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Re: serializing the facts



At 08:28 AM 8/21/00 -0500, Glenn A. Carlson wrote, regarding the
relationship of scientific facts:

a better word than "serial" is "hierarchical."

The notion that facts are arranged hierarchically is a common
misconception. Feynman addressed this point. I believe it was in _The
Character of Physical Law_ but I can't quote chapter and verse; my copy of
the book seems to have escaped.

Feynman used the following example: In high school, Euclidean geometry was
deduced, hierarchically, starting from a few postulates. But there is
nothing particularly fundamental about the conventional set of
postulates. You could take some of the Euclidean results and choose them
as your postulates, and deduce your way back to the Euclidean postulates.

Just because the topic was presented to you in hierarchical fashion doesn't
mean it is intrinsically hierarchical!

Another example: In group theory, one postulates a left inverse and a left
identity; one then proves that there must be a right inverse and a right
identity. It should be obvious by symmetry that one could have done it the
other way around.

Most of science is non-hierarchical. When we say F=ma, that does not mean
that F is more fundamental or less fundamental than m or a.