Wednesday, April 16, 2008

Bogus science in textbooks

When I was a kid, I read an article of Martin Gardner (in a book of collected columns originally published in the 1960s) observing that many textbooks "prove" that air is 20% oxygen by burning a candle in a plate of water, with a jar inverted on top. When the flame goes out, the water rises into the jar, to a distance of about 20% (of course, nobody measures this exactly). That, apparently, "proves" that the used-up oxygen constituted 20% of the air. Of course, this had been in my textbooks too (and even a class demonstration), and nobody had thought to question it.

A ten-year-old tends to be a bit uncritical of such "arguments". But surely anyone older -- such as the teachers teaching this -- would know that (a) The candle would't use up all the oxygen; (b) The oxygen is being used up in making carbon dioxide and water vapour, which are both gases (and water molecules, unlike oxygen molecules, have a single atom of oxygen), so if anything the volume of gas should have increased inside the jar; (c) the heat should have caused the air to expand; (d) the heat should have caused some water to evaporate from the plate, adding to the volume of air in the jar.

The only reason the water rises into the jar is (c) above. When you invert the jar on top of the candle, the air around the candle is already hot. When the candle goes out, the air cools, contracts and sucks in the water.

Another question was why do stars twinkle? One book attributed it to the stellar equivalent of solar flares, which is nonsense. Thankfully that was the exception: other books said, correctly, that atmospheric turbulence "bends" the starlight. But then why don't planets twinkle? Not one textbook that I remember explained the reason. (The reason is that stars are so far off they are effectively point sources of light, while planets are more disc-like -- one can see the discs with a quite modest telescope -- and the amount of atmospheric bending is small compared to the diameter of the disc.)

Today I came across another such bogus explanation posted by a commenter on Space Bar's blog in response to her (rhetorical?) question "Why do smells sit so heavily in the summer?" The explanation was that air moves faster, and carries smells more quickly. Plausible at first thought, but the math doesn't work out (as I show in my reply there). But I expect there are several textbooks out there that trot out some such explanation all the same.

How many such bogus "scientific" answers were there, and are still there, in school textbooks that I have forgotten about (or continue to believe credulously)? Richard Feynman reports regularly blowing up like a volcano when asked to review some California state school science books. I suspect my own temper may be hard to keep when my son starts learning science in school.

But no textbook, however atrocious, could compare with the the unauthorised "guide books" / "sample questions and answers" that were, and are, a staple of kids preparing for exams. The following, I remember, was a source of hilarity for my brother. "Question: Though India's north-south dimensions are about the same as its east-west dimensions, the difference in longitudes between east and west is much greater than the difference in latitudes between north and south. Why is that? Model answer: Because Bangladesh comes in the middle."


Space Bar said...

Rahul: I suspect that schools go for the 'common sense' answer - one that is easily comprehended in verbal terms - and leave nuance for later years.

I was being rhetorical, but I'm glad the other stuff came up!

km said...

"Nuance in the later years" is scary, because misconceptions in Physics and Chemistry often become hindrances in higher education.

Rahul: I would be interested in hearing your views on how middle school and high school science textbooks can walk that thin line between "complex but true" and "simple but inaccurate".

Rahul Siddharthan said...

space bar, km: well, of the examples I gave only the "why don't planets twinkle" question can be called a matter of nuance. Everything else is just wrong. It's not "sort of right." It's better to give no explanation at all than a wrong explanation.

The candle experiment illustrates a different principle -- hot air expands, cold air contracts. It can be used from that point of view, rather than to "prove" that air is 20% oxygen.

"Simple but inaccurate" is fine, not only in school, but even later -- physics in practice is about making (justifiable) approximations, no real system can be solved exactly but you can often get an answer that's "good enough". So it's good to give that lesson to students too, like "a pendulum's time period is independent of its amplitude". School students can easily verify that for small amplitudes. It explains why pendulum clocks keep time correctly even as the pendulum amplitude decays, but these days you don't see pendulum clocks any more (except with fake decorative pendulums). It's not true for larger amplitudes, and you can tell them it isn't (and they can verify it too). Understanding why this follows from Newton's laws can wait for later years...

Come to think of it, the idea of "small changes not mattering" was taught in a very confusing way in physics classes in school (because we didn't know calculus). We didn't understand why, when a small change x causes an error x^2, you can ignore the error (or when it is safe to do so).

