Transterrestrial Musings

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In 1988 I got a B.S. in mathematics, with concentration in abstract algebra and group theory.

In fall of 1990 I went back to school for my M.S. in computer science.

In spring of 1991 I took a class in differential equations for no particular reason, basically for fun (my Master thesis advisor was against it).

Can you spot an incongruety in the above sequence of events?

Posted by Ilya at May 17, 2007 01:21 PM

Wow. The problem's even worse than I thought. I've never looked at the catalog requirements for a math degree, but I'd have never imagined that you could get one without learning differential equations.

Do you mean partial, or full, or just not at all? I mean, you had to at least have calculus, right?

Posted by Rand Simberg at May 17, 2007 01:25 PM

a collapse of belief in Christianity over the past several decades among university faculty has been accompanied by a collapse in the belief that there is fundamental truth which should be imparted to students.

Post hoc, ergo...

But we can test this theory, causally relating christianity to scientific virtue. Are any non-christian religions overrepresented in the Nobel Prize winner population?

(Note: this is a rhetorical question.)

Posted by Paul Dietz at May 17, 2007 01:26 PM

Math degree required two years of calculus -- multivariable calculus in the second year, -- but not further if your specialty did not involve it. And group theory is about as far from calculus as you can get.

Are any non-christian religions overrepresented in the Nobel Prize winner population?

I believe it begins with "J"...

Posted by Ilya at May 17, 2007 01:38 PM

Actually, better question is, are atheists overrepresented in the Nobel Prize winner population? (I don't know the answer.)

Posted by Ilya at May 17, 2007 01:47 PM

Paul - Since when does observing concomitant phenomena equate with post hoc ergo propter hoc?

The author's point is that nihilism is destroying the academy. Nothing in the article that indicates that the man was trying to lead you to Christ for the sake of relativity and Shakespeare...so chill. Or are you still trying to determine what the definition of "is" is? And your faith in the Nobel Committee is duly noted. I'm sure they've never been tainted by anything mundane...cough...like...cough...politics (the Russian Judge just gave that joke a 2.1 ooooooow).

Posted by Gunga at May 17, 2007 01:58 PM

I guess we could say about Nihilism that you canoot replace nothing with a bigger nothing.

Posted by Mike Puckett at May 17, 2007 02:04 PM

I don't agree with Tipler here. The problem is that general relativity requires the introduction of several complex topics not usually covered in undergrad classes. It's not just a little more material IMHO, but requires the introduction of a couple of major areas of mathematics in addition to the proper theory itself (eg, the Einstein equations). Then you have models like the Schwarzschild blackhole to cover. (It may or may not really exist, but the model is an exact solution to the Einstein equations.) And predictions like the bit of precession of Mercury's orbit around the Sun and the bending of light around masses.

Posted by Karl Hallowell at May 17, 2007 02:05 PM

Karl, one can cover the subject at least from a lay standpoint, even if undergraduates don't have all the math. I can't believe that everything you just described can't be handled in a single course. And he notes that it's not even required for a physics PhD.

Posted by Rand Simberg at May 17, 2007 02:15 PM

I'm inclined to agree with Karl. And I'll add that General Relativity is sort of a "dead end" in physics in the sense that practically nothing depends on it. You can't really use it for anything. A physics curriculum should include mechanics, electricity and magnetism, waves and vibrations, optics, maybe some statistical and thermal physics, heat transfer, experiment, and a heavy dose of quantum physics. You can DO things with this knowledge. For the moment, General Relativity is of interest to the cosmologists and people working on Theories of Everything. But that's a niche in physics and is fairly left to the graduate student.

Posted by Jane Bernstein at May 17, 2007 02:19 PM

For an English degree, Shakespeare is often not required. Also, diagramming sentences is no longer taught anywhere. I'm convinced the latter is because teachers who teach grammar do not fully understand the grammar they are teaching.

On the other hand, an English degree does guarantee that its holder is fully capable of using deconstructionism to remove all meaning from anything ever written.

Now there's a useful, uplifting talent.

Posted by MJ at May 17, 2007 02:19 PM

What do you get when you cross a mafioso with a deconstructionist?

Someone who'll make you an offer you can't understand.

