4
1 Introduction
required to overcome these problems, even a highly sophisticated model generally
represents only a rough approximation to the actual system.
For these reasons, fully validating a mathematical model is not possible (Oreskes
et al. 1994). Regardless of the number of tests a given model may pass, new
experimental results may someday contradict a theoretical prediction. This is true
in physics as well as biology. Even quantum mechanics and Einstein’s theory of
relativity face serious issues at large and very small scales, respectively.
On the other hand, a good model can be used to help understand complex behavior and can provide reasonably accurate statistical trends, as long as limitations are
acknowledged. Models also can provide information (e.g., stress in the heart wall)
that cannot be measured directly.
Consequently, it is helpful to keep in mind the following quote attributed to the
statistician George E.P. Box (Box and Draper 1987):
Essentially, all models are wrong, but some are useful.
1.3.2 Using Mathematical Models to Predict Future Behavior
Can predictions of a mathematical model for a biological system be trusted?
Unfortunately, the answer is no. 4 No matter how realistic a model may be, and no
matter how thoroughly it has been tested experimentally, model predictions always
should be treated with caution. This is the case even for relatively simple biological
systems.
A useful analogy is numerical weather prediction. Interestingly, mathematics
entered the fields of biology and meteorology in major ways almost simultaneously.
While D’Arcy Thomson was writing his famous treatise on biological form about
100 years ago, Lewis Fry Richardson was busy developing numerical methods based
on the fundamental equations of thermodynamics and physics to predict the weather
(Richardson 1922).
Although biology and meteorology may seem quite different, there are similarities. For example, both involve complex physical processes that depend on a
large number of parameters, and both involve unknown initial conditions. A crucial
difference is that organisms must adapt to changing conditions as they try to survive,
while survival apparently is not a top priority for the atmosphere. Robust adaptation
requires feedback loops and backup systems that add enormous complexity to the
design of an organism. Thus, predicting the behavior of a biological system is
inherently less reliable than predicting the weather. On the other hand, advances in
computer technology have fostered dramatic improvements in weather forecasting
the last couple of decades, so maybe there is hope for the future.
4 Just my opinion, based on decades of experience with modeling.
1 Introduction
required to overcome these problems, even a highly sophisticated model generally
represents only a rough approximation to the actual system.
For these reasons, fully validating a mathematical model is not possible (Oreskes
et al. 1994). Regardless of the number of tests a given model may pass, new
experimental results may someday contradict a theoretical prediction. This is true
in physics as well as biology. Even quantum mechanics and Einstein’s theory of
relativity face serious issues at large and very small scales, respectively.
On the other hand, a good model can be used to help understand complex behavior and can provide reasonably accurate statistical trends, as long as limitations are
acknowledged. Models also can provide information (e.g., stress in the heart wall)
that cannot be measured directly.
Consequently, it is helpful to keep in mind the following quote attributed to the
statistician George E.P. Box (Box and Draper 1987):
Essentially, all models are wrong, but some are useful.
1.3.2 Using Mathematical Models to Predict Future Behavior
Can predictions of a mathematical model for a biological system be trusted?
Unfortunately, the answer is no. 4 No matter how realistic a model may be, and no
matter how thoroughly it has been tested experimentally, model predictions always
should be treated with caution. This is the case even for relatively simple biological
systems.
A useful analogy is numerical weather prediction. Interestingly, mathematics
entered the fields of biology and meteorology in major ways almost simultaneously.
While D’Arcy Thomson was writing his famous treatise on biological form about
100 years ago, Lewis Fry Richardson was busy developing numerical methods based
on the fundamental equations of thermodynamics and physics to predict the weather
(Richardson 1922).
Although biology and meteorology may seem quite different, there are similarities. For example, both involve complex physical processes that depend on a
large number of parameters, and both involve unknown initial conditions. A crucial
difference is that organisms must adapt to changing conditions as they try to survive,
while survival apparently is not a top priority for the atmosphere. Robust adaptation
requires feedback loops and backup systems that add enormous complexity to the
design of an organism. Thus, predicting the behavior of a biological system is
inherently less reliable than predicting the weather. On the other hand, advances in
computer technology have fostered dramatic improvements in weather forecasting
the last couple of decades, so maybe there is hope for the future.
4 Just my opinion, based on decades of experience with modeling.