Comments on: Unsolicited Advice VIII: Make your integrals dimensionless

By: Ben

Ben — Mon, 22 Dec 2008 05:30:09 +0000

Charon says (in response to my snide remark about people who demand facility with integrals but don’t know one end of an Allen wrench from another):

“Yes, well, they are astro grad students, not bike mechanics.”

This attitude is why astro and physics departments have an overabundance of aspiring string theory students, but good astronomical instrument builders are in short supply and high demand.

Yes, of course, an astro grad student should know how to do integrals. And ideally, scientists (Verily, even unto the heights of Theory Division) ought to know something about the tools and instruments that produce the results.

Lots of people do not know everything. This is why we are educators, we teach people who don’t know things; teaching people who already know everything is superfluous. Julianne’s post was in that teaching vein. Comments, like the first one, about how students should know all this integral stuff already are missing the point.

By: More Cowbell and other topics « blueollie

More Cowbell and other topics « blueollie — Fri, 19 Dec 2008 21:55:48 +0000

[...] Fail Talk about different ends of the spectrum. Cosmic Variance has advice for physics graduate students who encounter nasty [...]

By: End-Of-Semester Bullets « The First Excited State

End-Of-Semester Bullets « The First Excited State — Fri, 19 Dec 2008 05:50:06 +0000

[...] at Cosmic Variance has some good Unsolicited Advice, namely, making all of your integrals dimensionless. I really had this point driven home to me [...]

By: Lab Lemming

Lab Lemming — Fri, 19 Dec 2008 02:27:37 +0000

Brett, etc:
For what it is worth, in geoscience the Rayleigh number is way more common than the Reynolds number.

But just because students learn to love dimensionless variables doesn’t necessarily mean that they will take the initiative to dedimensionalize their own calculations.

By: Lab Lemming

Lab Lemming — Fri, 19 Dec 2008 02:19:04 +0000

Charon says:
“Yes, well, they are astro grad students, not bike mechanics. ”

So when the dome won’t open, you fix it how? Integrating by spare parts?

Since starting college 17 years ago, I have learned and forgotten calculus four times.

I have learned and forgotten soldering three times.

Which is more important depends entirely on the scientific problem you are trying to solve.

By: End of the Semester; Obama’s picks, etc. « blueollie

End of the Semester; Obama’s picks, etc. « blueollie — Fri, 19 Dec 2008 00:15:59 +0000

[...] enough, integrals came up in a blog that I read: Having recently slogged through grading an enormous pile of graduate-level problem sets, I am [...]

By: Count Iblis

Count Iblis — Thu, 18 Dec 2008 21:38:39 +0000

TimG, I agree. I think the point made by Warren Siegel here is that textbooks should simply explain what light is according to modern physics and not present the entire history of discoveries and failures first.

By: TimG

TimG — Thu, 18 Dec 2008 21:26:25 +0000

By the way, thanks for the link to Michael Duff’s article. The part that makes my head spin is where he basically says this (paraphrasing):

Duff: Whether the speed of light is constant depends on your units. Obviously if you choose light-years as your unit of length and years as your unit of time, then the speed of light has to have a constant value of 1.

Magueijo: Then what the hell was Einstein going on about?

This has me a bit flummoxed. Of course Einstein was saying the speed of light was Lorentz invariant, not that it was constant over all time. But still, as Duff’s example shows, if you define the speed of light as your unit of speed, this invariance is trivial. On the other hand, if you define your unit of speed as something that depends on your reference frame (e.g., the speed of the Earth), then of course the speed of light changes from one frame to the other (since the speed of the Earth changes.)

I’m thinking maybe the correct interpretation of Einstein’s postulate is that the speed of light in units of any non-reference-frame-dependent speed is Lorentz invariant. That is, if we take our unit of speed to be something like “The speed of the Earth in the rest frame of the Sun at a particular time t”, then the speed of light in that unit must be Lorentz invariant.

Is that right? It seems a bit convoluted . . . .

By: TimG

TimG — Thu, 18 Dec 2008 20:53:54 +0000

Count Iblis, of the objections to textbook explanations the one I don’t really get is this one:

“Refraction of light is claimed to have no explanation in terms of particles, quoting Newton’s failure. Of course it does: As we know from quantum mechanics, Newton’s mistake was to confuse phase and group velocities.”

The refraction of light really doesn’t have an explanation in terms of classical particles, does it? To say Newton mixed up phase and group velocity makes no sense, since classical particles have neither. That is, they just have one velocity.

By: Count Iblis

Count Iblis — Thu, 18 Dec 2008 16:57:17 +0000

Even some physicists don't understand units. But that's no surprise given the way sometextbooks explain physics