Posted by Jane Bernstein at May 17, 2007 02:25 PM

I'm with Karl on this. I have a doctorate in EE and there absolutely are areas of EE I know nothing about, let alone being exposed to General Relativity, which by the way I would love to have the time to study at a level beyond Brian Greene's popular expositions.

As knowledge explodes and technical specialities grow, it becomes harder to educate a generalist.
Which is why it really requires one to be thoroughly self-educated in areas that are of great interest not just for the science but the history behind the science, which to me is at least as much fun.

In any case, while the author may have seen some rather nasty symptoms of a disease, his diagnosis in terms of this being somehow associated with an absence of the teaching of Christianity is truly nutty.

Posted by Toast_n_Tea at May 17, 2007 02:26 PM

I'll add that General Relativity is sort of a "dead end" in physics in the sense that practically nothing depends on it. You can't really use it for anything.

That would be news to the guys who designed the GPS satellites, Jane. It would also be surprising to people who have to do orbital predictions for near-earth objects.

What would you "use" Newtonian gravity for? I mean, Galileo had it figured out well enough for flat earth and ballistics.

Posted by Rand Simberg at May 17, 2007 02:31 PM

Nicely stated Rand.

Posted by Toast_n_Tea at May 17, 2007 02:47 PM

Shakespeare -- if there is one author vital to the continuation of the "Anglosphere" it would be Shakespeare.

If I were education dictator, there would be four years of Shakespeare in high school AND college.

Posted by Bill White at May 17, 2007 03:05 PM

BTW, has anyone noted that this is an extended and interesting and useful discussion?

Who is it missing? Bueller? Bueller? Anyone?

More evidence for banning RGO, IMO.

Posted by Rand Simberg at May 17, 2007 03:06 PM

Given the relative sizes of the aviation and space industries, I suspect that a lot of aero"space" engineers never do anything that would touch on orbital mechanics after graduation. (This is probably a truth in labelling issue more than anything.)

In my opinion, Shakespeare should be taught in theater departments, not English departments. Shakespeare wrote his plays to be performed and that's the only way they can be understood -- not counting the participles and try to prove they were written by Sir Francis Bacon.

Posted by Edward Wright at May 17, 2007 03:09 PM

Shakespeare -- if there is one author vital to the continuation of the "Anglosphere" it would be Shakespeare.

Bill, it's very nice to be able to completely agree with you.

At a debate about transhumanism a couple years ago, Joel Garreau made an interesting point about how to recognize what was human, and what not. He proposed the "Shakespeare test." Would Shakespeare recognize it as human? He may have been the greatest genius in human history in that skill (disregarding, of course, the many who might have been as good, or greater, but didn't have the opportunity to write down their observations, or have them published).

Posted by Rand Simberg at May 17, 2007 03:12 PM

BTW, has anyone noted that this is an extended and interesting and useful discussion?

Another aspect of this topic is the relative difficulty of finding a Left/Right or GOP/Democratic angle to exploit. That might help cool the rhetoric.

= = =

I have read Tipler's "Physics of Immortality" and it is a very interesting book and yes it offers a plausible (if very wildly speculative) theory on how God could provide for our personal immortality without violating the known laws (theories) of physics.

I also have enjoyed reading Kip Thorne's books which propose thought experiements involving an "infinitely advanced civilization" to explore what may be possible.

Posted by Bill White at May 17, 2007 03:14 PM

It is a "truth in labeling issue," Ed. Read the post title.

Posted by Rand Simberg at May 17, 2007 03:17 PM

Rand, I think you just cited the exception that proves the rule when you referenced GPS. Where else do you use general relativity on a regular basis? It's an interesting topic, but doesn't seem to be core to a physics degree.

Posted by George Skinner at May 17, 2007 03:22 PM

What would you "use" Newtonian gravity for? I mean, Galileo had it figured out well enough for flat earth and ballistics.

Newtonian Gravity is the basis of orbital mechanics. I believe it's possible to solve many problems at the undergraduate level in finding your way around the solar system with it; I recall a boyfriend in college doing precisely that while I was busy with thermo or o chem or something.

I grant that General Relativity is useful in correcting clock rates on GPS. And that there's a separate Special Relativity correction as well. And maybe for long-duration predictions of some asteroids, it might be useful. But these are niches. There are thousands of applications of quantum mechanics, some of which I'm using right now as I type this.

