Almost every bit of health advice I’ve heard has been contradicted. Should you eat more carbs or fewer carbs? More fat or less fat? Take vitamin supplements or not? It reminds me of this clip from Sleeper in which Woody Allen wakes up after 200 years of suspended animation.

Offhand I can only think of a couple things on which there seems to be near unanimous agreement: smoking is bad for you, and moderate exercise is good for you.

Here are a couple suggestions for evaluating health studies.

Be suspicious of linear extrapolation. It does not follow that because moderate exercise is good for you, extreme exercise is extremely good for you. Nor does it follow that because extreme alcohol consumption is harmful, moderate alcohol consumption is moderately harmful.

Start from a default assumption that something natural or traditional is probably OK. This should not be dogmatic, only a starting point. In statistical terms, it’s a prior distribution informed by historical experience. The more a claim is at odds with nature and tradition, the more evidence it requires. If someone says fresh fruit is bad for you, for example, they need to present more evidence than someone who says an newly synthesized chemical compound is harmful. Extraordinary claims require extraordinary evidence.

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A couple days ago I compared different ways of approximating Earth and other ellipsoids by spheres. The earth is so nearly spherical that the difference in the approximations would only matter when you need fairly high accuracy. Elliptical galaxies, however, can be much more eccentric than Earth and so the difference in approximation approaches can matter more.

The Hubble classification of elliptical galaxies uses a scale E0 through E7 where the number following ‘E’ is 10(1 – b/a) where a is the major semi-axis and b is the minor semi-axis. An E0 galaxy is essentially spherical. The most common classification is near E3. The limit is believed to be around E7.

The image above is a photo of Messier 49, an E4 galaxy, taken by the Hubble telescope.

For an E3 galaxy, the minor and major axes are around 7 and 10 in some unit. The average of these is 8.5. A sphere with the same volume would have radius 8.88 and a sphere with the same surface area would have radius 8.98, about 5.7% larger than the average of the axes.

For an E7 galaxy, the minor and major axes would have a ratio of 3 to 10. This gives an average of 6.5. Matching volumes gives a radius of 6.69 and matching surface area gives a ratio of 7.67, about 18% larger than the average of the axes.

Richard Feynman on imagining electromagnetic waves:

I’ll tell you what I see. I see some kind of vague showy, wiggling lines  — here and there an E and a B written on them somehow, and perhaps some of the lines have arrows on them — an arrow here or there which disappears when I look too closely at it. When I talk about the fields swishing through space, I have a terrible confusion between the symbols I use to describe the objects and the objects themselves. I cannot really make a picture that is even nearly like the true waves. So if you have difficulty making such a picture, you should not be worried that your difficulty is unusual.

From The Feynman Lectures on Physics, volume II.

Other Feynman posts

• Richard Feynman and Captain Picard try to prove Fermat’s Last Theorem
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After I finished an electromagnetism course in college, I said that one day I’d go back and really understand the subject. Now I’m starting to do that. I want to understand theory and practical applications, from Maxwell’s equations to Radio Shack.

I’m starting by reading the Feynman lectures on E&M. After that I plan to read something on electronics. If you have resources you recommend, please let me know.

I’ve started new Twitter account, @GrokEM. I figure that tweeting about E&M will help me stick to my goal. My other Twitter accounts post on a regular schedule (plus a few extras) and are scheduled weeks in advance. GrokEM will be more erratic, at least for now. (In case you’re not familiar with grok, it’s a slang for knowing something thoroughly and intuitively.)

[Update: GrokEM has become ScienceTip and is about more than E&M.]

Here’s what Feynman said about mathematicians learning physics, particularly E&M.

Mathematicians, or people who have very mathematical minds, are often led astray when “studying” physics because they loose sight of the physics. They say: “Look, these differential equations — the Maxwell equations — are all there is to electrodynamics … if I understand them mathematically inside out, I will understand the physics inside out.” Only it doesn’t work that way. … They fail because the actual physical situations in the real world are so complicated that it is necessary to have a much broader understanding of the equations. … A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist.

Heinlein coined grok around the same time that Feynman made the above remarks. Otherwise, Feynman might have said that only studying differential equations is not the way to grok electrodynamics.

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