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How to do Theory
as an Amateur
George
E. Hrabovsky, President MAST
The following was presented at
the Poster Session (Fig. 1) of the 2006 meeting
of the Society for Amateur Scientists. Editor.
What Does A
Theorist Do?
A theorist attempts to find patterns
in data, then assuming such a pattern to be real, creates
mathematical or computational models to predict outcomes
that can be tested experimentally or observationally.
How Does a Theorist Do It?
Through the use of a deep scientific
intuition coupled with strong experience in applying
mathematics to scientific problems, the theorist creates
or uses existing mathematical structures that correspond
to the scientific problem at hand.
The process is something like this:
1. Ask a question of the data.
2. Find a pattern that seems to answer
the question.
3. Does this pattern agree with what
we already seem to understand? If not, why not? Do you
think it is valid anyway? If not, start again.
4. Assume the pattern to be correct.
Choose proper mathematics to build a simple model.
5. Predict specific outcomes of the
model.
What
Do You Need To Do Theory?
Develop scientific intuition by working
lots of problems from textbooks that have answers.
Learn physics and chemistry, if nothing
else. Work your way all the way through both the Feynman
Lectures on Physics and Linus Pauling's General Chemistry.
Then work your way through books on mechanics, electricity
& magnetism, thermal physics, quantum mechanics,
and physical chemistry.
Develop mathematical experience by
working lots of math problems from textbooks that have
answers.
Learn calculus, linear algebra, differential
equations, abstract algebra, complex functions, combinatorics,
and probability and statistics.
You are looking at nine years of formal
study!
What Sorts of Theoretical Contributions Can
An Amateur Theorist Make?
Make a list of open problems that
are of interest to you. Ask yourself, in all honesty,
where you are right now. Learn what you can
about each open problem of interest. Try to fill in
the blanks between where you are and each open problem.
Begin working towards one or may of them.
This allows you to make your study
incrementally, while gaining deep insights into what
you are studying and into the problems, too.
Created
by Mathematica
(September 14, 2006)
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