I’m not sure what I did to PZ Myers to make him draw my attention to Fred Hutchison, but whatever it was, I apologize. Mr. Hutchison is apparently a columnist writing for a web site run by Alan Keyes– the right-wing kook for people who find David Horowitz to be a little too sedate– and prides himself on his knowledge of science. In fact, he’s currently taking great pride in “defeating” two professional scientists in email debates about relativity and global warming. He has also previously posted an amazingly loopy piece about how Einstein is wrong about everything.
Now, it’s been a bad couple of weeks at Chateau Steelypips, so it’s tempting to just dismiss Mr. Hutchison out of hand. But really, what we have here is a teaching opportunity. Not an opportunity to teach Hutchison– I’ve got about as much chance of getting him to accept relativity as I do of getting PZ Myers to join Opus Dei— but an opportunity to teach people about an important and often neglected part of teaching physics.
You see, one of the hardest things about teaching science is understanding the wrong answers that students give. Not identifying them– that’s easy– but figuring out what the underlying misconception is that has caused them to choose that particular wrong answer. This is often complicated by the fact that confused students tend to write their wrong answers in a remarkably opaque manner, that often obscures the real misconception behind a thick cloud of poor grammar and incoherent babble.
I’ve often been tempted to write about this phenomenon, but I can’t really bring myself to quote from actual student papers that I have received. There’s a chance that one of my students might stumble across this blog, and read what I wrote, and take offense. Mr. Hutchison presents a golden opportunity, however– even if he does stumble across this blog, and take offense, I really couldn’t care less. So, I will offer one of Mr. Hutchison’s arguments as an example of how to identify underlying misconceptions, below the fold.
To choose an easy example, consider his writing about gravitation. In his bragging piece, he writes:
I argued that Einstein offered no explanation of why an apple falling from a tree moves straight down. A warp in the space-time continuum — i.e., Einstein’s gravity — seems to cause a moving object in space to curve as it passes by the warp. However such a warp is not a direct force of attraction, as is Newton’s gravity. Newton explained that an apple falls straight down from the tree due to a direct attraction between the mass of the apple and the mass of the earth. A warp in the space-time continuum is not a direct force of attraction. Such a warp can only change the direction of a moving object, if the object passes the warp in a flanking movement. The trajectory of the object curves as it passes nearby. That is why an asteroid passing near the earth can be captured by earth’s gravity and either enter a stable orbit or spiral inwards in a whirlpool motion.
He proudly proclaims that this argument stumped his adversary in this particular debate, and I agree, it’s a real head-scratcher. For a minute or two, I couldn’t figure out what the heck he was talking about. There’s a clearer statement in his earlier article, though, that makes it all come clear:
Einstein’s gravity has an oblique effect on moving bodies. A space ship flying near a planet will enter the “warp in the space-time continuum” surrounding the planet. The pilot will think he is maintaining a fixed course, but his movement relative to the planet will curve. If the ship does not change course and enters a rotation which spirals towards the planet, his movement will resemble a whirlpool. The standard illustration of Einstein’s illustrates a whirlpool effect, not a falling body. Imagine a gigantic mattress with a heavy weight placed in the center which warps the center down a few inches. A rolling pool ball on the surface of the mattress will curve towards the mattress in a whirlpool trajectory.
Here, we see the true source of the misconception. The problem is that he’s mistaken the map for the territory. He’s not talking about Einstein at all, he’s talking about popular descriptions of Einstein’s general relativity, and taking the metaphors and examples used in those treatments to be the full and complete description of the theory. The real source of confusion here is shockingly elementary– he’s assuming that because all the examples used in pop-science descriptions of general relativity show spiraling motion, that general relativity only describes spiraling motion.
We’ve all seen the pictures he’s talking about– giant masses distorting checkerboard sheets of space-time, with smaller masses as small balls rolling in the wells thus created. An example (image taken from this site) is visible at right. Whenever you see these, they show orbiting particles, or rays of light being bent by a gravitational lens (incidentally, there’s a cute little applet at the Astrophysical Spectator that lets you generate lensed images of a point source, found when I was Googling for a good curved sheet graphic).
