Structure and Interpretation of Classical Mechanics

Rating:
Summary: Structure and Interpretation of a Great Text
Review: Among the horrors of modern education is the production of vast quantities of poorly written, error ridden science text books. This is in spite of the fact that many if not most of the great scientists of the 20th century have been excellent writers and lecturers. Einstein and Feynman are important examples: brilliant in their discoveries, they were equally brilliant in their abilities to describe and explain some of the most difficult concepts of science. We should be asking why these people can write about their work with such perfection while the "professionally produced" text books in our high schools and colleges are so mediocre.

The MIT Press stands among those publishers producing the very best work. Sussman's and Wisdom's text, "The Structure and Interpretation of Classical Mechanics", provides a wonderful example. Here is a book providing further proof that (a) great science necessarily includes excellent writing and communications, (b) brilliant scientists tend to be the best writers in their fields, and (c) a text book on a difficult subject can be remarkably enjoyable as well as informative when well conceived and well written.

The very first chapter, "Lagrangian Mechanics", is worth the price of admission. It has all the attributes which make the entire book a gem: it is concise, efficient, clear, compact, full, and rewarding. Every sentence contains important ideas and information, yet each sentence is clear and direct. These are attributes usually associated with poetry, and one could argue that this text book approaches that level of literature. In the first three pages of the chapter, the authors present as complete a discussion as I've read on the relationship of mathematics to natural phenomena, the basic project of classical mechanics, and the "remarkable discovery that the same mathematical tools used to describe the motions of the planets can be used to describe the motion of the juggling pin." Furthermore, the chapter introduces and describes the concepts of configuration paths, variational formulation (and why that has some advantages over the classical Newtonian formulation), generalized coordinates, and the relationship of these formulations to a computer program in Scheme.

By the end of the chapter, students will be immersed in the subject out of interest, and will fully appreciate the themes and likely outcomes of the book. Classical mechanics will essentially "come to life" through a well structured use of computers to achieve a very deep understanding of classical systems.

Jump next to the book's Appendices, which present an introduction to the computer programming language of Scheme and a full explanation of the authors' adaptation of functional mathematical notation. Scheme is wonderfully crafted language for exploring, describing, and demonstrating science and mathematics. The mergence of Scheme, functional notation, and classical mechanics in a single text while retaining almost luminescent clarity ranks among great educational achievements!

This is almost too incredible to say, but the truth is that an entire semester could be dedicated to the first chapter and the two appendices, and everyone involved --- teacher and students --- would be entirely satisfied. But in this text, and in a course based on this text, these sections would serve as appetizers, and we would all want more. Fortunately, there is plenty more.

The authors write that they prefer using functional notation to traditional mathematical notation because, "In functional notation mathematical expressions are unambiguous and self-contained." This statement is, in fact, the best description of the entire book.

I believe that the book could be used effectively in high school, if there was some capacity for integrated curriculum planning. Students could be learning Scheme --- an excellent language to learn if programming is a major interest or even hobby --- and physics and math. Not least importantly, students would also learn the importance of good writing.

Some will argue that the book is more a college text, although I think we tend to underestimate the powerful minds and interests of younger learners. In either case, this book belongs in those places promoting good science and quality education, and, if you simply enjoy learning and reading, it has a place on your home bookshelf.

Rating:
Summary: New milestone
Review: I can't rave enough -- by page 27, Sussman crisply solves a fundamental problem that I noticed as a schoolboy dacades ago, and for which I never found a satisfactory solution despite discussing it with generations of the world's finest physicists, and that is, how, in Lagrange's equation, can @L/@q be treated independently of @L/@q_dot when q_dot depends on q through dq/dt=q_dot by assumption? Having had a lifelong mystery dispatched in a footnote, I am breathlessly working my way through the rest. I expect this will be a book I revisit every few years or so, like SICP, Abelson & Sussman's book on Computer Programs.

Rating:
Summary: Expensive book... worth a look online
Review: If you're reading this review now, you're considering whether this text is worthy of your [money]. Well, stop the guessing, and just read the darn thing for free at [the website]

I've found the first part of it is the same classical stuff I've seen over and over, but in a new light, differently perceived, and worthy of, sometimes, just closing the book and thinking about the implications. Take what I say with a grain of salt, as I've not nearly read everything. See for yourself, as well. There'll be no mystery.

(The famed "sister text," SICP, is also online as well at the appropriate address)

Rating:
Summary: The tragedy is
Review: that despite being a brilliant book, the best part, the executable code is
extremely difficult to run as it works only on an obscure MIT scheme implementation. It would easily earn 5 stars if it ran in PLT scheme for instance.