Science: Not As Simple As We Tell You

I’m preparing to teach a couple introductory physics courses, beginning in about a week, and it is very common for textbooks to spend time in their first chapter considering questions like “what is science” and “what is physics” and “how do scientists work”. And of course we present our students with this beautiful picture in which science is a flawless cycle of observation-hypothesis-prediction-observation-…-theory, that could probably be carried out by computers if they weren’t so darn expensive.

Of course, it isn’t quite that simple.

I’ve just started reading the book Science, Faith, and Society, by Michael Polanyi, and he makes a couple interesting points to show that, indeed, science is not that simple. Point #1,

There are an infinite number of mathematical formulae which will cover any series of numerical observations. Any additional future observations can still be accounted for by an infinite number of formulae. Moreover, no mathematical function connecting instrument readings can ever constitute a scientific theory. Future instrument readings cannot ever be predicted. But this is merely a symptom of a deeper inadequacy, namely, that the explicit content of a theory fails to account for the guidance it affords to future discoveries. To hold a natural law to be true is to believe that its presence will manifest itself in an indeterminate range of yet unknown and perhaps yet unthinkable consequences. It is to regard the law as a real feature of nature which, as such, exists beyond our control.

OK, if you’re like me, after one read-through you’re thinking “now what did he just say?” But just the first two sentences make an interesting point – we tell intro students that a good theory is one that explains the facts, and that has predictive power. And those are the most important aspects of a good theory – but they probably aren’t the only aspects of a good theory. Because after all, you can come up with an infinite number of explanations (or mathematical formulae), with predictive power, to explain any set of observations.

And doesn’t history bear this out? Today we know that the planets travel in elliptical orbits about the sun. If memory serves (and I shall look this up before class!), we previously thought that the planets traveled in circular orbits. But when the scientists of the day found that the planets weren’t where the theory of circular orbits said they should be, instead of jumping straight to elliptical orbits, they came up with the concept of epicycles – circles on circles. Or circles on circles on circles – as many as you needed. And it worked. The epicycle theory explained observations and had predictive power. So why prefer the theory of elliptical orbits to the epicycle theory? How do you pick between competing theories that both explain your data? That’s not something we often discuss with intro students. But I think those of us who have been in science for a while have heard some of the answers – simplicity is a virtue, a hard-to-articulate mathematical beauty is often present, and so on.

And then,

Every established proposition of science enters into the current premisses of science and affects the scientist’s decision to accept an observation as a fact or to disregard it as probably unsound. To show this, a long series of such cases is given in the appendix, and many other examples can be found in my later writings. This material refutes the widely held view that scientists necessarily abandon a scientific proposition if a new observation conflicts with it. The material collected in the appendix also refutes the view that the progress of science affects only the interpretation of the facts and leaves the accepted facts unchanged.

I think one of the big points to be made here is – scientists are people too. And science is messy! If we find a fact that contradicts a long established theory, we may be inclined to find something wrong with our fact! (That isn’t something we tell intro students!) It isn’t so hard really – there is always instrument error, there could be human error. This reminds me of a passage from Feynman’s “Cargo Cult Science” lecture:

We have learned a lot from experience about how to handle some of
the ways we fool ourselves. One example: Millikan measured the
charge on an electron by an experiment with falling oil drops, and
got an answer which we now know not to be quite right. It’s a
little bit off, because he had the incorrect value for the
viscosity of air. It’s interesting to look at the history of
measurements of the charge of the electron, after Millikan. If you
plot them as a function of time, you find that one is a little
bigger than Millikan’s, and the next one’s a little bit bigger than
that, and the next one’s a little bit bigger than that, until
finally they settle down to a number which is higher.

Why didn’t they discover that the new number was higher right away?
It’s a thing that scientists are ashamed of–this history–because
it’s apparent that people did things like this: When they got a
number that was too high above Millikan’s, they thought something
must be wrong–and they would look for and find a reason why
something might be wrong. When they got a number closer to
Millikan’s value they didn’t look so hard. And so they eliminated
the numbers that were too far off, and did other things like that.
We’ve learned those tricks nowadays, and now we don’t have that
kind of a disease.

Hmm. I wonder if the situation has improved as much as Feynman wants to think.

OK, now I have to decide what should be said in class on this topic.

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