10 August 2008


I've started reading a book discussing probability theory: Chances Are: Adventures in Probability, by Kaplan and Kaplan. So far I'm enjoying it. It's intended as a lay introduction to probability, but I'd say the minimum pre-req thusfar is Math 108. That's not what inspired me to post.

Since they're discussing statistics, they bring up the question of testability, and what is a scientific question vs. a non-scientific question. Their example of a non-scientific question is, "Why is an apple sweet?" Er, sorry, but WHAT?!??!. I'm going to generously assume that they have no background whatsoever in biology or anything remotely related. In fact, that is a scientific question, and one to which I can think of several correct answer, depending on exactly what you mean.

If you mean, "What is it in the apple that makes it taste sweet?", then the answer is "sugars." If you're going a bit deeper and wonder what makes these things called sugars taste sweet, it gets more complicated, but the evolutionary answer is, roughly: "Sugar contains nutrients useful to mammals, thus it is advantageous for its taste to appeal to us. We describe this appeal as 'sweet'". Maybe you mean, "Why should an apple contain things that taste sweet to us?" Answer(1): We've bred and cross-bred apples over the years to give them an appealing taste. Answer(2): Having a taste that appeals to animals helps the apple's seeds propagate.

I think that, maybe, what the authors really mean is that "Why is an apple sweet?" is not a question that we can answer with numbers, and since numbers are the focus of the book, the question is not of interest to them. But to proclaim it's not scientific is pure nonsense. I'm trying to think of a non-scientific question that is not, well, just silly. Pretty much, as soon as you make a generic claim across any sort of class, you've made a scientific question. An exception might be: "Do all apple trees like the color blue?" or something equally bizarre. Even then, I can think of ways of testing it, and so that's still a scientific question, even if it's a strange one. So... "Are all apple trees in contact with an invisible dimension that we cannot detect in any way, shape or form?" Okay, that one's completely untestable by nature and hence unscientific.

Another way of creating a non-scientific question is to put it in terms of a particular circumstance or individual, particularly concerning something that happened in the past for which inadequate records exist. For example, I've hated boiled egg yolks for as long as I can remember. I love the whites, but I cannot stand the yolks. Why? I have no idea. I can tell you what I hate: the texture. I've tried getting over it, as it seems wasteful to throw away half the egg*, but as soon as I get more than a tiny amount of boiled yolk in my mouth, I want to throw up. Asking "Why does Qalmlea hate the texture of boiled egg yolks?" is not scientific because we have no good records of my reactions to food before I started remembering them. I can speculate that maybe I choked on something with a similar texture, or became ill, etc., but with no means to test that, it isn't a scientific question. We can make a general case that is scientific: "Do infants who experience negative reactions to a particular food retain an aversion to that food later in life?" That is something science can test and answer.

So there is one very simple way of reformulating their question to make it unscientific. "Why is this particular apple sweet?" If it's already been picked and we have no idea from which tree it came, this is not a question for science. If we do know which tree it came from, we can run tests on the tree to see if consistently produces sweet apples and even examine the chemistry involved. I suppose it's possible that this is the question they had in mind, but mathematicians should know better than to use poorly defined statements as counter examples.

Back to the book, I expect the Kaplans are paying blind homage to N.O.M.A. as it's sometimes formulated: "Science answers the how; religion answers the why." That's always seemed like a false dichotomy to me. Consider the case of the apple again. Apples that tasted sweet were more likely to be eaten by animals and have their seeds propagate further from the original tree, so sweet apples would have a better chance of producing offspring that produced more apples, which were more likely to be sweet, which were more likely to be eaten and have their seeds propagated far enough from the parent tree ... Why? Natural selection. How? Natural selection. I don't see a meaningful distinction between 'how' and 'why' in this instance.

*Now the cats get the yolks, so it bothers me less.


John said...

I think the 'why' questions are meant to be a sort of existential search for deeper meaning, and the 'how' questions the 'nuts-and-bolts' of the matter.

That said, I really don't see much difference either, except in a childish 'but, why?' regression ad infinitum sort of way, in the general case anyway

Qalmlea said...

I get the existential thing in the "Why are we here?" type questions, but I'm not seeing it at all in this case. Perhaps "Why is this apple here?"

Propmaster: You said you wanted an apple, so I brought you an apple!
Kaplans: That's not—
P: Sheesh. Next time, you can go get your own apple!

(couldn't resist)