Earlier this year, as I said when it happened, someone asked me if there was a book about string theory at a popular level. I had thought I was going to have to recommend one fairly challenging book (Brian Greene’s “The Elegant Universe”) and one anti-string book (Lee Smolin’s “The Trouble with Physics”).
There is an elementary book. As far as I can tell, there is only one… but that could change.
And where would we look for such a book?
Stuff “for Dummies”.
There is a “String Theory for Dummies”, ISBN 978–0–470–46724–4. I hope people aren’t put off by the title, but it’s one of a series of introductory books about just about anything.
No equations… broken into bite-size chunks and thoroughly cross-referenced, so it’s a book you can dive into for a topic rather than have to read cover-to-cover… it appears to be well-written and accurate (as far I know, which isn’t much).
Further, it’s the only book I’ve seen that looks readable by an educated layman. Second best, for prerequisite knowledge, was “Quantum Mechanics for Poets” by Leon M. Lederman and Christopher T. Hill… and it wasn’t anywhere near as readable. Nor did it have much if anything about string theory!
(I could have sworn that I wrote more about Smolin and Woit, but apparently not.)
The primary author of the book is Andrew Zimmerman Jones, who is the “physics guide” for about.com . His website is here .
While I was checking him out, after reading his book, I came across this post of his . It seems that since it opened in 1938, the Bronx High School of Science has had 7 of its graduates go on to win Nobel prizes in physics.
Well, just who was the physics teacher?
It turns out that the graduates cite the school atmosphere rather than any one teacher. They were encouraged to ask questions.
Ostwald shows up in the history of color theory. He was an artist, apparently, and after he retired professionally, he worked on color theory. I can’t seem to find a clear reference, but he may have championed the description of colors as hue-black-white. (I really should remember that, but I don’t)
Unfortunately, I don’t trust the reference which told me that he had three students who won Nobel prizes.
The reference in question is “Color for the Sciences” by Koenderink. The book was recommended in this comment. I bought it… I’m reading it… and I’m looking forward to finishing it, but I already have mixed reactions. It has a few typos and some poor English, but it is nevertheless clearly and well written, and it seems worth reading, so far.
For now, let me focus on one small issue that has weakened my trust. On page 43, Koenderink says
“A Hilbert space is a separable space (given any two distinct points, there [exist two] disjunct open sets such that each set contains one of the points) that is complete (every Cauchy sequence has a limit) and has an inner product.”
There are two problems with that sentence.
One, for at least the past 45 years, a Hilbert space has not been required to be separable. Yes, the definition changed over time. Still, he could simply assume that he has a separable Hilbert space instead of a Hilbert space. Only the words change – except that then he no longer has a general Hilbert space.
A Hilbert space is just a complete inner product space.
Two, he has mis-defined “separable”. A space is said to be separable if it has a countable dense subset; the real numbers, for example, are separable because the rational numbers are a countable and dense subset. (Dense? The real numbers are the closure of the rationals.) More to the point, what he did define is the separation axiom named T2 or Hausdorff.
As it happens, this second mistake is in fact irrelevant: every inner product space is a metric space, and every metric space satisfies very strong separation axioms; in particular, every metric space is Hausdorff.
So. Koenderink is shaky on his math. Well, so am I sometimes. I still intend to read him.
(Look, I make mistakes. Most people do. And it may be that no mistake in this book will invalidate its criticisms of the decomposition of spectra – he may be right even if the details are wrong – but I’m now hesitant to assert that Ostwald had 3 Nobel-prize-winning students just on the basis of Koenderink’s statement.)
And in preparation for Koenderink’s arguments I’ve been looking at infinite-dimensional vector spaces again. (That’s “functional analysis”.) But that’s for technical posts.
Oh, so far there have been no magnitude 7 or higher earthquakes this month.