From: "Koichiro Matsuno" <CXQ02365@nifty.com>
To: <fis@listas.unizar.es>
Folks,
John Collier's distinction between "restrict and enable" in the
form of
constraints reminds me once again of the remarks on boundary conditions
made by Michael Polanyi back in the sixties. This time, it came through
Goedel's incompleteness theorem stating that both the decidability (either
true or false, and not in between) and the consistency of the statements
made in an arbitrary axiomatic system cannot coexist. There should be a
statement or a theorem which could be right but not proved right within the
given system. A negative aspect of the incompleteness theorem is
restrictive as literally respecting the axiomatic manipulation or
algorithm, while its positive aspect is found in enabling as admitting a
possibility that such an algorithmic computation cannot stop. An explicitly
positive form of the enabling aspect can be found in the occurrence of an
inductive judgment.
Suppose we ask a kid of the second or third grade in elementary school
to find out an odd number made out of the sum of three even numbers only
through an arithmetic computation. The kid may quite possibly find that
such a computation cannot easily stop though he cannot prove it. However,
once the kid learns algebraic computation, he can quite probably prove that
such an arithmetic computation does not stop, by writing a few lines of
algebraic operations. What makes the transition from arithmetic to
algebraic computation possible is the experience the kid has accumulated so
far, and by no means latent in arithmetic computation alone. Of course,
mathematicians appreciate the role of inductive judgment explicitly like
every school kid practices it implicitly.
What is more, even atoms and molecules directly participate in
inductive processes. When two hydrogen atoms form a hydrogen molecule in an
empirical arena, no computation for getting a hydrogen molecule can stop
insofar as one sticks to the axiomatic formalism preserving the hydrogen
atom as an nonnegotiable element. This has been my entry to approaching
Jerry Chandler's chemical logic.
The term information is too loaded. It would be hard to distinguish its
restrictive usage from the enabling counterpart, every time. Information
may not be a useful analytical tool, though quite powerful in the
bookkeeping. Haste may make waste.
Cheers,
Koichiro
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Received on Wed Feb 7 11:04:49 2007
