CULTURE AND RESEARCH INFRASTRUCTURE 363
role in a biologist’s education. Traditionally, mathematics (apart from statistics) is not particularly
important to biology education; indeed many biologists have entered the field because they wish to
pursue science that does not involve a great deal of math. Although there is a common core of knowl-
edge among most biologists, there is an enormous amount of highly specialized knowledge that is not
tightly integrated.
A second issue, often encountered in conversion programs, is the difficulty of expanding one’s
horizons to choose intellectual approaches or tools appropriate to the nature of the problem. Disciplin-
ary training in any field entails exposure to the tools and approaches of that field, which may not be the
best techniques for addressing problems in another field. Thus, successful researchers and practitio-
ners at the BioComp interface must be willing to approach problems with a wide array of methodolo-
gies and problem-solving techniques. Computer scientists often may be specialists in some specific
methodology, but biological research often requires the coordination of multiple approaches. Con-
versely, biological labs or groups that address a wide range of questions may be more hospitable to
computational researchers, because they may provide more opportunities in which computational
expertise is relevant.
10.3.1.3 The Role of Theory
Theory plays a very different role and has a very different status in the two fields. For computer
scientists, theoretical computer science is essentially mathematics, with all of the associated rigor, cer-
tainty, and difficulties. Of particular interest in theoretical computer science is the topic of algorithmic
complexity. The most important practical results from algorithmic complexity indicate the scaling rela-
tionships between how long it takes to solve a problem and the size of the problem when its solution is
based on a specific algorithm. Thus, algorithm A might solve a problem in a time of order N^2 , which
means that a problem that is 3 times as large would take 3^2 = 9 times as long to solve, whereas a faster
algorithm B might solve the same problem in time of order N log N (that is, O(N log N)), which means
that a problem 3 times as large would take 3 log 3 = 3.29 times as long to solve. (A specific example is
that when asked to write a program to sort a list of numbers in ascending order, one of the most
common programs written by novice programmers involves an O(N^2 ) algorithm. It takes a somewhat
greater degree of algorithmic sophistication to write a program that exhibits O(N log N) behavior—
which can be proven to the best that is possible.)
Such results are important to algorithm design, and all computer programs embody algorithms.
Depending on the functional relationship between run time and problem size, a given program that
works well on a small set of test data may—or may not—work well (i.e., run in a reasonable time) for a
larger set of real data. Theoretical computer science thus imposes constraints on real programs that
software developers ignore at their own peril.
Computer scientists and mathematicians derive satisfaction and pleasure from elegance of reason-
ing, logic, and structure. Being able to explain a phenomenon or account for a dynamical behavior with
a simple model is highly valued. The reason for this penchant is clear: the simpler the model, the more
likely it is that the tools of analysis can be used to dissect and understand the model fully.
This sometimes means that a tendency to oversimplify overwhelms the need for preserving realistic
features, to the dissatisfaction or derision of biologists. Computer scientists, of course, may well per-
ceive a biologist’s dissatisfaction as a lack of analytical or theoretical sophistication and an unwilling-
ness to be rigorous, and often fail to recognize the complexity inherent in biological systems. In other
cases, the love of elegance leads to fixation with elegant, but irrelevant, models far beyond their value
outside the field, simply because the inherent model is clean and simple. In still other cases, the lack of
training of computer scientists in eliciting from users the precise nature of their problems has led
computer scientists to develop good solutions to problems that are not interesting to most biologists or
relevant to real biological phenomena.
By contrast, many—perhaps most—biologists today have a deep skepticism about theory and