I’m feeling a bit under the gun this morning. I want to relax and chat about mathematics – but a friend is coming in from out of town at about noon, and I really need to clean up the house.
At the very least, let me assure you that a technical post should go out this Monday evening. The draft is out there… the screenshots have been inserted… all that remains is final editing of the narrative, and inserting one link. Even with a guest in my house, I should have time to do that.
Between my two-day trip last weekend and my guest this weekend, I knew I was going to need some time off from work. I worked Monday, and I was off Tuesday through Friday. So why isn’t the house clean? Because I did mathematics instead.
Tuesday I looked at regression again… outliers and single deletion statistics… and I finished off the technical post for this coming Monday.
I also looked at Lee Smolin’s “The Trouble With Physics” and – briefly – at Brian Greene’s “The Elegant Universe”. Someone had asked me over the weekend if I could recommend a popular book on string theory. Those are the only two that are even close to readable by an educated but non-technical person.
They also capture the two extremes. Greene is optimistic about string theory, and talks about it as though its results have been clearly worked out. I find it difficult to read him precisely because he seems to me to be making at present unfounded assertions.
Smolin criticizes string theory on two grounds. One, not only has it made no real predictions, but it isn’t even a specific theory. Two, the sociology and finance of physics research has made it virtually impossible for theoretical physicists to investigate any alternatives.
(I tend to side with Smolin: string theory appears to be beautiful and ground-breaking – dare I say breath-taking? – mathematics… but that doesn’t make it physics. BTW, Yau’s “The Shape of Inner Space” and Woit’s “Not Even Wrong” talk more about – and I mean talk, not do – the mathematics of string theory than either Smolin or Greene.)
Smolin and Greene will probably be my recommendation to my questioner. But I have another book on the way from Amazon: “Quantum Physics for Poets” by Leon Lederman. He is a Nobel Laureate, and the author of “The God Particle” – and I thoroughly enjoyed that book, so I’m willing to try another.
But no, I wouldn’t order just one book from Amazon. I found a book that looks like it is dedicated to stellar interior computations… and another book on aircraft control… and another book on string theory – but it won’t qualify as a popular book: “String Theory Demystified” by David McMahon.
What I like about his books is they present lots of fascinating, introductory, computations; I can get my hands dirty while trying to wrap my head around the physics and mathematics.
What I dislike about his “Demystified” series is that the books generally have a lot of typos. Well, I know enough to survive the typos – but for a newcomer, they might be devastating. Still, the books are only $14 apiece.
Having looked at string theory Tuesday evening, I dug out my books on particle physics in general and “the standard model” in particular.
“The standard model” describes the electroweak and the strong interactions as gauge theories; in particular, it unifies electromagnetism and the weak interaction.
A graduate-level text needs to do quantum field theory – second quantization –but the undergraduate level texts don’t go that far. Quantum field theory, I believe, gets us the Feynman rules for doing calculations about particle events – so an introductory text can skip the derivations and just hand us the Feynman rules.
Furthermore, an introductory text can show the Lagrangian and the corresponding classical field – the field to which we would apply second quantization – and thereby impart insight into the physics and the model.
Anyway, I pretty much spent Wednesday and Thursday reading particle physics.
Yesterday I picked up two things. “Conics and Cubics” by Robert Bix (a Springer UTM – undergraduate text in mathematics) and Landau and Lifshitz’ “Theory of Elasticity”, volume 7 in their Course of Theoretical Physics 10-volume series.
“Conics and Cubics” is a beautiful precursor to elliptic curves; along the way, it’s a nice introduction to the real projective plane. I need to work through this book. (Silverman & Tate have a UTM, “Rational Points on Elliptic Curves” – but it presumes the reader knows about the real projective plane. I’d love to do it after “Conics and Cubics”.)
As for the Landau and Lifshitz… I’ve been hung up on the stress in thin-walled structures from chapter 5 of the Pilkey & Pilkey “mechanics of solids” – but the Landau and Lifshitz has what I need: a derivation of the complete stress tensor. I’m looking forward to showing it to you.
So. Now that I’ve put off cleaning the house until I have two hours left, let me get about that business. As I said, although this weekend, like last weekend, is not a weekend for doing mathematics, there should be a technical post Monday evening.
It will be about simple projectile motion. To be specific, it’s the ship and fort problem: firing the same guns, a fort at higher elevation can hit a ship on the sea before the ship can hit the fort… over what range of distance is the ship unable to return fire?