TITLE: Mere Skills
AUTHOR: Eugene Wallingford
DATE: July 07, 2011 12:58 PM
DESC: 
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BODY:
Last week I ran into this quote
<A HREF="http://quotationsbook.com/quote/32471/#axzz1O3nynqTU">
   attributed to Einstein</A>:

<BLOCKQUOTE><EM>
The formulation of a problem is often more essential than
its solution, which may be merely a matter of mathematical
or experimental skill.
</EM></BLOCKQUOTE>

I don't like "merely" here, because it diminishes the value
of "mere" mathematical or experimental skills.  I understand
why problem formulation is so important, usually more
important than problem solution.  For one thing, it is hard
to solve a problem you have not formulated yet.  For another,
problem formulation is often more difficult than solving the
problem.  As a result, as skills go, problem formulation is
the scarcer resource.

But problem-solving skill matters.  Most of us need to be
able to
<A HREF="http://www.cs.uni.edu/~wallingf/blog/archives/monthly/2010-12.html#e2010-12-01T15_45_40.htm">
   execute</A>,
too.  And, at some point,
<A HREF="http://www.cs.uni.edu/~wallingf/blog/archives/monthly/2010-04.html#e2010-04-22T20_36_56.htm">
   you gotta know stuff</A>
-- and be able to do the little things.

Maybe if you are Einstein, you can get by without the skills
you need merely to solve the problem.  If you can discover
ideas like relativity, you can probably find grad students
to turn the crank.  But the rest of us usually need those
skills.

(I'm even skeptical about Einstein.  I've heard stories,
perhaps apocryphal, perhaps exaggerated, about Einstein's
lack of mathematical skills.  But even if there is a grain of
truth in the stories, I suspect that it is all relative.
There is a big difference between the math skills one needs
to work out the theory of relativity and the math skills one
needs to do the kind of work most scientists do day-to-day.)

One important reminder we get from the quote is that there
are two skills, problem formulation and problem solution.
They are different.  We should learn how to do both.  They
require different kinds of preparation.  One can learn many
problem-solving skills through
<A HREF="http://www.cs.uni.edu/~wallingf/blog/archives/monthly/2004-07.html#e2004-07-12T18_58_55.htm">
   practice, practice, practice</A>:
repetition trains our minds.  Problem formulation skills
generally require a more reflection and thinking <I>about</I>.
Lots of experience helps, of course, but it's harder to get
enough practice to learn how to tame problems through only
repetition.

For most of us and most domains, mastering problem-solving
skills is a useful, if not necessary, precursor to developing
problem formulation skills.  While developing our problem-solving
skills, we get a lot of repetition with the syntax of semantics
of the domain.  This volume of experience prepares our brain
to work in the domain.  It also give our brains -- engines
capable of remarkable
<A HREF="http://www.cs.uni.edu/~wallingf/blog/archives/monthly/2007-04.html#e2007-04-05T20_57_33.htm">
   feats of association</A>
-- begins to make connections, despite our own inattention to
the bigger picture.  Our brains are doing a lot of work while
we are "just" solving problems.

Then we need to take that raw material and work on learning how
to formulate problems, deliberately.  In that, I agree with
Einstein.
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