More on information geometry
Some blogs use different categories to sort out their posts. However, in my experience, things that interest me enough tend to show themselves to be related somewhere down the line. A while ago I was pondering the question -
How much of the mathematics used in physics is describing our knowledge and ways of observing and intervening, and how much the physical world itself?- in the context of Caves and Fuchs' interpretation of quantum theory. Now I see Ariel Caticha has an article trying to understand general relativity in terms of information geometry:
The point of view that has been prevalent among scientists is that the laws of physics mirror the laws of nature. The reflection might be imperfect, a mere approximation to the real thing, but it is a reflection nonetheless. The connection between physics and nature could, however, be less direct. The laws of physics could be mere rules for processing information about nature. If this second point of view turns out to be correct one would expect many aspects of physics to mirror the structure of theories of inference. Indeed, it should be possible to derive the “laws of physics” appropriate to a certain problem by applying standard rules of inference to the information that happens to be relevant to the problem at hand.Elsewhere, work is underway to generalise information geometry to the infinite dimensional spaces used in nonparametric statistics. There are important papers at Jun Zhang's site, including 'Nonparametric information geometry: Referential duality and representational duality on statistical manifolds.' Zhang is a psychologist who uses this mathematics to model psychometric testing.