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On Agent-based Models: Email Exchanges with
Professor John Holland
03/17/2007
Dear professor,
Thank you very much for the nice comments on my paper. I was very excited
when I was writing it and when I just got it done. But later when I thought
about it again, I started to have a mixed feeling. This mixed feeling is not
just about the model I built but also about the modeling approach in general.
How could I validate my model? Did not I interpret the model results in a overly stretched way? Somehow I feel I got those nice
insights from the model only because I had them in my mind and I then chose
the factors (only part of the system) and a representation (one of many
possible representations of the same system) and constructed the model in a
way that could prove those subjective points of mine.
In general, how do we know that a model really captures the key mechanism in
this system (comparing the generated patterns with observed patterns in the
real world does not tell anything as we know that we could produce the same
pattern by making up totally different mechanisms)? In addition there are so
many possible representations of the same system in models, which could all
generate the same patterns and people usually only model part of the system
that favors their points.
For instance, I am sure somebody who has totally different views than those
of mine, could build a model that also gives rise to cities/towns and proves
his points as well. Actually the readings for Rick's class were all about
this matter and came right after I started to think about these issues. Some
people have expressed their deep doubts on modeling in their papers. These
are the questions they asked:
Are we pretending to do what can not be done?
Are we trying to predict the unpredictable?
After all, what good are models?
Qing
03/18/2007
Dear Qing,
Model validation is, of course, an important
question: Are the mechanisms postulated the ones that are really
operating? Even Maxwell's equations require validation, and the
mechanisms postulated change over time. We go from fields, to photons
exchanging energy, to quantum interactions, and so on. The
interpretation determines what we consider as validation.
Here we're back to the purpose of the
model. If it is "data-driven" then prediction is the
key. That has been the strength of Newton, Maxwell, and Einstein in the
equation-based models they propose. However, in some cases, it is
extremely difficult to think of ANY set of mechanisms that will produce the
desired outcome. That was the strength of von Neumann's mechanistic
model of self-reproduction -- no one had been able to exhibit a mechanistic
model before that.
This is what we called an existence proof model
in class. I think your model falls in this category -- choosing
relevant factors is part of the "art form" (and it depends upon
your subjective insights). As with von N., you had an objective and you
showed it could be implemented with certain mechanisms.
If there is a second set of mechanisms that will
yield the same result, then the objective is to find "real world"
experiments that will distinguish between the two models. That's the
difference between the work of Einstein (theorist) and the work of Eddington
(experimenter). Good models, like good theories, tell us where to make
new observations in the real world. Even cas have
repeating, controllable patterns. The object of theory is to help us to
find them.
Now, what do you think about THIS tirade?
John
03/18/2007
Dear professor,
THIS tirade is well received. I am still not very sure about "The
interpretation determines what we consider as validation." Do you think
every model should be validated in one way or another? Do you think
generating patterns that match the real world is enough for validating my
model?
Probably science, not just modeling, itself can not be totally objective.
Just came across an article for Rachel's class. Here are some quotes from it:
"Science is more art than truth, created by people, who operate, like
all of us, in a conscious and unconscious universe. Guided by "inner
voices", researchers are inspired to discovery."
"Scientists are more like artists, assembling and mixing the colors of
an awesome, complex and dynamic story into a coherent picture. Data maybe the
paint on their pallet that creates a picture, but, inevitably, what we see is
the artists' rendition. Decisions are made at multiple steps along the way:
on relevant facts; on the boundaries between what we know and don't know; and
on what we care about."
"Data are not just data. Information is always accompanied by
interpretation."
Remember what James said about perceptions: perceptions are never pure sensations
but more of interpretations based on the past experiences.
So I guess it is OK to have subjectivity in models now that it is inevitable.
Still I think we need to be careful about models: some times people tend to
take it for granted without any validation. Even if it is an exploratory
model, there should be a certain level of rigor in them.
Qing
03/19/2007
Dear Qing,
This is a good dialogue!
I try to think of the model as a kind of axiom
system: First, I try to make the basis of the model (the axioms) as
clear as possible. I actually try to write an explicit list of
assumptions. Then I try to make sure that the construction adheres to
just these assumptions and no others. This is hard, but possible.
The whole purpose of setting up axioms is to move
all questions of interpretation to them. From that point onward, the
rules of deduction, or the program, are a "mechanical" working out
of consequences, with no interpretation involved in that part (unlike
arguments of rhetoric and persuasion). That is what, in my mind,
separates the scientific method from other methods (say, philosophical
argument).
In short, when the "axiomatic" approach
can be followed, the art and interpretative cleverness are concentrated in
selecting the axioms. Then consequences are "proved" without
resort to interpretation.
Note, however, that intuition usually guides us
in what consequences we would LIKE to show. But you cannot
"cheat" the deductive method -- the consequences may, or may not,
follow from the axioms chosen.
Do you agree?
John
P.S. The quotes you give, in my opinion, mix up these two aspects of
science. There is certainly all sorts of interpretation and intuition
in setting up the axioms (say, Maxwell's equation), but the deductive
consequences are then fixed (and no amount of social opinion can change
them).
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