These are the only examples you ever see, because those are the really interesting cases. Those give you the conic sections that got Mr. Hutchison so worked up about Kepler in his article about debating a scientist, and the really cool phenomena having to do with general relativity. All of those cases involve objects that are moving with a component of velocity perpendicular to the line between their position and the mass in question. Nobody talks about the case of a body released from rest falling straight down a gravity well, because it’s not nearly as interesting.
I assure you, though, it works perfectly well, even within the confines of the metaphor– you can even try it yourself. Get a heavy weight, and put it in the middle of a large mattress (preferably a really smooth one– if you don’t have one of those fancy space-age Tempurpedic mattresses, you can go to a local mall, and test it out there. The weight will distort the surface of the mattress in exactly the same way that a mass in general relativity bends space-time.
Now, take a small spherical object– a ball bearing, a marble, a pool ball– and place it near the edge of the depression caused by the mass. Let it go, being careful not to give it a push in any direction. Note that it follows a perfectly straight path down to the mass– if you have trouble seeing it, consider coating the ball with soot or ink and looking at the track that it leaves. You’ll see that it’s straight.
You’ll also see that it’s stupid and boring, and that it’s much more fun to give the ball a little transverse velocity, and watch it spiral on down to the mass. Or start it farther out, where the sheet is almost flat, and watch it trace out conic sections. It’s pretty cool, and can keep you entertained for hours, or at least until the mall police arrest you for messing up the fancy space-age Tempurpedic mattress.
So, you see, the real source of Mr. Hutchison’s confusion is– well, actually, based on his articles, I suspect the phrase “undiagnosed neurochemical disorder” probably figures in the real source, so let’s just say that the proximate cause of Mr. Hutchison’s problems with relativity is a combination of an overly literal reading of the examples offered by pop-science texts, and a failure to actually follow through on the logical implications of the very analogy he quotes as an example.
So, you see, given a couple of writing samples, and a little patience, we can identify the core misconceptions that cause a student to say utterly baffling wrong things about science. Now we know the cause of the problem, and knowing, as they say, is half the battle. The other half requires more patience, a new set of analogies, and a mix of counseling and medication.
I knew a physicist would find this one a tempting target.
Oh god. I got serious Usenet flashbacks from reading that.
On the other hand, I am happy that we have a global warming denier and a relativity denier all at once.
I’ve often been tempted to write about this phenomenon, but I can’t really bring myself to quote from actual student papers that I have received. There’s a chance that one of my students might stumble across this blog, and read what I wrote, and take offense.
I have a similar problem at work. Leaving aside any immense howlers of my own, I’ve got a collection of remarkably misguided notions of junior engineers that I’ve had to correct over the years….
(Notions about engineering, mind you, not physics.)
Arn’t there also intersting dimensional issues he is confusing too? That graph you have there is clearly embeded in 3-space, but the sheet is two dimensional. So tracing the geodesics will give you paths on a surface. The example you gave with the mattress is still inherintly two dimensional as there is infact no freedom in the vertical direction. In order to talk about an apple falling off a tree you need one more dimension in the graph.
Please correct me if I am wrong.
My friend who is very good in GR, doing a PhD in it, said to me once that he does not believe in the possibility of explaining GR in layman’s terms without serious falsifications, or being seriously misunderstood. The example in the post is a prime example of that.
I think the crucial point which this Hutchinson does not grasp is that we are not stationary in 4-dimensional spacetime, never.
Roman,
No doubt your friend is quite right about GR being seriously misunderstood when attempts are made to explain it to laypeople, but the Hutchison example doesn’t seem to illustrate that, because the error of comprehension he made is so fundamental. “Fundamental” being a carefully chosen euphemism.
Aaron: Oh god. I got serious Usenet flashbacks from reading that.
The “GR only describes spirals” was a new one on me, but then, I was never a sci.physics.* person, so it may be a classic that I’ve just never encountered before.
