In graduate level special topics classes in physics and math, professors often pick and choose material from several different texts and research papers of interest. You might find that they just xerox their own copies of the articles, which often tend to have scribbles all over them. This is indicative of active reading. Professors don’t just curl up on the couch with a research article in the same way they might with a novel. As a matter of habit, they follow the argument presented by the author with a pencil in hand, filling in any skipped steps in the calculations. The benefits of mimicking this practice of marginal notes seemed, well, marginal, until I began teaching and could fully appreciate how much this aids in my understanding.
As I am reviewing basics physics by reading through some chapters in the Feynman Lectures, I often feel compelled to take this one step further. Feynman was a brilliant theorist who could have easily confounded readers by lecturing at a mathematically over-sophisticated level, but rather he describes his subject in a very applied, intuitive manner. His lectures are strewn thick with what I call “numerical nuggets”, indicating his ability to perform numerical analysis in his head, if only at qualitative level. You can tell that he arrives at an analytic expression using calculus only after he deeply ponders the limiting process underlying it. To fully benefit from Feynman’s insight, therefore, I am attempting to quantify some examples of this.
Since FLoP is an acronym for the Feynman Lectures on Physics with an appropriate numerical pun, it makes for a good title, I think. And it certainly describes my blogging effort overall as viewed by my girlfriend, who deems it an utter failure. In any case, it provides me additional motivation to not review college physics passively and at the same time keep up with my coding skills.
I am currently reading chapter 26, Optics: The Principle of Least Time. As an easy example, consider Feynman’s description of refraction studies prior to the discovery of Snell’s Law
We can take a few angles in air and verify the interpolation Feynman mentions in parenthesis. The fact that they fit to a parabola is indicative of the nonlinearity of Snell’s law. The following code will give us a plot:
air = [10 30 60 80];
water = [7.5 22 40.5 48];
plot(air, water)
title('Refracted angle vs. incident angle at an air-water interface')
We can then go to tools, basic fitting, select ‘linear’ and ‘parabolic’ and check ‘show equation’, to produce
from which we see that the linear fit is way off.
For the most part, time constraints will prohibit me from walking through the MATLAB code, so I’ll ordinarily toss the m-files in a paste-bin and just present the results.
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