Another example of acceptable "nuance" would be "why do rainbows form when it rains?" The answer is "because light refracts through the raindrop". That's an acceptable answer for school students, and you can draw a diagram and even experiment with a giant model of a glass raindrop (a paperweight or something will do) and a torch and a dark room. But why do all those raindrops all over the place conspire to make a rainbow at one specific spot in the sky? That's a harder question to answer at the school level (the answer involves the fact that rainbows need two internal reflections of light in the raindrop, in which case there will be a direction of maximum deviation; and also uses the above notion that, near a maximum, small changes in the parameter lead to very little change in the function -- so lots of raindrops "add up" their contributions in that direction alone).

Sunil said...

rahul, i'm with km here in asking how middle and high school textbooks can walk the thin line between complex/true and simple/inaccurate.

And then scientists wonder why the general public thinks evolution doesn't happen. Go figure.

The damage done to science and higher education in science due to these books is quite substantial. Too many students need to be "unschooled" and then retaught in higher level college courses.

gaddeswarup said...

Just looked at the comments n space-bar's blog. I have a query. I noticed in my garden that roses do not smell as strong when it is raining ( directly with nose more or less on the rose). Is this because there is no chance of bees coming anyway. That assumes that scent has some thing to do with attracting bees which I do not know for sure.

gaddeswarup said...

Unless somebody knows the answer offhand, pl. ignore my question. I got some information by google, for any thing more precise it seems that I have to ask a specialist.

Rahul Siddharthan said...

Sunil - to repeat, there is no problem with "simple/inaccurate". All science is inaccurate if you look closely enough. And correct but incomplete explanations are a good start -- maybe a good student will spot the incompleteness and question further.

There is a problem with wrong. Most of the examples I gave in my post were wrong, and there is no excuse for teaching them. (Another example, which crops up all over the place, is the myth that water spirals the other way down the drain in the southern hemisphere, because of the Coriolis force. It spirals both ways in both hemispheres and the Coriolis force is far too weak to be relevant.)

I don't think it's that hard to fact-check school textbooks for accuracy.

Rahul Siddharthan said...

gs - interesting observation. I have no idea. As you say, the explanation could be quite complex.

km said...

Best comment thread I've read all this week.

gawker said...

At least with bogus science textbooks you know what your child is learning incorrectly. What about the teacher who could be saying all kinds of unscientific nonsense. You wouldn't even know what it is.

For example, I had a geography teacher in school who told us that eskimos live in igloos instead of brick houses because igloos stayed warmer in winter. The reason being, cold wind can pass through bricks more easily that it can through ice because of the small holes in a brick.

I believed this reasoning to be true for most of my college life.

Wavefunction said...

One very simple way to note the fallacy of the original argument is to note that if you light TWO candles, the water level goes up TWICE as much, with three candles, thrice as much and so on...
This surely won't happen, unless with two candles the amount of oxygen in the air is 40% :)

km said...

Rahul, gaddeawarup et al:

"Unsmelly" flowers could have a more ominous reason. Read this article.

gaddeswarup said...

km: Thanks. Saw a shorter version in science daily. Why I thought it might be complex was the following passages:
"Strongly sweet fragrance from fewer flowers is usually used to attract bats. This is why such flowers are most noticeable on warm evening. Many plant species are endemic to areas with different vectors that are not present here. However, they continue to produce the fragrance that was so effective back home--sad if you think about it. There would not be such variability in fragrance if all flowers were designed to attract the same vector.
Incidentally, there are a few flowers that are pollinated by flies, generally in the family Araceae. Fragrances attractive to flies, however, are not so appealing to people."
It is from a gardening news item.

Rahul Siddharthan said...

gawker: Yes. Of course, even the best teachers may make mistakes, so the most important thing to teach children is skepticism in authority. Of course, that doesn't go down very well in society.

ashutosh: good point.

km: interesting. Thanks.

Tabula Rasa said...

the most important thing to teach children is skepticism in authority


km said...

If I remember my math and physics classes, one boy's skepticism quickly turns into 30 kids screaming "kya time waste kar raha hai, yaar...syllabus to poora karne de".

Rahul Siddharthan said...

tr - welcome back. So what do you tell your students?

km - I don't remember my classmates being that studious. And the ones who were did the "portions" by themselves anyway (or via IIT-JEE tutorials).

Tabula Rasa said...

i tell them they're free to do as they wish but if they do they'll get screwed on the exam.

but then they're adults.

gaddeswarup said...

Like TR, I too am skeptical of teaching 'skepticism in authority' at a very early age. It is possible that different strategies have to be adopted for different children. I do not remember any science that I learnt in school; I remember only village scenes, games, films and songs. Scepticism in authority developed later in the university at which stage I stopped attending classes. It is ironic that I became a university teacher. I usually told students in the first class of a course not to trust text books or teachers.