Re: definition of parsimony

[Vaughan Pratt <pratt@cs.stanford.edu>]

Without going into its relevance to category theory, I would put the SEP
article on parsimony that Axel Rossberg pointed to alongside the
Wikipedia article on spice (the vegetative substance described at
http://en.wikipedia.org/wiki/Spice, not the rock group).

On the one hand spices, as the latter article points out, "have been
prominent in human history virtually since their inception.  Spices were
among the most valuable items of trade in the ancient and medieval world."

On the other hand what restaurant serves only spices on its menu?
Cuisine is a complex art for which spices are merely a valuable adjunct
that can make a big difference in a catalytic kind of way.

Parsimony is the catalytic converter of mathematics.  It is not the main
engine, but can be helpful in cleaning up the noxious byproducts of
inefficient thinking.

Too much however can be a bad thing: overdoing parsimony undermines its
efficacy for mathematics while adding to the cost, just as overdoing
spices does for food and platinum for catalytic converters.

Rossberg's suggestion that modern physics describes only the wave
function of the universe illustrates this nicely.  If this were really
true, physics would not be a degree major, let alone a career option,
but merely a module of a course in some other major.

In any event it is contradicted by the standard model Rossberg refers to
in the next paragraph.  Explaining the standard model by a suitably
parsimonious Theory of Everything is a nice thought, like an antigravity
belt when you're stuck in traffic, but the standard model is a complex
and evolving account of how the huge zoo of particles fits together.
"Parsimony" in any account of the standard model today is only
accomplished by leaving things out.  The Particle Physics Booklet
(formerly the Particle Properties Data Booklet) is some 200 pages of
densely packed information about uncountably many particles parametrized
by nearly a score of fundamental physical constants each determined by
careful measurement.  (The number of particles is uncountable because
many are merely conjectured to exist, although billions of dollars are
being spent today in the expectation of confirming at least some of
those conjectures.  If only the Riemann Hypothesis were so
well-endowed!)  Some idea of the parsimony achieved by the PPB can be
had from its expansion as the Review of Particle Physics, the PPB's
1100-page big brother.

Ironically the parsimony article is considerably less parsimonious than
the spice article.

As a talisman against the off-topic rule, I should relay here an
unverified report from the fourth millennium to the effect that
"categories were prominent in human mathematics virtually since their
inception, and were among the most heavily trafficked items of
metamathematical discourse during the third millennium."  They're a good
investment, I have some in my own kitchen but many on this list who take
their cooking more seriously have invested much more heavily.

Vaughan Pratt