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Science and Simplicity

1.

When asked to name, without reflection, the greatest scientific work that has ever been done, people who are themselves scientists will usually say “Newton’s Laws of Motion” or “Einstein’s Theory of Relativity.” Such answers are revealing of the image of ideal science with which we have been brought up, an image that has been of immense importance in the intellectual formation of working scientists. What we might call the “Newtonian Ideal” in science is the formulation of some principle of great generality, if not universality, a law or small set of laws that applies at all times and in all places.

This emphasis on the Newtonian Ideal differentiates the awarding of prestige within the community of scientists from the awarding of prizes and of popular recognition which, quite properly, often give considerable weight to the impact of science on the human condition. One can get a Nobel Prize for inventing a very useful gadget like the transistor1 or for finding a treatment for prostate cancer,2 and we are reminded daily at breakfast that Louis Pasteur invented a way to keep milk from growing bacteria before we can pour it on our cereal. Scientists, however, value most those assertions about nature that apply to the broadest possible domain of the material world, giving short notice, if any, to revelations about nature that apply only to a particular chemical or physical or biological object. There is a new crop of Nobel laureates every year, but there was only one Isaac Newton.

One consequence of the value placed on great generality is that there is necessarily a tenuous connection between what has actually been observed in the world of physical phenomena and the theoretical claim. Between the idea and the reality falls the shadow of abstraction. Newton’s First Law, that bodies at rest tend to stay at rest and bodies in motion tend to stay in motion in a straight line unless perturbed by an external force, could not possibly have been a generalization of the motions actually observed by him. Neither he nor any other seventeenth-century observer ever watched a body move in a perfect vacuum with no external forces operating on it.

The secret is in the word “tend.” Tendencies are not observable. They are an abstraction around which the observations of the actual movement of bodies in different circumstances can be organized, in an attempt to understand the “perturbing” forces. In a world in which real material objects have a diversity of sizes and composition and are being acted upon by a variety of forces, Newton’s First Law does not describe the motion of any particular object. The law that for every action there is an equal and opposite reaction may tell us what happens in the collision between two perfectly elastic bodies, but it is a poor prescription for winning at billiards.

The problem of the relation between the abstract structure of universal claims and the real world of particular events is especially acute in biology. Unlike planets, which are extremely large, or electrons, which are extremely small and internally homogeneous, living organisms are intermediate in size and are internally heterogeneous. They are composed of a number of parts with different properties that are in dynamic interaction with one another and the parts are, in turn, composed of yet smaller parts with their own interactions and properties. Moreover, they change their shapes and properties during their lifetimes, developing from a fertilized egg to a mature adult, ending finally sans teeth, sans hair, sans everything. Even the single-celled bacterium changes its internal properties from the moment that it is born from a division of its parent cell until the moment that it too divides. Organisms are a changing nexus of a large number of weakly determining interacting forces. As a consequence we have no universal laws in biology. The Biogenetic Law, “All life from life,” was only enacted a couple of billion years ago and could not always have been true or there would be no one to write for, publish, or read The New York Review of Books. Presumably once life arose from a handful of molecules it prevented more such events by gobbling up the rest of the soup.

Of Mendel’s famous three laws, inferred by him from studying a few characters in one species, two turn out to be untrue in a large fraction of cases and the third has a few very revealing exceptions. Is biology inevitably a story of different strokes for different folks, a collection of exquisitely detailed descriptions of the diverse forms and functions of organisms down to the molecular level, obtained from an unending history of experiment and observation? Or, from this booming, buzzing confusion can a biologist derive some general claims that are freed from the dirty particulars of each case, claims that, while not of the universality of Newton’s laws, at least characterize the properties of a very large part of the living world? Can there be a theoretical biology? Is there a possibility of Making Sense of Life?

One might have thought that Evelyn Fox Keller, by training a mathematician, would take an upbeat view of a program to formalize, mathematize, and generalize the observed diversity of living forms and processes. She is, however, by trade a philosopher and historian of science who, in analyzing the attempts to construct a theoretical biology, has come to a rather skeptical conclusion. Both history and epistemology seem to speak against it:

No one can deny the extraordinary advances that have been made over the course of this past century in our understanding of vital processes….

Yet I would argue that, despite such unquestionable success, biology is scarcely any closer to a unified understanding (or theory) of the nature of life today than it was a hundred years ago. The models, metaphors, and machines that have contributed so much to our understanding provide neither unity nor completeness. They work to answer some questions while avoiding (even obscuring) others.

