Discussion by Fred L. Bookstein
John Barrow’s paper emphasizes hard physical theories of how galaxy clustering arises, but puts forward mainly soft statistical tactics for their study, tactics that do not often incorporate any empirical physical constants among the statistical parameters for which point estimates are to be generated. To bridge this gap, I refer to the literatures of image processing and stochastic geometry, which respectively extract and account for the sort of features produced by the astronomer’s eye as geometric shape variables subject to a possibly isotropic and homogeneous (i.h.) distribution of location and orientation. One hard model yields the Minkowski functionals of i.h. convex grains. Another yields an indefinite series of three-dimensional pictures of features such as filamentness or sheetness at every point of the space, and at every physical scale, so that their isotropy and homogeneity may be studied empirically. I comment briefly on many of Barrow’s specific statistical hints and suggestions in light of these two major possibilities, which link the galactic clustering problem to statistics via the neurophysiology of human vision.
KeywordsGalaxy Cluster Physical Scale Gravitational Instability Stochastic Geometry Minkowski Functional
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