Consider a Different Physics Textbook | Hacker News Reader

Consider a Different Physics Textbook

wired.com

59 pointsRougeFemme13 comments

"We live in a world of cheap and fast computers such that numerical calculations are a fairly standard solution method in just about every scientific and engineering field. Students might as well start using them right away, right?"

Sez a Wired author who's probably never had to deal with numerically unstable integrals, poorly-conditioned matrices or sampling rate errors.

Numerical calculations are powerful, but they're also subject to a whole host of issues related to finite-precision arithmetic; it's quite possible to set up a numerical calculation that returns nonsense if you don't have a solid intuition for what's going on.

The author is Rhett Allain, who is apparently an associate professor at Southeastern Louisiana University. I don't know about his background in numerical work, but I suspect he knows more about it than a typical Wired author who is not a professor of physics.

> Numerical calculations are powerful, but they're also subject to a whole host of issues related to finite-precision arithmetic; it's quite possible to set up a numerical calculation that returns nonsense if you don't have a solid intuition for what's going on.

Very true, but I think that is another argument for students doing this right away - it's a great opportunity to teach students about the issues with numerical methodologies.

The computation is not the physics.

Students need a firm grounding in the analytical and empirical foundations of physics in order to comprehend the issues with numerical methodologies for investigating complicated physical systems properly, though. I've done plenty of work investigating unstable, nonlinear systems for which no closed-form analytical solution exists (they abound, of course, for any non-trivial problem). I'm not sure that having my undergraduate and basic graduate education "mixed up" with issues around numerical solutions would have made the work any easier to understand or deal with. It might have made it harder.

There is no reason they cannot be taught together, though, and perhaps it might be a better approach for some students. I believe that every undergraduate physics curriculum ought to have a senior level course in computational physics.

I agree with you that learning the physics is distinct from learning the numerical aspects. However, I think there is value in learning computational techniques early on (and possibly in parallel with the physics). If my experience is representative (and it might not be), the majority of undergrad physics majors do not wind up pursuing a physics research career, and the numerical skills might not be of more use than the analytic skills. Of course, it's certainly true that these numerical skills can be obtained in a separate class. I'm not sure it's clear-cut whether having them together is better or worse than having them separate. I think one could make a reasonable case either way.

I have checked the book on Amazon through the look inside and it has not convinced me. I have the impression that it is the kind of book that spend loads of pages to talk about a simple idea. I am more inclined towards books that are not very thick and that force you to be a quite active reader. My personal choice for 1st year physics text book is Physics by Alonso Finn. Their attempt to build all the concepts from basic ideas is what appeals to me most. It also present some rather challenging problems for an undergraduate.

The best undergraduate mechanics textbook I've seen is Morin's, though it probably requires a certain kind of student (one who is not fazed by taking things up one level). Morin does a great job of showing how experts actually solve problems (e.g., looking for symmetries, doing dimensional analysis, checking extreme cases) rather than just plugging in formulas. The downside is that if you just want to apply formulas, his methods can look like a bag of magic tricks.

There is a long history of trying out different ways to teach physics to undergraduates. In my undergraduate college the faculty experimented with starting with quantum mechanics and ending up with classical physics; introductory calculus was sometimes taught using nonstandard analysis. My thesis advisor in graduate school wrote an intro physics text that included simulations from the beginning, in the `80s. He even wrote a special version of Basic that used vectors to make it easier for students. In Germany it's popular to teach mechanics using momentum currents instead of the force concept.

I agree that introducing numerics early is risky: it's easy to get what looks like a smooth, convergent solution from a naive calculation that happens to be wrong.

Richard Feynman taught simulation (of planetary orbits) in his famous first-year lectures (which became the famous text book) with a page long table of computed values, and remarked that this was a powerful new technique that was going to dominate physics as computers increased in power.

This might have been what inspired my advisor, who's thesis advisor was Feynman (making Feynman my grand-advisor).

We used Six Ideas that Changed Physics in my introductory course (which the author of this article mentions as another non-traditional text, and dismisses without discussion. I thought that it was an excellent text, probably the best textbooks that I used during my physics undergrad (with the exception of the E&M section. That was poorly written). Our professor combined it with a nontraditional course format: You read the chapter and do problems before the lecture on that subject, and the lecture is dedicated to more in depth discussion, clarification, and some amount of group and individual work), which I thought was a really effective and engaging way to teach a large introductory course.

I'm not saying this is a good or a bad thing, but: intro physics courses are not designed to teach physics, really. They're designed to give intuition about mechanics. In practice, physicists don't really think much about concepts like forces; although that's what an engineer building a bridge needs to worry about. If you want a technical and conceptually pure understanding of physics, well, that's what the next 3-8 years of study is for.

I've never seen such in-depth discussion of electrical currents anywhere else than in these books. I came to these books through the amasci.com website.

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