Happenings — Mar 6

“Live as if you were to die tomorrow. Learn as if you were to live forever.” Mohandas (“Mahatma”) Gandhi.

(That’s one of the inspirational quotations on the wall of my study.)

Regardless of what else I might choose to talk about this week, the dominant subject was, in fact, particle physics.

I went to the annual “Oppenheimer lecture” at Cal last Monday in the late afternoon. Frank Wilczek, a co-winner of the Nobel Prize in Physics 2004,”for the discovery of asymptotic freedom in the theory of the strong interaction”, was the speaker.

“Cal”, of course (!), is the University of California — at Berkeley. I’m pretty sure that it is usually referred to as “Berkeley” elsewhere, but in this neck of the woods, I have learned, I had better call it “Cal”. Some people associated with the University have bridled at the implication that it is on a par with other campuses of the University of California — instead of being the original, the real one, the one that need not be tied to a town or city.

Well, I had occasion to look up “Bishop Berkeley” a few weeks ago… and I discovered that the town of Berkeley — excuse me, the city of Berkeley — excuse me, the People’s Republic of Berkeley — was named for the Bishop.

When some people assembled to found the University in the mid-1800s, they knew perfectly well that a town would grow up around it — so they planned, and they named, the town at the same time.

I find it amusing. The original University of California is an inseparable part of Berkeley and conversely. They were created together. One might argue that it has a better right than most to be referred to by its location.

Oh, well.

Why was I looking up Bishop Berkeley? You may remember him having something to do with the foundations of the calculus. He really, really objected to “infinitesimals”; I would like to think that he would be satisfied by the modern treatment of limits and derivatives. He lived from 1685 to 1753, so he was about 20 years older than Euler. In particular, he predates the beginning of rigor in analysis. (That’s a rather sloppy statement, but let me just leave it there.)

What I was looking for was a quotation something to this effect: the only prerequisite for accepting some particular piece of mathematics, is that you be insane. (I’m still looking for that quotation. Can you help me out?)

I thought it might have been something the Bishop said… but I can’t find it.

Why was I looking for that quotation? Over breakfast with a physicist friend, I mentioned that there was a surface — mathematical, of course — with finite volume but infinite surface area. I thought that quotation was associated with this surface.

This is a rather interesting surface. You can fill it with paint, specifically with a finite amount of paint — but you cannot paint it.


Let me put that another way. There is paint in contact with every point of the surface — it’s literally full of paint — so how can we be unable to cover it with paint?

There is no reason for me to say very much about this surface: Wikipedia has a fine article.

(It is a surface of revolution. Take a rectangular hyperbola, say y = 1/x. Rotate that curve about the x axis. In fact, restrict the curve and the surface to x >= 1. It is still an infinite surface, but only in one direction instead of two. It is called Gabriel’s Horn and / or Torricelli’s trumpet.)

Okay, let’s get back to Monday afternoon in Berkeley at the University of California.

As one would imagine from his Nobel prize and current events in physics, Wilczek’s lecture was about the particle physics which the Large Hadron Collider will be investigating. It’s not just the Higgs boson which they hope to find, but also some of the particles required by supersymmetry.

The Higgs boson is predicted by “the standard model”; supersymmetry is a theoretical extension of the standard model.

The standard model is the description, in theory and in practice, of fermions and bosons (matter and field particles), i.e. quarks, electrons and neutrinos, the photon, the Ws and Z, and gluons. (Everything but gravity and the graviton.)

It was a pleasant lecture, interesting without being challenging or intimidating.

Nevertheless, it reminded me that amidst my pile of quantum mechanics books, including quantum field theory and gauge theory, I have only one book that addresses “the standard model” per se.

Just before I went to bed Monday night — that is to say, when I was tired and my judgement was fading — I searched Amazon for books on the standard model.

I bought three. (My judgement actually wasn’t bad; they look pretty good. I spent yesterday evening looking thru them, and others.)

The problem is that my pile of quantum mechanics books is on a par, numerically, with my books on time series, or control threory; it is smaller than my differential geometry collection — even with Lie Groups and Lie Algebras separated out of differential geometry — but it is, in fact, larger than my dynamical systems collection.

I really, really need to stop buying books on quantum mechanics — or start reading books on quantum mechanics. In fact, of course, I should try to do both.

Hence the quotation that begins this post. I am sure that I own more mathematics books than I can read before I die. Heck, whether I own the books or not, there exists more mathematics then I can understand before I die.

I might as well study whatever I feel like.

Hmm. My brain has finite volume but I act as though my bookcases have infinite area.

So, “the big four” has become “the big five”. All this means is that one more book has been added to the small desk: Griffiths’ “Introduction to Elementary Particles” (bibliography).

I have removed “the Mathematica Navigator” from the small desk. The total remains at 18. (For what it’s worth, just for fun, I’ll probably publish the current list once a month.

Oops, how did I get to 18? In addition to adding a particle physics book, I added a statistics book.

Not because I wanted to study it, but because I remembered that I had read some of it while eating out, and enjoyed what it had to say. It is on the small desk specifically as interesting reading rather than actual work. FYI, it’s Hair et al., “Multivariate Data Analysis”, sixth edition, Pearson Prentice Hall. (Not all of the books on the small desk are suitable for dinnertime reading.)

Okay, my kid has already played this morning… now I’m going to try to spend an hour with one of the books on the small desk… then I will find some mathematics to do… and, finally, I will try to draft a post for this weekend.

Mathematics? Probably color, logic, or orbits. The blog? Most likely color or logic.


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