Saturday, November 27, 2004

Two books

The bulk of my library consists of books on mathematics or computer science -- or the intersection of the two -- but an increasing fraction of my books also deal with topics in engineering and physics. Part of the reason is that it's impossible to build models that are tractable and meaningful without first building some guiding physical intuition; part of the reason is that they keep coming up -- guess what journals contain a lot of the great work on spectral perturbation theory, symmetry-breaking, or all these other words that keep appearing in my favorite books and papers?; and part of the reason is just that I like learning about these things.

So here are two of the physics books that I have been perusing recently.

  1. In my freshman year, I took a seminar course called From Crisis to Chaos, which was about the major advances of 20th century physics and how they came about. The crisis in the title comes from a notion discussed by Thomas Kuhn in The Structure of Scientific Revolution; if you've never heard of Kuhn, go look him up -- we need more people in the world who know what paradigm shift actually means. Anyhow, besides an appreciation for Kuhn, that class also left me with The Character of Physical Law by Feynmann and The Force of Symmetry by Icke. I've read and re-read the former, but somehow I kept never re-reading Icke's book. Being a good packrat, I held onto the book regardless of its value; and on Wednesday evening, I picked it up again. I made myself put it down eventually, but I think I'm going to have to finish re-reading it.

    I think I might have picked it up because I was still thinking about the effects of symmetries after some reading earlier this week on numerical bifurcation analysis in the presence of symmetries; or maybe it was from reading about symmetry-breaking bifurcations in the review of quantum mechanics section of the book by Rob Philips on materials. Or maybe I just picked it up because I like the color blue. Whatever the reason, it's humorous and interesting, and it covers a lot of fun material in a non-technical way. Go read it, and tell me what you think! And don't skip the preface -- in fact, read it twice if you've read any book recently which tries to mix philosophy and physics.

    On a tangential note, let me quote a footnote by Werner Heisenberg from his book on Principles of Quantum Theory (English translation by Eckart and Hoyt):

    In this connection one should particularly remember that the human language permits the construction of sentences which do not involve any consequences and which therefore have no content at all -- in spite of the fact that these sentences produce some kind of picture in our imagination; e.g., the statement that besides our world there exists another world, with which any connection is impossible in principle, does not lead to any experimental consequence, but does produce a kind of picture in the mind. Obviously such a statement can neither be proved nor disproved. One should be especially careful in using words reality, actually, etc., since these words very often lead to statements of the type just mentioned.

    I like the sentiment.

  2. I may have previously mentioned Rob Philips' book Crystals, Defects, and Microstructures: Modeling Across Scales. If not, let me now recommend it to the handful of people reading who have a current interest in computational mechanics and related fields. All -- uh -- one of you, I think. Or maybe more than one (Rick, you do some condensed matter stuff, right?).

    The book has four main parts: Thinking about the material world, Energetics of crystalline solids, Geometric structures in solids: defects and microstructures, and Facing the multiscale challenge of real material behavior. I've browsed in all the sections, but I've only thoroughly read parts of the first section (most of it by now) and the last section. I really like the first section, particularly the chapters on Continuum mechanics revisited and Quantum and statistical mechanics revisited. The continuum mechanics chapter not only covers the usual basics of kinematics, linear elasticity, and variational characterization and finite element approximation; it also includes descriptions of Eshelby's notion of configurational forces, with intriguing teasers about defect dynamics, plasticity, and fracture dynamics. (If that last sentence seemed to make no sense, think of it this way: most of basic solid and fluid mechanics boils down to the balance of linear momentum -- also known as F = ma. The framework of configurational forces turns lots of other things that seem superficially more difficult to manage -- like crack propogation or permanent material damage from large deformations -- into yet another instance of F = ma.) The section on quantum mechanics is simple enough that I can follow it (one day, I swear, I'll take a class on quantum mechanics -- but that day hasn't come yet), and includes a few basic particle-in-box models (treated analytically or with finite element analysis); an example calculation to approximate the density of an electron-gas metal (which is used to develop a few important approximations); and a non-metal bonding example (bond energy in an H2 molecule). The section on statistical mechanics emphasizes information theoretic connections that make me happy, since I have a much better notion of entropy in that context than I do in any sort of physical context.

    The Further Reading sections at the end of the chapters are categorized and annotated, and I highly approve both the annotations and the choice of references: on the topics where I know something (continuum mechanics, finite elements), he has included some of my favorite texts; and on topics I've heard a little about second-hand (plasticity, quantum mechanics, computational statistical mechanics), he has included texts of which my friends have spoken approvingly.