"Dead end" was an overstatement. But it's a narrow lane, surely. And "Not a through street." And the shops are mostly closed down that way anyway.

Yeah, leave it to the girl to come up with a shopping metaphor.

Posted by Jane Bernstein at May 17, 2007 03:30 PM

As far as learning Shakespeare, I will stand by a tactic my college professor required of us.

We were told to go to the library listening room and check out an LP (vinyl - yup, I'm old) and listen with headphones as we read along in the book. The recordings were made as "audio only" by an English acting company especially for read along programs.

Hearing the words and reading the text side by side taught the nuances of the plays with greater depth than "merely" reading or "merely" watching.

Live performances can be uneven and disappointing if badly done but Chicago Shakespeare Theater on Navy Pier has been doing a superb job and we attend three or four productions each year.

= = =

Yale literary critic Harold Bloom also strongly influences my reading of Shakespeare and he is withering in his de-construction of the de-constructionists.

Posted by Bill White at May 17, 2007 03:33 PM

I believe it's possible to solve many problems at the undergraduate level in finding your way around the solar system with it,

Yes, as long as you don't give a damn about precision. Do you really think that the folks at JPL don't account for it in their trajectory programs, Jane?

If I were hiring at JPL, I'd be quite disturbed to think that I was hiring a "physics" major who was unfamiliar with it. But maybe that's just me.

Posted by Rand Simberg at May 17, 2007 03:41 PM

> you just cited the exception that proves the rule when you referenced GPS

Argh!!! You just hit one of my pet peeves.

"The exception proves the rule" is like "I could care less" or "irregardless."

The original expression is "the exception improves the rule." Finding an exception to a rule doesn't "prove" the rule -- how would that work? -- it tells you that you need need to refine (improve) the rule.

Posted by Edward Wright at May 17, 2007 03:45 PM

Ed, you're using the wrong sense of "Prove".. it's an old enough saying that "prove" is meant in the sense of "test" or "verify".. "Proving Grounds" is a similar vestige of the same sense of the word, which I believe derives from the German Prüfen - to test.

Posted by Jane Bernstein at May 17, 2007 04:25 PM

As far as learning Shakespeare, I will stand by a tactic my college professor required of us. We were told to go to the library listening room and check out an LP (vinyl - yup, I'm old) and listen with headphones

That's a bit like trying to learn how to cook just by listening to Julia Child records. You might learn something about cooking, but you won't learn cooking.

Live performances can be uneven and disappointing if badly done but Chicago Shakespeare Theater on Navy Pier has been doing a superb job and we attend three or four productions each year.

A college degree should train the recipient to do more than consume entertainment, however. That by itself is not a marketable skill.

Posted by Edward Wright at May 17, 2007 04:38 PM

Personally, I don't see what the big deal is about Willy. He wrote decent plays and poetry, maybe even way ahead of his time, but genius on the level of Einstein or Newton? I don't think so.

Posted by Mac at May 17, 2007 04:44 PM

Ed, you're using the wrong sense of "Prove".. it's an old enough saying that "prove" is meant in the sense of "test" or "verify

Jane, those definitions make little sense in this context. The existance of an exception does not "test" or "verify" a rule; it invalidates it.

Posted by Edward Wright at May 17, 2007 05:00 PM

As I understand it, most of the corrections, even for such things as trajectories and (probably) GPS use linearized general relativity which is just the linear approximation of general relativity (intermediate between special relativity and full general relativity). One probably could learn that directly or just copy the formulas out of a book. Now, if you're trying to figure out your trajectory around a binary neutron star pair or near a blackhole, then you just might need the whole theory.

My take is that there's nothing wrong or burdensome with exposing people to some of the implications of general relativity, but my suspicion is that isn't what Tipler is advocating. Then you need a lot more background to understand what is going on. I don't think all that can be adequately packed into a single semester.

