where A, α, and β are constants and L is the input of labor and K the input of capital
services, in a process that produces say, widgets at rate Q. But to a chemist, this is
the law of mass action at work. Q is the production rate of some product made from
the reaction of L and K, two chemicals that combine to produce the product. The
constants α and β reflect temperature or perhaps pressure effects on the reaction
rate. Or if you were an epidemiologist, you would say that Q is the rate at which
people are getting sick, that L is the size of the healthy population, K is the size of
the sick population, and A is the contact coefficient. If you are a metapopulation
theorist in ecology, L would be the number of patches occupied by an inferior
species, K the number of superior species, A is the colonization rate of the superior
species, and Q is the rate of conversion of the inferior patches to superior ones.
Some ecologists use a variant analogy to the economic production function
above. They say that Q, an insect birth rate for example, equals a maximum growth
rate for the insect (A) times a series of factors each of whose value varies from 0 to
1, where 1 is the factor value associated with the maximum possible growth rate.
These are usually graphically based, experimentally derived factors that naturally
show diminishing returns. Examples of such factors are temperature and humidity.
Under the exact condition of optimal temperature for the growth rate for this insect,
the temperature factor would be 1.0.
In its various uses of the equation described above, the factors are assumed to be
completely independent. Capital and labor can be substituted for one another
without concern about the availability of the other. But actually, it clearly takes
labor to make more capital to substitute for the displaced labor. So the factors are
not actually independent although they are commonly assumed to be. Neither are
temperature and humidity independent, despite the assumptions in the insect model
for example. For a single firm, the independent factor assumption is not a terribly
bad one, but to make this assumption for the economy as a whole is absurd. Such
assumptions are usually a matter of expediency of model building. Be careful how
you use them.
Analogies can also help you spot anomalies. Lightman and Gingerich [5] point
to the “retrorecognition” phenomenon, where anomalies in one theory are only
recognized when they are explained later by a superseding theory. For a variety of
reasons, we scientists are essentially blind to those facts not explained by the
dominant theory. By the use of appropriate analogy, de rigor for the nineteenth
century likes of Lord Kelvin and J. C. Maxwell, we should be able to turn up
anomalies in our current explanations of the way things work. A rule of thumb for
anomaly-finding is to push your model to its reasonable limits.
Our discussion on the use of analogy is intended to raise your optimism about the
idea of dynamic modeling. But not everyone is optimistic. We might be able to
accurately simulate some very complex biological system but can we actually learn
more about these systems from such models? Can we learn to make wiser decisions
from our modeling exercises? We think the answer is “yes” but our view has its
dissenters. (For an excellent summary of this argument, see Denning [6].) The
counter argument is based on the idea the human problem solving is very contextdependent, while most computer models are not. This sounds to us more like a
1.3 Analogies, Anomalies, and Reality
9
services, in a process that produces say, widgets at rate Q. But to a chemist, this is
the law of mass action at work. Q is the production rate of some product made from
the reaction of L and K, two chemicals that combine to produce the product. The
constants α and β reflect temperature or perhaps pressure effects on the reaction
rate. Or if you were an epidemiologist, you would say that Q is the rate at which
people are getting sick, that L is the size of the healthy population, K is the size of
the sick population, and A is the contact coefficient. If you are a metapopulation
theorist in ecology, L would be the number of patches occupied by an inferior
species, K the number of superior species, A is the colonization rate of the superior
species, and Q is the rate of conversion of the inferior patches to superior ones.
Some ecologists use a variant analogy to the economic production function
above. They say that Q, an insect birth rate for example, equals a maximum growth
rate for the insect (A) times a series of factors each of whose value varies from 0 to
1, where 1 is the factor value associated with the maximum possible growth rate.
These are usually graphically based, experimentally derived factors that naturally
show diminishing returns. Examples of such factors are temperature and humidity.
Under the exact condition of optimal temperature for the growth rate for this insect,
the temperature factor would be 1.0.
In its various uses of the equation described above, the factors are assumed to be
completely independent. Capital and labor can be substituted for one another
without concern about the availability of the other. But actually, it clearly takes
labor to make more capital to substitute for the displaced labor. So the factors are
not actually independent although they are commonly assumed to be. Neither are
temperature and humidity independent, despite the assumptions in the insect model
for example. For a single firm, the independent factor assumption is not a terribly
bad one, but to make this assumption for the economy as a whole is absurd. Such
assumptions are usually a matter of expediency of model building. Be careful how
you use them.
Analogies can also help you spot anomalies. Lightman and Gingerich [5] point
to the “retrorecognition” phenomenon, where anomalies in one theory are only
recognized when they are explained later by a superseding theory. For a variety of
reasons, we scientists are essentially blind to those facts not explained by the
dominant theory. By the use of appropriate analogy, de rigor for the nineteenth
century likes of Lord Kelvin and J. C. Maxwell, we should be able to turn up
anomalies in our current explanations of the way things work. A rule of thumb for
anomaly-finding is to push your model to its reasonable limits.
Our discussion on the use of analogy is intended to raise your optimism about the
idea of dynamic modeling. But not everyone is optimistic. We might be able to
accurately simulate some very complex biological system but can we actually learn
more about these systems from such models? Can we learn to make wiser decisions
from our modeling exercises? We think the answer is “yes” but our view has its
dissenters. (For an excellent summary of this argument, see Denning [6].) The
counter argument is based on the idea the human problem solving is very contextdependent, while most computer models are not. This sounds to us more like a
1.3 Analogies, Anomalies, and Reality
9