definition of parsimony
Dear List Members, I am looking for a formal definition of parsimony for fundamental scientific theories. From the tiny bit I understood of category theory, I had the impression it might provide the right framework for such a definition. The problem of motivating and defining parsimony is being discussed in analytic philosophy. An overview over the discussion can be found at http://plato.stanford.edu/entries/simplicity/ , which starts off with the sentences Most philosophers believe that, other things being equal, simpler theories are better. But what exactly does theoretical simplicity amount to? Syntactic simplicity, or elegance, measures the number and conciseness of the theories basic principles. Ontological simplicity, or parsimony, measures the number of kinds of entities postulated by the theory. One issue concerns how these two forms of simplicity relate to one another. I am interested in the "ontological simplicity, or parsimony". However, if one understands modern physics as describing essentially only one thing, the wave-function of the universe, then even the idea of defining parsimony in terms of numbers of kinds of things seems to be a bit odd. Yet, I think the idea is intuitively clear. The minimum requirement for a formal definition of parsimony is perhaps that it should identify theories such as the dynamics of Newtonian point-particles or the current "standard model" of particle physics as parsimonious, while the same theories with some oddities added, which do not themselves affect the "real" physics, should be identifiable as non-parsimonious. Beyond this, such a definition should presuppose as little as possible about the nature of the theories it applies to. Does somebody know about applications of category theory to this problem, or have an idea for who to do it? Cheers, Axel Rossberg --- Evolution and Ecology Program International Institute for Applied Systems Analysis Schlossplatz 1 A-2361 Laxenburg AUSTRIA ++++++++++++++++++++++++ reprints http://axel.rossberg.net/paper and more http://axel.rossberg.net
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
(Out of fairness to *the* standard model, the Higgs boson is its only remaining unobserved particle. The other particles being sought at Fermilab and CERN belong to supersymmetric (SUSY) extensions of the standard model. Ironically such an extension while having more particles could nevertheless claim to be more parsimonious than the current standard model as measured by the number of its free parameters, in particular fewer Yukawa constants. Disclaimer: if you knew SUSY like I know SUSY no physics lab would even think of hiring you.)
participants (2)
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Axel Rossberg -
Vaughan Pratt