Last summer, at a meeting outside Aspen, Colorado, several dozen physicists gathered to celebrate what the journal
*Nature
* described as the "growing feeling that their discipline's mindset will be crucial to reaping the harvest of biology's post-genomic era." In fact, with genetics set to improve everything from human health to agriculture, physicists and mathematicians worldwide are pouring into the life sciences. Biology is where the scientific action--and the money--will be in the coming century.

But this is not the first time that physicists and mathematicians have looked to biology for new fields to plow, and the history of such efforts has been fairly dismal. Biologists and physicists have different goals and traditions, and they look for different kinds of answers, because they ask different kinds of questions.

My first glimpse of this disciplinary divide came many years ago while teaching a course on mathematical methods in biology. After introducing a biological problem with 11 variables, I used a simple method called dimensional analysis to demonstrate that only three needed to be studied empirically; the relations among the rest of the variables could be inferred logically. "But you haven't done the experiments," the students complained, "so how can you know?"

I've been thinking about that question ever since. As a theoretical physicist, I had been trained to trust only mathematical and logical arguments and to view experimental evidence as fallible. But to many, if not most, biologists, experimental evidence, however fallible, still provided a surer path to truth. Where, in a purely deductive argument, was there room for nature's surprises, for mechanisms that look nothing like what we imagine in our initial assumptions?

Philosophers of science have traditionally approached questions concerning what counts as knowledge, explanation, and theory as if they could be answered universally. But the communication gap between experimental and mathematical biologists suggests that the answers depend on specific disciplinary cultures.

Consider the interdisciplinary efforts--and ultimate failure--of Nicolas Rashevsky, a Russian theoretical physicist who emigrated to the US in 1924. Rashevsky wondered whether a similar mechanism might account for the division of biological cells and the onset of instability in liquid droplets. Soon, he set out to build "a systematic mathematical biology, similar in its structure and aims to mathematical physics." By 1940, he had published his magnum opus,
*Mathematical Biophysics
*, established a program by the same name at the University of Chicago, and founded the
*Bulletin of Mathematical Biophysics
*.

But by 1954, Rashevsky had lost his grants and budget, and today little remains of his institutional and scientific efforts. The main criticism against him was that he failed to engage with practicing biologists. But Rashevsky did make at least one early effort to interest biologists in his work. In 1934, he presented a "physico-mathematical" analysis of the forces acting on an idealized spherical cell, a model that he argued was sufficient to explain cell division.

When the biologists objected that not all cells are spherical, Rashevsky responded that the theory must first be applied to the simplest cases. E. B. Wilson, the proverbial giant of cell biology, had the last word, concluding in a brief paper following Rashevsky's presentation that mathematics may be helpful in studying the growth of populations, but not individuals. Wilson's colleague, Eric Ponder, was even more pointed, saying that what is required "is more measurement and less theory."

By the early 1950's, however, biologists still could not explain how an organism reproduces its characteristic form from one generation to another. In 1952, Alan Turing--best known for his work on computation and the mind--proposed a mathematical model consisting of a pair of equations describing the reaction and diffusion of two imaginary chemicals. His model, which he admitted was "a simplification and an idealization," aimed to highlight the "features of greatest importance" in an embryo's development. He emphasized that the reactions he described bore no resemblance to those in nature. They reflected only the desire "that the argument be easy to follow."

Turing appears here as a caricature of the mathematical physicist. Like Rashevsky, he had been steeped in mathematical and physical scientists' belief that an imaginary construction making no pretense to literal truth can nonetheless capture the "features of greatest importance" and hence serve a useful explanatory function.

But experimental biologists ask a different question: not whether organisms
*could
* grow as an imaginary model suggests, but whether they
* do
*. On this score, Turing's reaction-diffusion model has been greatly disappointing. Over the last 20 years, molecular biologists have found that the progressive activation of a hierarchy of genes--which play no role in Turing's model--defines an organism's final structure and form. More broadly, the best explanations of how biological systems solve particular problems come from experimental genetics, not mathematics and logic.

Physicists and mathematicians nonetheless have reason to celebrate. Since 1983, the proportion of funding for mathematical and computational research that comes from the Biological Division of the US National Science Foundation has increased about 50-fold.

To their credit, many new programs in mathematical biology encourage researchers coming from the mathematical sciences to become practicing biologists themselves. Meanwhile, "user-friendly" computer programs enable biologists to build their own mathematical/theoretical models.

The net effect could be a new disciplinary culture that transforms the aims, methods, and epistemological basis of research. Theoretical biology's models will be formulated not in a few simple equations, but in a complex of algorithms, statistical analyses, and simulations. And, recognizing the ever present possibility of exceptions, they will aspire to "generalities" rather than "laws," leaving room for accidental particularities of biological structure. Biology is not physics, and to ignore its evolutionary history is to invite irrelevance.

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