The brilliant conservation and ant biologist E. O. Wilson wrote a bizarre piece for the Wall Street Journal recently. It is modified from an upcoming book of advice for young students. It has inspired an intense flurry of highly negative comments that have mostly focused on a tiny piece of his argument, so I think it might be worthwhile here to first summarize what he says.
1. Students drop out of science because they fear math, which is a shame.
2. Strong math skills are unnecessary to become a brilliant scientist.
3. E. O. Wilson himself has weak math skills.
4. Strong math is needed in few areas of science, like some physics.
5. The ability “to form concepts…by intuition” is far more important.
6. Dreams and fantasies “ramped up and disciplined,” are the basis of creative thinking.
7. Discoveries do not come from pure mathematics.
8. Ideas also need thorough study of some part of the world.
9. Mathematics and statistics are a follow-up on new ideas and can be outsourced.
10. Wilson took the creative lead in his collaborations with mathematicians.
11. Most mathematical models are irrelevant or wrong; maybe 10% are valuable, generally those from people with knowledge of living systems.
12. Learn more math if you are weak but avoid fields with “close alternation of experiment and quantitative analysis…including a few specialties in molecular biology.”
13. Newton needed calculus, so he invented it. Darwin was fine without math, which came later.
14. Find something you love to study.
What is fascinating to me about this piece is that it describes scientific inquiry as Wilson experienced it himself. It is a bit sad that he cannot imagine it might be any other way. It is also sad that he treats his collaborators so poorly. Does he really think that caste allometry, which must have been from Oster, is not a contribution? How about the theory of island biogeography? Did Robert MacArthur just put a few graphs on Wilson’s brilliant ideas?
An important and compelling point that Wilson tries to make involves where ideas come from. He talks about dreams and fantasies building on intuition and resulting in understanding of pattern where none was before. Then these ideas tell us what to test. They give us the hypotheses, which we then test. For Wilson, these burning nights of churning ideas come from intense empirical study, in his case, mostly of ants. I can well imagine that theoreticians also have nights of struggle, with many ideas demanding attention, then finally falling into pattern. I don’t see why Wilson views math as threatening the creative process.
Actually, where new ideas come from is in itself a field of study. They do come from churning. They come from contact outside your group. They come from sudden inspiration. We could all do better if we paid attention to what is known about where new ideas come from and put that knowledge into practice.
Wilson talks about the many wrong ideas of theoretical biology. Anyone who even reads their own letters or emails of a couple of decades ago, or perhaps even a few weeks ago, will know how many good people have wrong ideas. The trick is to let them go, to keep searching for the gems that stand the test. If Wilson is right, that 10% of theoretical papers are valuable, then they are succeeding beyond most people’s greatest dreams.
Some people seem to have more good ideas than others. This could be because they have more ideas, because they are better at rejecting the ones that don’t seem to work, because they reach outside their group, or because they are simply amazing, like William D. Hamilton, or Richard D. Alexander, in the field I know best. I don’t see how math or no math enters in. We can all become better at retaining good ideas if we pay attention and don’t fall in love with ideas that fail us.
Wilson seems to equate mathematics, theory, statistics, and quantification. It is beyond the scope of this piece to fully sort these out, but here is an outline, also throwing in experimental design.
1. Quantification is measuring things. You can’t know if things are different unless you measure them. Some characteristics might seem more like categories, but they could also be quantified, for example color, or presence/absence of a trait. You must measure things in nearly all areas of science.
2. Statistics tells us when sets of things that we have measured are the same or different and how confident we can be. It is particularly essential in multivariate arenas, or those where there are small effects. Chemists and molecular biologists often do not use statistics because they are looking at experiments with few variables of large effect. Anyone unfamiliar with statistics can get into trouble if they are not familiar with its rules, for example, independence, normalcy of distribution.
3. Experiments need to be designed so you can answer the question. At its most basic, you need replicates within treatments so you can compare variation within a treatment to variation between treatments. A treatment could be an experiment, or be based on comparison. It is important that replicates be independent and that whenever possible the measurements be done blind, that is that the person measuring is unaware of the treatment so no inadvertent bias is introduced. The longer you spend thinking about how to do your study, the easier and better it will go.
4. Theory organizes the facts. Theory tells us what ideas to test. Theory is predictive. Supported theory tells us how the world is organized and how change happens. All areas of human understanding need theory, for only with theory can we predict what will happen or has happened in cases we have not yet seen. Theory comes from the creative processes mentioned earlier. Theory works best when it is precise, so we know exactly what observations will support it and what observations will cause us to reject it. Theory is an abstraction, but its point is to understand the real world. The more you know about the real world, the more likely you are to arrive at useful theory. But theory that can be expressed abstractly may be most generalizable and testable.
5. Mathematics is not arithmetic. It is not even algebra or calculus. The Free Dictionary by Farlex defines it as: “The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.” Wikipedia talks about mathematics as the study of quantity, structure, space, and change involving pattern discovery and mathematical proofs and much more. Mathematics is necessarily more abstract than much of science, but it is an essential component if you want to develop clear, general theories. Do you need exceptional math ability or training for all areas of biology? Obviously not, but it can’t hurt, just as a good memory, or deep knowledge of any given taxon can’t hurt.
To me there are two important points to take from Wilson’s piece, one about respect and one about education. Wilson seems to be disrespecting theoretical or mathematical biologists, undervaluing their contribution. I do not agree with this, but it may be coming from the shovels of disrespect some of those types have been hurling at the more empirical end of the spectrum. I feel that I got that in buckets from a few of the folks at KITP in Santa Barbara earlier this semester. Like Wilson, I am tired of so-called scientists that think they can do useful work by ignoring empiricists and deriving everything from first principles.
With better early education, Wilson might not have had to take calculus as a tenured Harvard professor. He might not have lacked sufficient mathematics for his ideas, bringing him to collaboration.
There may be other things he missed with his Alabama education. Others might not have been as gifted at making up for early deficits as he was. It is a shame that public school education is still as bad as it is. It is still true that Alabama does not offer nearly what it should to its students in public schools. No individual teacher, no matter how dedicated or gifted, can make up for a system that does not value and pay for good education.
Universities also could greatly improve their educational offerings. Is the problem Wilson mentions with calculus turning off students to science a problem with something intrinsic to the material, or the lackluster way it is taught? At Michigan I had excellent and engaging courses in calculus. I would venture that more students are turned off to science by the facts-first weed-you-out approach to introductory biology than ever leave the field because of calculus. Why do so many professors stick to the proven-faulty lecture-test style of teaching? Why do we discourage students with horrible, huge introductory courses, then ponder the deep mystery of students leaving science? At least Wilson is out there and thinking about what might be good advice for young students. I do not agree with everything he says, but at least he is engaged.
Written from the Double Helix Ranch Writer’s Retreat.