A cornellian: Arn’t there also intersting dimensional issues he is confusing too? That graph you have there is clearly embeded in 3-space, but the sheet is two dimensional. So tracing the geodesics will give you paths on a surface. The example you gave with the mattress is still inherintly two dimensional as there is infact no freedom in the vertical direction.
In the analogy, “vertical” is one of the in-the-plane directions. You have to imagine that moving objects move only in two dimensions, confined to the surface of the sheet.
I can’t represent four-dimensional space on my computer monitor, or I’d give you the real picture.
Roman: My friend who is very good in GR, doing a PhD in it, said to me once that he does not believe in the possibility of explaining GR in layman’s terms without serious falsifications, or being seriously misunderstood. The example in the post is a prime example of that.
That’s true of most disciplines in physics, if you want to get anal about definitions. It’s a question of how willing you are to tell lies-to-children.
This particular case is not an especially good example of that problem, because the mistake being made is so bizarre and fundamental.
Curse you, Chad! Now I’m going to waste half the day reading this guy’s crap. You caused that highway pileup just to cause me to rubberneck, didn’t you?
Seriously, I’ve said since usenet days that it takes very little knowledge to misrepresent science, and a great deal more to expose the misrepresentation. Unfortunately, it also takes an ability to follow reasoning that is “not even wrong”.
I have had students whose questions in class completely throw me because I can’t immediately see the misconception that motivates the question.
My initial reaction to this guy would have been to recommend that he read Cliff Will’s excellent “Was Einstein Right?” before commenting further. I strongly recommend this book to anyone who’s curious.
In re: Orzel’s “It’s a question of how willing you are to tell lies-to-children.”
First, sir, we are all children. Any pretension of adulthood vis a vis physics is arrogance and hubris.
Second, the teaching of physics, and indeed, the learning and research of physics, are successions of lies. All of these may be attributed to our inabilities to understand and communicate, matters that may be improved upon but never made ideal. It is inherent to the making of models that they will be inaccurate and thus in the vernacular, contain lies. It is inherent to the exchange of information between humans that the exchanged information, and the knowledge preceeding and postceeding the exchange, will be inaccurate and thus contain lies.
Thus, sir, the question is relativist rather than absolute. It is not a matter of whether we shall “tell lies” but rather, what “lies” shall we “tell”?
The “GR only describes spirals” was a new one on me, but then, I was never a sci.physics.* person, so it may be a classic that I’ve just never encountered before.
It was actually the twin paradox explanation that gave me the flashbacks.
“I think the crucial point which this Hutchinson does not grasp is that we are not stationary in 4-dimensional spacetime, never.”
Or rather, the only time when we are “stationary” in respect to spacetime is when we do not feel gravitaional effects, such as in a freefall. This is the cause of gravitational time dilation.
Mr. Upright: Curse you, Chad! Now I’m going to waste half the day reading this guy’s crap. You caused that highway pileup just to cause me to rubberneck, didn’t you?
Misery loves company– it’s all PZ’s fault.
Simple Country Physicist: Thus, sir, the question is relativist rather than absolute. It is not a matter of whether we shall “tell lies” but rather, what “lies” shall we “tell”?
“Lies-to-children” is a term of art, in some sense. The origin is with Terry Pratchett, and amounts to basically what you say in your second paragraph (not quoted).
Aaron: It was actually the twin paradox explanation that gave me the flashbacks.
Yeah, that’s a nice piece of work. I was going to talk about that one, too, but the GR stuff took up enough space that I didn’t bother.
Maybe I’ll make this a weekly series…
I’m the “Dr. M” from the column. I think that Mr. Hutchinson’s “spirals/whirlpools” thing goes beyond the rubber sheet analogy: notice the picture of the spiral galaxy in his “Critique of Einstein” article: he may well think that the spiral arms are actually tracing out the flushing/whirlpool motion of the galaxy. He’s definitely got a problem connecting celestial gravity with Earth’s surface gravity; it took a while to explain (and I’m not sure he got it) that the arc of a baseball is *really* a short segment of an elliptical orbit.
