Thursday, April 11, 2013

E. O. Wilson on Science and Math

Prominent biologist and science writer E. O. Wilson has a provocative Wall Street Journal opinion piece about the link between mathematical ability and scientific achievement. Perhaps the central ambiguity of his argument is illustrated by the two different titles the article seems to have. The browser heading is "Great Scientists Don't Need Math", while the actual title is "Great Scientist Does not Equal Good at Math". While the latter claim is almost trivial, the former claim seems very contentious. Of course, I am biased on this issue, having written a book arguing that mathematics makes several crucial contributions to the formulation and justification of our scientific knowledge. But setting that philosophical discussion aside, it is somewhat disturbing to find such a simplistic view of the way mathematics helps in science being presented by such a distinguished scientist.

Wilson's basic idea is that great scientists don't need to be good at math because they can always call on specialists in the relevant areas of mathematics. On Wilson's picture, the great scientists come up with great ideas, and these ideas are then implemented and tested via mathematical models. But the ideas themselves are completely non-mathematical:

Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition.
Everyone sometimes daydreams like a scientist. Ramped up and disciplined, fantasies are the fountainhead of all creative thinking. Newton dreamed, Darwin dreamed, you dream. The images evoked are at first vague. They may shift in form and fade in and out. They grow a bit firmer when sketched as diagrams on pads of paper, and they take on life as real examples are sought and found.
Pioneers in science only rarely make discoveries by extracting ideas from pure mathematics. Most of the stereotypical photographs of scientists studying rows of equations on a blackboard are instructors explaining discoveries already made. Real progress comes in the field writing notes, at the office amid a litter of doodled paper, in the hallway struggling to explain something to a friend, or eating lunch alone. Eureka moments require hard work. And focus.
Ideas in science emerge most readily when some part of the world is studied for its own sake. They follow from thorough, well-organized knowledge of all that is known or can be imagined of real entities and processes within that fragment of existence. When something new is encountered, the follow-up steps usually require mathematical and statistical methods to move the analysis forward. If that step proves too technically difficult for the person who made the discovery, a mathematician or statistician can be added as a collaborator.
Now, it is clear that some ideas that drive scientific discoveries are non-mathematical. But I do not see much evidence that most of these ideas are like that or that scientists should trust non-scientists to implement their ideas in mathematical terms. It is precisely at this stage that some of the most important and innovative work is done, and it is not clear to me how collaborations can work if one side, the scientist, doesn't understand what the other side, the mathematician, is doing.

See here for another critique of Wilson.


Marshall Abrams said...

Hi Chris,

I'm leery of generalizations on this issue that are overly strong, but you might agree. Darwin seems not to have used mathematics very much, even though he did derive insights from conclusions of mathematical arguments given by others, such as Malthus. I also think there are good biological and social scientists who have been brought up to speed on the basics of the statistics they need enough to be careful researchers, but still require consultants to help with the details sometimes. I think there is a lot of good scientific work that involves copying of statistical methods developed by others--or simply applying a menu choice in SPSS--without a deep understanding of how those methods work. However, I do think that understanding the math on one's own can be a good thing: It allows integration of mathematical reasoning with other reasoning in a way that's impossible or difficult when the two have to cross from one person to another.

Anonymous said...

Wilson's comments are just another example of a scientist thinking they know how scientific discovery works and over-generalising, of course, and typically from their own experience. Its frustrating for me in that it ignores all the work thats been done on heuristics in science and particularly those that operate at the 'theoretical' level - e.g. Redhead's emphasis on the role of 'surplus structure'.
Steven French