I just started reading an interesting book, “How Mathematicians Think,” written (naturally enough) by a mathematician (William Byers). It got me thinking not only about mathematics but also science, what it is and why I do it. Here’s the paragraph that triggered it:
The most pervasive myth about mathematics is that the logical structure of mathematics is definitive–that logic captures the essence of the subject. This is the fallback position of many mathematicians when they are asked to justify what it is that they do: “I just prove theorems.” That is, when pressed, many mathematicians retreat back to a formalist position. However, most practicing mathematicians are not formalists: “what they really want is usually not some collection of ‘answers’–what they want is understanding [cite is to an interview with mathematician William Thurston].” The statistican David Blackwell is quoted as saying, “Basically, I’m not interested in doing research and I never have been. I’m interested in understanding, which is quite a different thing.” (Byers, How Mathematicians Think, pp, 25-26; emphases in original)
I read this and my first reaction was disagreement, although I couldn’t figure out why. The obvious reason was that I consider myself a researcher and I am interested in research. But I’m also interested in understanding, and I didn’t see those things as in opposition, although I had to agree that doing research and understanding are different, so there was a problem somewhere. When people ask what moves me to do science, I almost always say something like, “I want to find out how the World works.”
I like to think of myself as an altruistic person and naturally I hope that what I do will make the world a better place for everyone. That does direct my curiosity to some extent. I’m not indiscriminate about what parts of the world’s workings I’m interested in. But if I am completely honest with myself (and like everyone I’m probably often not honest with myself) I think I’d say that the strongest motivator is just wanting to know the basic principles of the world I live in. That’s more than just a description of the mechanism but the general plan which governs how the mechanism works. Like most scientists, I assume these principles are knowable, regular and that science is the way to know it.
None of that sounds incompatible with Blackwell’s goal of “understanding,” but there is one additional element that is crucial and goes beyond it. “Understanding” is something an individual has. It’s subjective. It’s a slippery concept, but it’s like assimilating an explanation that satisfies us in some way. But if something is going to be scientific, the product of research, then it must be intersubjective. That’s why religious or supernatural concepts aren’t science for me. They can’t be displayed in a way for all to see but depend on individual and subjective knowledge. The question isn’t so much testability or falsifiability as it is what those things imply: the ability to make the evidence available to anyone and everyone. So when I say that research is trying to figure out how the world works, I mean producing explanations that are shareable and intersubjective, not just a form of my own understanding.
Science is a social enterprise, not a solitary one, even if some of us carry it on in a solitary fashion, alone with our computers, or paper and pencil. I do what some people might refer to as Grand Theory, but it is not meant to be Grand Theory just for me, but Grand Theory for the Ages. Pretty ambitious. But how else should we do it?
We all know that hard won science is in a sense temporary. That at some point a revision will come along that will sweep away what was considered true in the past. It doesn’t matter. I’m still trying to build something that will last forever because it’s True. We all lie to ourselves. Even when we think we are being honest with ourselves. Go figure.