But, Chad, here’s the difficulty with treating this as an education problem: he was, apparently, so excited about “catching me” using Newtonian ellipses in a discussion of GR, I don’t think he was even *thinking* about physics any more. He was simply thinking, “If I can get this nerd to say ‘GR orbits are approximately ellipses’ one more time, I’ll have won! Let me ask him again!”
I *did* send him one last email in response to his column; he has promised to read it carefully. My prediction: he’ll say I’m “avoiding the issue” with “pedagogical corrections”, and that the real issue is Spinoza blah blah uncritical blah blah Kuhn blah blah postromantic nature worship.
A couple of comments: First, about spirals. The reason that a ball moving along a dented mattress spirals inward is because of friction. It has nothing to do with the nature of the force pulling it towards the center.
Second, about Hutchison’s remark “A warp in the space-time continuum is not a direct force of attraction. Such a warp can only change the direction of a moving object…”. That actually is true and is an interesting insight into General Relativity. It is easy to see how warped space can cause a moving object to travel a non-straight path. But warped space will not cause an object at rest to start accelerating. The mistake on Hutchison’s part is that it isn’t space that is warped, but spacetime, and it isn’t the object’s path through space that is curved, but its path through spacetime. From the point of view of spacetime, there is no such thing as an object at “rest”, the worldline of every object has a nonzero component of 4-velocity in the time direction.
Ben M.: But, Chad, here’s the difficulty with treating this as an education problem: he was, apparently, so excited about “catching me” using Newtonian ellipses in a discussion of GR, I don’t think he was even *thinking* about physics any more.
To clarify a bit, I’m not entirely serious about casting this as an educational problem. I just used that as a slightly more novel approach to the classic blog technique of “Here’s a crazy person, let’s poke holes in their arguments.”
I agree with you that he’s not actually thinking about physics. He’s latched on to some misconception about physics, and used that to spin some vast edifice of delusion that’s gone far beyond the original physcis misconception.
I think he’s really pretty much the science equivalent of Alec Rawls.
I survived being a witness of 1 (one) single attempt at discussing physics with a crank and explaining him that he is wrong. It was a very unpleasant experience. Since then I think that it is a total waste of time. It’s not worth your time to write to these people or talk with them. Half of them are crooks who want to cash on naive people, half of them are simply people with psychological defects, who should be taken care of by psychocologists. Just ignore them.
Okay, I managed to read some of his crap, and it is beyond stupid.
Ben, I’m sorry you put yourself through that. Nothing he said about relativity (in the 1.5 essays I’ve read so far) has any relationship to reality…yet he confidently declares that he was only wrong on one minor arcane point.
Clearly you would have been better off arguing with Robert E. McElwaine! At least his rants were occasionally entertaining.
My general feeling was, “Either I can get some science across to this guy, OR something interesting/entertaining will happen when he runs out of objections.” He gave me some hope of the former when he sort of came around on the bending-of-light question; with this column, he came through big time on the latter.
That’s something which always confused me too. With the rubber sheet, I could get the deflection (space-time isn’t homologous, it’s being distorted so that a straight line actually goes off to the side) but not the inward acceleration (which was caused by gravity pulling the marble down the “gravity well” of the heavy object).
Of course, I sensibly scratched that one up to my own confusion rather than a flaw in the theory. 😉 So, the inward acceleration from apparent rest is due to the object moving in the time dimension?
Alexander:
Such humility is notably absent in Mr. Hutchison’s writings. Perhaps it’s equally correct to say that, unlike Mr. H, you did not take the analogy to be the embodiment of the theory!
There are different ways of looking at the path problem in GR. A particularly simple way is to consider geodesics. If an object is not under the influence of any force other than gravity then it is considered to be “freely-falling” (or, as I believe Wheeler likes to say, “freely-floating”). The path of a free-float object is a “geodesic”.
