Maths and Science 2013: Reaction to Wilson and Frenkel

Famous Harvard biologist E. O. Wilson wrote a Wall Street Journal essay in April of this year downplaying the need to learn maths for scientists.  I suppose he wanted to start a lively conversation about the matter, but it it clearly was a “WTF, mate” moment. In response and four days later, Berkeley mathematician Edward Frenkel wrote an essay for Slate disagreeing with the eminent biologist and philosopher.

Both are available from the American Mathematical Society in a single PDF. Professor Frenkel has gone on to write Love and Math: The Heart of Hidden Reality, a book which continues the thoughts expressed in his essay.  I have not yet read Frenkel’s book, but will, and may place a review here.  (There is a review in American Scientist available by their own Brian Hayes which gives guarded praise.) But I thought, in the closing hours of 2013, I might give my thoughts on the discussion here.

While I respect the man, I find Wilson’s mercantile approach to professional relationships with mathematicians and statisticians foolish, and a tad offensive. I am referring to the part of his essay where he writes:

Over the years, I have co-written many papers with mathematicians and statisticians, so I can offer the following principle with confidence. Call it Wilson’s Principle No. 1: It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations. This imbalance is especially the case in biology, where factors in a real-life phenomenon are often misunderstood or never noticed in the first place. The annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail. Possibly no more than 10 percent have any lasting value. Only those linked solidly to knowledge of real living systems have much chance of being used.

I cannot disagree more.  On the practical side, the revelations of biomechanisist Steven Vogel of Duke University, such as reported in his books such as Life in Moving Fluids or Comparative Biomechanics demand both a deep understanding of quantitative aspects of what are deep subjects (e.g., fluid mechanics) and a facility with quantitative models. On the less practical side (for I don’t know what “theoretical biology”really means), ecology and intracellular biochemistry have seen an explosion of useful results.  Consider:

• S. P. Ellner, J. Guckenheimer, Dynamic Models in Biology
• K. Soetaert, P. M. J. Herman, A Practical Guide to Ecological Modelling
• M. A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life
• H. Kokko, Modelling for Field Biologists
• J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics
• S. C. Amstrup, T. L. McDonald, B. F. J. Manly (eds.), Handbook of Capture-Recapture Analysis
• S. T. Buckland, D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers, L. Thomas, Introduction to Distance Sampling
• S. T. Buckland, D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers, L. Thomas, Advanced Distance Sampling: Estimating abundance of biological populations
• P. Yodzis, Competition for Space and the Structure of Ecological Communities
• J. Harte, Consider a Spherical Cow
• J. Harte, Consider a Cylindrical Cow

These are just titles directly relevant to biology from my personal bookshelf, neglecting books which have major sections devoted to biological problems, most of them very recent.

I applaud Frenkel for taking on the challenge to respond.  I think one specific counterpunch might have been a little rough, namely,

It is interesting to note that Wilson’s recent article in Nature and his book claiming to show support for so-called group selection have been sharply criticized, by Richard Dawkins and many others. Some of the critics pointed out that one source of error was in Wilson’s math. Since I’m not an expert in evolutionary theory, I can’t offer an opinion, but I find this controversy interesting given Wilson’s thesis that “great scientists don’t need math.”

it’s clear Frenkel loves his subject and felt a need to defend it, perhaps feeling insulted by Wilson’s flame. Surely, however, Wilson does harm downplaying the need to master mathematics, or suggest that it all can be delegated to maths boffins.

Consider the vehicle of Wilson’s essay, the Wall Street Journal. Professor Andrew Lo suggests one reason for the misuse of derivatives instruments and their relationship with the 2008 financial crisis is that those in authority did not understand their statistical and mathematical limitations, delegating this understanding to various “quants”. The trouble with delegating without understanding is that they would want to get ahead by saying what they think the audience wants to hear will do so, at the expense of those saying cautionary, more conservative things and trying to get the audience to understand.  If an audience does not understand the technology enough to make decisions and set policy, it’s entirely possible to run off the rails. In the case of the financial crisis, the decision makers did not understand statistical correlation.

I’d say climate science falls into that category. And biologists who “hire” mathematicians and statisticians to advise them, may run the risk of needing Fisher’s advise,

To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. He can perhaps say what the experiment died of.