Re: serializing the facts

[Leigh Palmer <palmer@SFU.CA>]

At 7:48 PM -0700 8/19/00, John Denker wrote:

> Science is not serial.  It is a very high-dimensional tangled latticework
> of facts.  There is no natural ordering of the facts.

I think this view is the one that we want to get across to our students;
it is certainly my own view. Science is not serial. The one thing John
has omitted here is that this tangled latticework is *self consistent*,
and that this consistency is demonstrable *mathematically*. This view of
Nature permits us to sort the nodes of our latticework to find the few
that are not quite consistent with the others, and we tend to prune the
latticework (discard new nodes inconsistent with the greater structure)
to preserve this consistency. This latter process is, of course, a
cognitive error. It precludes revolutionary corrections strictly on the
basis of seniority: a particular node must be preserved solely because
it is old and venerable. Sometimes major pruning must be done to correct
previous error. Sometimes the latticework can be felt to be incomplete,
like a triangulated polyhedron of sticks with some missing elements; the
polyhedron must be rigid; our description of Nature must be unique to be
fully satisfying. This lack of rigidity can be corrected by parametric
prescription (the natural physical constants) and/or by demonstration
that other, previously unrecognized connections exist (the unification
of gravity and the other forces, for example).

The serialization is an artificial one, largely imposed by physics
teachers who must arrange to instruct their students according to a
serial schedule which, conventionally, follows an order that is
perceived to be natural in its increasing level of mathematical
sophistication. That is not an intrinsic property of the latticework;
it is largely cultural, arising as it does from the Gibbsian (as
opposed to, for example, the Cliffordian) farmalistic paradigm*.

I guess you can tell that I have to work on a particularly scary apple
tree today (and a couple of rhododendrons). Still, the metaphor is good,
except I really don't like the physicists' locution, "self consistent",
that I have used above. While it is conventional and well understood by
all of us, it is redundant and thus inelegant. Left to my own preference
I would have used the simpler term "consistent".

Leigh

* Don't worry if that makes no sense; it's a whole 'nother discussion.