The
Big Picture
What
have we been doing? Computer simulation is
a method of performing
experiments without costly hardware. To
be in this business, you need to become a very good experimentalist. Always remember that your experiments are
performed in virtual worlds where the physical laws may be close to
those of
the real world, but never really match.
You’ve got to use your full training as an engineer to detect
the
differences in physical laws and understand their impact.
Never trust the results of a computer
simulation until you (or someone you know and trust) have thoroughly
tested the
relationship between the virtual and real worlds.
If
you haven’t learned the skills
already, spend time learning how to construct controlled experiments. One major advantage of computer simulations
is that you have far more opportunities for highly controlled
experiments than
you do in the real world. During this
process you will be applying basic scientific method:
1.
Make careful observations
of a system;
2.
Make a hypothesis to
explain those observations;
3.
Design a test (or tests)
for the hypothesis;
4.
Perform the test;
5.
Either confirm your
hypothesis, or revise it (loop back to 2).
When
designing a test, limit the
changes you introduce into the system.
In computer simulation, there is almost never an excuse for
introducing
more than one change at a time.
While
we’re talking about
science, I want to remind you of a broader definition. Science is a
discipline that we have built over millennia, to help us see what is
really
there, not what we want to see. When
properly used Computer
Simulation is a tool that can help us see what is really there. However, be cautious of your fundamental
nature. Do not except the results of a
computer simulation (or any other observation) because they are what
you want
to see. Use all of your experience and
training to be certain that the results adequately reflect reality.
1.
Determine appropriate
mathematical model
2.
Classification of partial
differential equation
3.
Transformation of
mathematical model
4.
Select grid pattern
5.
Formation of finite
difference equations
6.
Solution algorithm
7. Perform auxiliary calculations
In
theory, this is the end of my career as a college teacher. Since many
of you will be considering this as a profession, I'd like to pass on
some
thoughts. One of the flaws in the
university system is that it is too inbred. Countless generations
pass of
professors training students who immediately become professors. Before entering college teaching, go out and
experience
the broader professional world. Come
back to the university and share that experience with your students. However, if you intend to come back, remember
the adage “publish or perish.” You
should have a goal of two papers a year in refereed journals during
your time
away from the university.
You
should think about your motivation for becoming a university
professor. If you enjoyed your research
and see the university as a way to continue doing such research, there
are
better places to do research. Government
laboratories and good industry research centers will give you far more
opportunity to focus on research than you will have as a university
professor. As a professor you are pulled
in too many directions and don’t get the opportunity to become one with
your
research project. Another consideration
is that university professors normally don’t do research, they manage
research. This is an easy way to get low
level
management experience, but if you want to head down this path, you will
normally find opportunities to manage better quality research teams
elsewhere.
You
should also understand the intensity of the profession before starting
down the road. I have worked as staff
and management in government labs, worked closely with industry
researchers,
and come up through the tenure track process as a university professor. I can tell you that the work environment at a
university is far more brutal than that of the other two options. The rewards associated with teaching, and
running your own small scale research operation come at a heavy price
to your
broader life.
One
other aspect of the profession deserves comment. Much
is made of “academic freedom.” However, my
observation has been that if you
behave responsibly towards your students and colleagues, your practical
level
of freedom is not significantly higher than found in other scientific
and
engineering professions. Your freedom is
restricted by the need for projects with a useful learning content, and
by the
natural limits associated with sleep deprivation.
I’d
like to close with some observations related to Mahaffy’s second law
of human nature:
There is no obvious
correlation between intelligence and wisdom.
Pursue
wisdom as
you move through life, but don’t mistake caution for wisdom. I commented on several occasions that you
develop a successful record in research by going with the odds. However, you need to keep track of the
odds. Something that on first glance
appears to be the safest approach, may when you consider it carefully
just be
headed for a dead end. There are times
when approaches that are popularly regarded as foolhardy have the best
chance
of success. There are times when you
need to do something foolhardy to preserve your sanity.
Learn to sort this all out and you are well
on the path to wisdom.