For an object starting from rest in the reference frame of Earth, the geodesic path points directly toward the center of the planet, accelerating relative to the Earth coordinates. If you let it go so that it is in free-fall, it will follow that path. If you throw it at an angle, the geodesic path is the parabolic trajectory of the projectile.
In a sense (one which Mr. Hutchison would certainly abuse) this “gravity is not a force” view of classical GR revives the Aristotlean view of “natural motions”, albeit in a much more mature and quantifiable way. If you hold an object, the force you exert is “accelerating” that object away from the geodesic paths it would follow if you let it go!
Mr. Upright,
I think Alexander’s question is this: Why isn’t “remaining at rest” a geodesic? The surface of a globe gives an intuitive understanding of geodesics: if an object is sliding on the surface of a frictionless Earth, it’s path will be curved—the shortest distance between two points on the Earth is a Great Circle route. However, on the surface of the Earth, an object at rest at one point (say, the North Pole) is a degenerate case of geodesic. Put something at the North Pole, and it is content to stay there. No matter what the shape of the surface, there will always be a degenerate geodesic corresponding to an object at rest.
In contrast, in curved spacetime there is no degenerate case of an object at rest. This difference cannot be understood in terms of rubber sheets alone. To understand it, you have to take into account the difference between curved space and curved spacetime, and you have to take into account the difference between a path through space and a path (or worldline) through spacetime.
It all becomes easier once you learn differential geometry 😉
Roman: It all becomes easier once you learn differential geometry 😉
Which reminds me of my third favorite way of shutting down a student question. The visiting professor who taught my undergraduate “cosmology for idiots” class once started an answer to a question about black holes by saying “Well, if you really understand General Relativity, you know that…”
Come to think of it, he was Polish, too…
Of course you can’t use differential geometry to explain GR to a layman, but teaching physics students GR should begin with a course of GR. It’s really much easier then to grasp GR, which is a *very* geometrical theory.
Sorry:
“… should begin with a course of GR” –> “… should begin with a course of differential geometry”.
Of course you are correct, Daryl, and your point does simplify the issue of that question. (It works nicely when considering the differential equation for the geodesic, but that’s not even important for the discussion.)
The rubber sheet analogy has many problems, which is why it’s only an analogy.
Roman’s comments reminded me of a quote I heard a long time ago, and can only remember now as a paraphrase. In the early days of GR, a prominent relativist (Eddington? Bergman? Tolman?) said something to the effect of “GR is so simple an eleven year-old could understand it…provided that eleven year-old understands tensor calculus.” I’ve done web searches to find the source, but have failed. Does anyone here know more about that quote?
I have commented on this Hutchinson thing over at Pharyngula. I took the converse approach to Chad’s sharing student misconceptions and gave the F.H. piece to my high school students to critique. Excerpts are in my Pharygula comment, but my students did a fine job deflating F.H.’s entire argument, such as it was. Two were able to explain, at least in part, why his twin paradox explanation was way off base. I think we need to go over that one again …
They were also dead-on in detecting that F.H. knows basically nothing really about Einstein, relativity or science. Refreshingly, they also realize they know only a little bit more than he does. That’s the key; knowing when you’re ignorant. F.H. hasn’t learned that yet.
I teach relativity to both my Conceptual and Honors students, since I want them to get a sense of where physics research is right now. Besides, it’s cool and some of the SF fans can relate to it better than Newtonian mechanics. When I present the curved waterbed analogy, I point out that it is just an analogy or a model, like representing a cube in a 2-dimensional drawing. It’s not the real thing.
There is always a danger in simplifying complex ideas for the “mass market” that the audience will take the simplification as the actual idea. But what alternative is there? One cannot expect to teach tensor calculus to high school students just so they can learn GR. One has to appeal to what they already know (or at times what they should know) to bring them up to the more correct explanations.
As my students pointed out in their critiques, F.H. needs to bone up on his subject and maybe find a better teacher than he himself before he tackles a Nobel Prize winner and a theory that’s been well verified over the last century. A black hole lies at the bottom of the depths of his ingnorance.