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We can develop a model at different levels of complexity. We can decide that
we want to reproduce behavior at the 17th decimal point of precision, or
we can decide that we are comfortable if we only get the direction of the
behavior correct. The decision about the level of precision we are
trying to capture
with our model is a form of abstracting the problem. When we abstract a
problem, we attempt to decide what is relevant and what is irrelevant.
Typically, when we create a model,
we start with the simplest, first order, behavior. The goal is to try
to get this right without worrying
if the time and space scales are correct. This is because if we
can not get the first order behavior right, then it is a waste of time
to try to get the spatial and temporal scales correct. Thus, at
different levels of model building, different levels of detail are relevant.
Another reason for starting with a first order approximation is that
sometimes that is
all you need. If, when you press deeper into the problem, the first
order model works, and it continues to work for each successive level
of complexity, then we have stumbled on a ``main idea''.
Even if we are not so lucky, as we try to characterize the
abstractions of multiple instances of our problem, we
may begin to see common denominators. This common denominator is a ``main
idea'', and is the scaffolding around which we can build very complex
descriptions of what we observe.
For an example of this latter method of uncovering ``main ideas'',
consider the problem from cardiology of reentrant cardiac arrhythmias.
In normal circumstances, the impulse that
initiates cardiac contraction forms as a continuous wave that propagates
away from the sinus node. Any continuous wavefront in the heart cannot
become reentrant simply because it will collide with and extinguish
itself. On the other hand, if a wave breaks and becomes
discontinuous1.4, then it is possible for the residual
wave fragments to evolve into
a spiral wave1.5.
Reentrant arrhythmias, rapid uncontrollable
reexcitations of the heart, are initiated
from wave fragments or discontinuous waves.
Therefore, forming a spiral front requires that a front arise
in a region with asymmetric excitability where propagation succeeds
in some directions and is blocked (or fails) in other directions -
1.6. Thus, all reentrant arrhythmias
can be understood as resulting from wave formation in a region
with a spatial asymmetry of
cellular excitability 1.7. If you can identify
the source of the asymmetry, then perhaps its possible to correct it.
Since this one
concept, asymmetric waves form as a result of propagation in a
region with a spatial asymmetry in excitability, enables us
to have a general idea about an entire class of
phenomena, we will call it a ``main idea''.
Modeling is thus an
essential step toward identifying main ideas, the recurring themes that we see
as we examine different, but related, systems.
We will see this when we explore excitable cells in cardiac tissue and
transcription switches1.8 in the DNA of small organisms.
What follows are some of the main
ideas we have developed about building and then testing models. We
begin with the
mathematics and physics required for model building end with
statistics for model evaluation. Along the way, we'll introduce some
of the software issues we have faced as we constructed tools that
promoted our development of main ideas.
Next: How to create a
Up: Why Create Models?
Previous: Implicit Models
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Frank Starmer
2004-05-19