[Editor’s note: of course I wasn’t going to string you along–this is the post for which this post was preparing you. If you read it, you’re all set. If you know the lion tamer’s sketch, you’re all set. If neither is true, but you’re in the mood to wing it, you’re all set!]
When you’re accustomed to the meaning of a certain word in one context, and then you find that word in another, it may be entirely understandable that you haul your first knowledge of the word along with you to your new surroundings. But that doesn’t mean it won’t be dangerous.
In his book, How Not to Be Wrong,* mathematician Jordan Ellenberg explains that when mathematicians have complicated concepts to discuss, they can either invent words (his examples are cohomology, syzygies and monodromy, and I somehow don’t feel I’m prepared to learn more about any of them), or they can use an existing word for something that might have a vague resemblance to the mathematical concept in question. It’s possible to find groups, bundles, rings and stacks discussed in papers published in esoteric theoretical mathematics journals, but any sense we might have that we know what is meant by those words in the world of math would probably be gravely misguided.
The invasion of vocabulary from one realm to another can have more serious consequences than just causing us confusion. Ellenberg gives this example: “I once had an uneasy moment with a colleague in an airport when he made the remark, unexceptional in a mathematical context, that it might be necessary to blow up the plane at one point.”
Can’t you just picture what would have happened if that conversation had taken place right about the time they were reclaiming the contents of their pockets from those dog-dish bowls after TSA officials had done whatever metal-detecting they deemed appropriate?
As potentially worrying as that might have been, I’m guessing they made it through okay–surely Ellenberg would have shared the story of the resulting detention, if such a thing had happened.†
The perils of vocabulary migration are actually quite serious for us when they affect our understanding of things scientific.
Like mathematicians, scientists sometimes use words that we understand and use ourselves, but we and the scientists may use them to mean quite different things. Let’s look at an example.
“I have a theory about that” can be the sort of thing you say if you have given a puzzling question the benefit of your concentration for the length of an elevator ride, and you now feel prepared to throw out a guess.
When a scientist uses the word theory, it’s something quite different. If she is at the “we’re not really sure” stage, “theory” is not the word she uses. Even the word “hypothesis” is likely to have more heft behind it than would be suited to typical elevator ruminations. Generally, by the time a scientist is willing to put “theory” in front of a statement, it means “we have measured and tested, argued and revised, measured and tested some more. This way of explaining things fits what’s happening.”
These two ways of using the word “theory” have a tendency to derail discussions (shouting matches?) about things like the theory of evolution. As usually happens when people aren’t listening carefully to each other, a certain amount of confusion ensues. I found this explanation by the American Association for the Advancement of Science to be helpful:
A scientific theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment. Such fact-supported theories are not “guesses” but reliable accounts of the real world. The theory of biological evolution is more than “just a theory.” It is as factual an explanation of the universe as the atomic theory of matter or the germ theory of disease. Our understanding of gravity is still a work in progress. But the phenomenon of gravity, like evolution, is an accepted fact.◊
Many people think there’s a big fight to be had in this arena, but I’m not interested in having it here. The point I wanted to make is that conversation just isn’t productive when one person means one thing by a word, and another person means something entirely different (although on occasion it can be highly entertaining–I’m thinking of the lion tamer sketch–you know the one?). There’s plenty to be confused about even if we all agree on the meanings of the words we’re using. No need to worry that getting us all on the same page with regard to vocabulary will mean there’s nothing left to talk about. At any rate, that’s my theory.
*Perhaps at some point I’ll get around to juxtaposing How Not to Be Wrong with Being Wrong, touched on in this post. Both books have very interesting things to say, and would probably get along better than their titles might suggest.
†My high school boyfriend grew up to be a math professor (hey, Ted!) and he kindly explained a bit about what blowing up the plane might mean. He reminded me that a point has no dimensions, so you can enlarge it all day, and it never gets any bigger. Mathematically, you can “blow up” a point P in a plane, which replaces P with a circle C, just as the North Pole gets replaced by the whole top edge of the map in certain projections, or by a whole circle’s worth of coordinates. I’m not sure what mathematicians get from such an exchange, but I bet that if you’re interested in getting more details, Ted would be willing to help us out. He’s that kind of guy.
◊I found the AAAS quote here.
These images are found on Wikipedia.