April 9, 2013 | 4

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Follow Jag Bhalla on Twitter as @hangingnoodles. Or visit their website.

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.

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couple of things:

Wilson doesn’t entirely diss math, but simply says “advanced” math isn’t necessary for success in science — the debate then becomes over what does or doesn’t qualify as “advanced” math.

Link to thisAs far as any restricted efficacy of math in the biological and social sciences, the question is whether that results from inherent limitations of mathematics (forever), or is it just that biology and social science are still at such a primitive stage that applicable math algorithms haven’t been discovered yet?

Faraday did some rather great physics, but could not do math. He referred to himself as “amathematical” and quipped that “the only mathematical operation I ever performed was turning the crank of the calculator.

He learned about electromagnetism via direct experiments on the physical world.

Our heroic theoretical physicists who have given us the barren creations of string theory, supersymmetry, “WIMPs”, anthropic pretzel logic, and multiverse fantasies might learn something from Faraday.

Study nature, not untestable theoretical thought-bubbles.

Robert L. Oldershaw

Link to thishttp://www3.amherst.edu/~rloldershaw

Discrete Scale Relativity/Fractal Cosmology

Let me add the point that some of Einstein’s greatest contributions were not mathematical discoveries. Rather they were conceptual discoveries about how nature actually worked.

Once he had the correct conceptual natural philosophy, then he would subsequently develop the mathematical formalism that gave the concepts the rigor and predictive power by which the conceptual ideas could be further developed and scientifically tested.

That is how real science is done.

As Einstein put it: “Books on physics are full of complicated mathematical formulas, but thought and ideas are the beginning of every physical theory.”

Robert L. Oldershaw

Link to thishttp://www3.amherst.edu/~rloldershaw

Discrete Scale Relativity/Fractal Cosmology

To expand on this point, the term “social sciences” was presumptuous at birth, and its scholars have done precious little but add mathematics to their tools wherever possible, to earn the name “science.”

If you can’t predict from theory all but infallibly within the limits of observation available to you, you ain’t doing science, whether math is involved or not. What you’re doing may be valuable, but value doesn’t define science either.

Link to this