{"id":105,"date":"2006-03-07T21:24:54","date_gmt":"2006-03-07T21:24:54","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2006\/03\/07\/fred-hutchison-teaching-opport\/"},"modified":"2006-03-07T21:24:54","modified_gmt":"2006-03-07T21:24:54","slug":"fred-hutchison-teaching-opport","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2006\/03\/07\/fred-hutchison-teaching-opport\/","title":{"rendered":"Fred Hutchison: Teaching Opportunity"},"content":{"rendered":"

I’m not sure what I did to PZ Myers to make him draw my attention to Fred Hutchison<\/a>, 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<\/a> in “defeating” two professional scientists in email debates about relativity and global warming. He has also previously posted an amazingly loopy piece<\/a> about how Einstein is wrong about everything.<\/p>\n

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<\/a>— but an opportunity to teach people about an important and often neglected part of teaching physics.<\/p>\n

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.<\/p>\n

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<\/strong> 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.<\/p>\n

<\/p>\n

To choose an easy example, consider his writing about gravitation. In his bragging piece, he writes:<\/p>\n

\n

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.<\/p>\n<\/blockquote>\n

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:<\/p>\n

\n

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.<\/p>\n<\/blockquote>\n

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.<\/p>\n

\"i-2f15f85ce776db763a9e3d059a3e843d-cg_courbure.gif\"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<\/a>) 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<\/a>, found when I was Googling for a good curved sheet graphic).<\/p>\n

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. <\/p>\n

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.<\/p>\n

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.<\/p>\n

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.<\/p>\n

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.<\/p>\n

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.<\/p>\n","protected":false},"excerpt":{"rendered":"

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… Continue reading Fred Hutchison: Teaching Opportunity<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,7],"tags":[],"class_list":["post-105","post","type-post","status-publish","format-standard","hentry","category-education","category-physics","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/105","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=105"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/105\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=105"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=105"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}