Having said that, a lot of the preliminary material is useful everywhere. I'd recommend replacing calculus in multiple variables with differential forms (a good idea IMHO anyway). For me, the classic book is Differential Forms with Applications to the Physical Sciences by Harley Flanders. A lot of multivariable math and physics can easily be expressed in terms of differential forms. The differential, applied twice, vanishes, which generalizes such things as the curl of a gradient or the divergence of a curl vanishing. The four Maxwell's equations of electromagnetism (EM) in vacuum or a dielectric collapse to two differential form equations. A whole host of integral equations collapse to special cases of Stokes' Theorem. All explained (among other things) in the book I listed. EM in particular gets easier to explain in terms of differential forms.

Then there's differential geometry which probably could be coupled to classes on partial differential equations and Lie group theory as practiced in particle physics. There's a lot of synergy there. I don't know enough to recommend a good differential geometry book oriented towards physicists, but they are out there. Most of the math concepts relevant to general relativity would by now be introduced.

Finally, you could then finish with a semester of general relativity with the assumption that special relativity was adequately covered by an earlier class. I don't know what'd be a good book here, since the stuff I'm familiar with is graduate level. Gravitation, by Thorne, Misner, and Wheeler is a huge book. I prefer General Relativity by Robert M. Wald, but it's got more mathematics. As I indicated, neither book seems undergrad friendly.

So as I see it, you could reasonably cover the subject with two additional classes (differential geometry and general relativity), substantial revision of calculus of multiple variables (which probably should be done anyway), and modifying several other classes to take advantage of the new math material. IMHO, that would be the most effective way to introduce the subject in a way that is highly relevant to other physics subjects.

Posted by Karl Hallowell at May 17, 2007 05:50 PM

How do people even get IN to first-year physics without having covered general relativity? We studied it in high school for crying out loud.

Posted by Ed Minchau at May 17, 2007 06:53 PM

Now that I think about it, it is quite easy to teach the basics of relativity to English majors. Observe:

------------------------

Your mass at rest
Is as small as it gets
It gets bigger the faster you go

If you travel at c
It's as big as can be
But your time and length drop to zero

Posted by Ed Minchau at May 17, 2007 07:02 PM

For my physics degree (undergrad) we studied [beyond the 100 level where relativity was cursorily covered]:

1. Hamiltonian Dynamics (Newtonian was covered in the 100 level courses).

In our Hamiltonian Dynamics course we used Einstein notation.

2. Electrodynamics

Maxwell of coure in all his permutations.

3. Thermodynamics

Statistical thermodynamics which is part of the foundation for many sciences.

4. Quantum Mechanics.

Lots of fun. One statement that stood out in our textbook.

"Anyone who tells you that they fully understand Quantum Mechanics, does not fully understand Quantum Mechanics"

We took lots o math, including Mathematical Methods of Physics, includeing DE, PDE, and many special functions such as Legendre, Bessel, Lagrangian, and Lorentz transformations which is the basis of relativity. I do remember that we had to derive E=MC2 as a class exercise but did not do anything with it as it really only applies in a restricted set of circumstances.

None of the trajectory programs out there use relativity, most of them use Runge/Kutta and other approximations. The planetary program uses relativity but even then the velocity is so low and the gravity wells are so shallow in comparison to what would really result in big changes that the first approximation ignores relativity.

Posted by Dennis Wingo at May 17, 2007 07:13 PM

If students weren't being taught thermodynamics or EM in a three year physics degree, I'd be worried. But for GR, even the lecturers who actually teach the course barely grasp it's implications.

Then you have models like the Schwarzschild blackhole to cover. (It may or may not really exist, but the model is an exact solution to the Einstein equations.)

There are other solutions that don't involve fairy dust like singularities.

Posted by at May 17, 2007 10:28 PM

There are other solutions that don't involve fairy dust like singularities.

Yes, I know of a few. vacuum states like de Sitter and anti-de Sitter space (positive and negative cosmological constant respectively) which describe possible shapes for the universe. The blackhole singularities though describe the GR analogue to point masses in Newtonian gravity. So they are worthy of study - especially if they exist.

Posted by Karl Hallowell at May 17, 2007 11:35 PM

None of the trajectory programs out there use relativity, most of them use Runge/Kutta and other approximations.

Huh?

Runge/Kutta is a standard numerical integration routine, and has nothing to do with the underlying model as expressed by the differential equations.

Posted by Rand Simberg at May 18, 2007 07:32 AM

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