted by Feynman and Dyson, Weinberg and Glashow. The material on the Bohr-Einstein debates about quantum mechanics are well told. Einstein comes off as a huge pest, a meddling nay-sayer whose best days are behind him, mucking up the works by making everyone stop to listen to his latest criticisms. Also well told is the story of Heisenberg’s ambiguous allegiance to Nazi Germany and its atomic bomb effort, which he was either actively leading or discouraging. After the war, the book seems to lose its narrative thread.
But I’m here to tell a different story, the sad story of the dying art of fact checking. Moment 20 takes place in Princeton in 1954. It’s a technical tale, about the strong force, quantum field theory, and the work of Chen Ning Yang. To get there, Baggott, backs up to talk about earlier work of Hermann Weyl, one of the giants of twentieth-century mathematics and a hero of mine. Like any mathematician who has done any work in the field known as representation theory of Lie groups, I am greatly in Weyl’s debt. Lie groups are the very objects that became crucial to further developments in quantum physics. Baggott explains that
Weyl had worked on the representation theory of types of symmetry groups called Lie groups, named for the eighteenth century Norwegian mathematician Sophus Lie.
Sigh. This is mostly true. The problem is, Sophus Lie didn’t live in the eighteenth century. He was born near the end of 1842 and died in early 1899. And anyone with the slightest knowledge of the history of mathematics would know that the objects named after Lie couldn’t possibly have come into existence in the eighteenth century, unless some mathematician headed back in a time machine.
It’s discouraging. In Bernstein’s rave review of the book, he writes that Baggott “manages to get the people right. I know this because for many of the scenes he describes I was there.” I suspect Bernstein doesn’t have Lie’s time in mind.
Baggott continues, in the very next sentence, with what I consider another clunker.
These are groups of continuous symmetry transformations, involving gradual change of one or more parameters rather than an instantaneous flipping from one form to another, as in a mirror reflection.
I realize this post isn’t the place to get technical, but Baggott’s sentence seems to confuse the continuous change of parameters defining elements of the group with the actions the group elements perform on space. Baggott follows with a description of the group U(1), which plays a role in the physics to follow, describing it (correctly) as the collection of rotations of the plane (or, say, a piece of paper) through all possible angles. This is “continuous” in the sense that one can move from one rotation angle to another smoothly through all angles. In contrast, the group consisting of just the 0 degree and 180 degree rotations would not be continuous, since one can’t go smoothly from doing nothing to doing the 180 degree rotation. I suppose Baggott understands that. But it’s not at all what he says. Even in a continuous or Lie group, the individual rotations do perform what he describes as “instantaneous flipping” from one form to another.
Maybe I’m just mis-reading him in his effort to explain mathematical concepts in ordinary language. It’s difficult to do. Then again, I have no idea why he even bothers trying, given all the other language he throws around at this point in the book with no explanation at all.
I’ll keep reading. I’m eager to learn more. But I’m also eager to get on to the next book.