E. O. Wilson says great scientists need be "no more than semiliterate" mathematically. He says: doing the math is often easier than generating ideas; the math is usually out-sourceable; we have more mathematicians than useful ideas; and science advances by better ideas which typically don't come from mathematical reasoning.
In this Wilson revives two old rivalries. One, "theory-tribe" versus "experimental-tribe," is well described here. The other "math-monks" versus "pluralist-reasoners" is described below.
Math-monks follow Galileo's faith that "the Book of Nature is written in the language of mathematics." They believe mathematical descriptions are the one-true-way, the best and most reliable kind of knowing. Plural-reasoners side with polymath Pascal who warned against over reliance on the "spirit of geometry," which sees only the mathematically characterisable. Physics' successes spread Galileo's gospel so far that J.S. Mill thought sociology would become "social astronomy." We live in the aftermath of Galileo's triumph, where rational is often reduced to meaning what can be shown by the numbers.
Wilson claims upset modern math-monks as detailed here. But why haven't their tools, honed for the inanimate world of physics, been as useful in biology or the social sciences? Here are some seed ideas on what physics and its classical-math methods (geometry, algebra, statistics etc) are good at, and what their limits show:
Physics is forgetful. It deals only with forces that are active now, not with what was happening before. Classical math similarly has no memory and had to be computer-extended to enable path dependent simulations and models. But programming isn't just math, it adds other logic.
Physics likes sameness. Protons and triangles are the same everywhere and at all times. The behaviours of rabbits and people are not. Though sometimes mathematically treating people the same has benefits, Tyler Cowen claims this helped economists become early promoters of universal human rights.
Physics prefers peripheral ifs. Like classic-math it isn't good at conditionals. Its ifs are used to decide which equations apply; they can't be used within the equations. But biological behavior is centrally structured by if-then logic.
Physics loves interactions between simple objects and stable forces. But the animate sciences play fundamentally different games: what A does depends on what B is doing. Imagine how complex Newton's third law would be if for every action there was one of n possible reactions, depending on how each biological billiard ball felt that day? Game theory is young but it can't be done with only classical-math.
Idolizing classical-math style reasoning is a legacy of physics' past triumphs. But such conventional number-smithing leaves out or doesn't deal well with the logic of life's conditionally scripted variable path dependent responses. So parts of biology need extensions to classical-math thinking. Wilson and Pascal's pluralist-reasoners know, over-reliance on conventional math can be like searching for lost keys only in the lit part of the parking lot.
In science, as in life, we see with our ideas. Mathematical ideas are powerful tools of reason and science. But not understanding their limits, limits what can be reliably built with them. Undervaluing non-mathematical thinking ignores useful tools. Why should we limit ourselves to what can be expressed or supported mathematically? Cyber-critic Evgeny Morozov worries about "numeric imagination" displacing "narrative imagination." Wilson agrees saying "scientists should think like poets and work like accountants" see TEDMED video below.
Images: E. O. Wilson: Jim Harrison via Wikimedia Commons; Galileo: H. J. Detouche via Wikimedia Commons.