It should not be supposed that Keller’s rather negative view flows from some particular and rigidly applied view of what counts as a successful explanation. On this matter she is more the sociologist than the philosopher, taking the position that each scientific community has its own “epistemological culture,” its own agreed-upon norms and standards of what counts as a sufficient understanding of a natural phenomenon. The epistemological culture that concerns her chiefly in Making Sense of Life is that of developmental biology, the science that is meant to explain how one fertilized egg cell, containing a variety of large molecules, including DNA and proteins, and intracellular structures, all organized in a particular spatial configuration, turns into a horse with a head at one end, a tail at the other, and legs at the four corners, while another fertilized egg cell, which looks pretty much like the first, turns into a clam.

There is an important distinction among theoretical structures in biology which Keller’s concept of epistemological cultures does not cover. Before even asking what counts as a sufficient explanation or understanding of some phenomenon, we need to decide what work a theoretical apparatus is supposed to do. Sometimes theoretical structures are nothing but calculating devices constructed from a complete and unproblematical knowledge of all the underlying mechanical details. The purpose of such a calculating device is to predict how differences in inputs into the system will be reflected in the output.

The classic example in biology is theoretical population and evolutionary genetics. All the relevant elementary processes are already known. These include all the mechanisms of inheritance, the phenomena of mutation, of migration, of the effect of limited population size, and of the operation of natural selection through differential survivorship and fertility. Theoretical evolutionary genetics assembles all these phenomena into a formal mathematical structure that predicts changes in the genetic composition of populations and species over time as a function of the numerical values of these elementary processes.

In contrast, sometimes theories are meant to help us “understand” a process whose outcome has been observed but whose dynamical details are not known from experiment or observation. The theory provides a formal structure into which, it is supposed, the actual mechanical details will fit if we ever get to know them. In the most extreme case the theory is without any direct reference to any underlying material phenomena. So there are theories of embryonic development that are nothing but networks of logical switches, formal components that act to increase or decrease the “output” (of unspecified physical nature) of other components. Even when some details of the phenomena are known from experiment, a model based on an incomplete knowledge leads to frustration. Keller describes a model of development that took into account interactions among five genes known to be among the critical elements in the normal formation of body segments in fruit flies. Even though only these five genes were considered, the mathematical model required 136 equations involving about 50 parameters that had never been measured experimentally.

In view of this absence of information, the investigators asked if there was any set of values of the parameters in a biologically reasonable range that would produce a stable development result resembling the observed pattern of body segments in flies. The answer was no. But Keller’s dissatisfaction transcends that failure. Even if the model had succeeded in mimicking the observed pattern of development, it was “cumbersome, messy, and, by itself effectively opaque to any kind of intuition (mathematical or otherwise).” That is, the work to be done by a model of development is not a computational one like those in evolutionary genetics or in the very cumbersome and messy models used for weather forecasting, but to help our “understanding” of the phenomenon. But this raises a very deep issue.

As Keller points out, models in physical science have traditionally aimed for an elegance and simplicity that would allow our limited mental powers to “understand” some aspect of nature. If models in biology are to advance our understanding, then they too must be simple and elegant. Keller devotes a chapter to two famous past attempts to construct a mathematical biology that is simple and elegant yet at the same time captures the essence of biological phenomena. The more ambitious was the founding of a school of mathematical biophysics by Nicolas Rashevsky in the late 1930s, with its own scientific journal and a formal graduate-degree program at the University of Chicago.

All aspects of biology were to be included in the intellectual program, but there was particular emphasis on cell biology, development, and the nervous system. The approach of the Rashevsky school was to make simplified physical models that were supposed to capture the essence of a biological phenomenon and then describe models in mathematical terms. What Rashevsky and his school failed to take into account was the conviction of biologists that real organisms were complex systems whose actual behavior would be lost in idealizations. The work of the school was regarded as irrelevant to biology and was effectively terminated in the late 1960s, leaving no lasting trace.3

  1. 1

    William Shockley, Walter Brattain, and John Bardeen in 1956.

  2. 2

    Charles Huggins in 1966.

  3. 3

    The reader ought to be warned that I am not a disinterested observer. As dean responsible for the basic biological sciences at Chicago it was I who refused to appoint Rashevsky’s hand-picked successor and who attempted to reorient the work of the group along more conventional lines.

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