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      Kendall's Shape Statistics as a Classical Realization of Barbour-type Timeless Records Theory approach to Quantum Gravity

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          Abstract

          I previously showed that Kendall's work on shape geometry is in fact also the geometrical description of Barbour's relational mechanics' reduced configuration spaces (alias shape spaces). I now describe the extent to which Kendall's subsequent statistical application to e.g. the `standing stones problem' realizes further ideas along the lines of Barbour-type timeless records theories, albeit just at the classical level.

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          Alignments in two-dimensional random sets of points

          David Kendall, Wilfrid S. Kendall (1980)
          Let n points in the plane be generated by some specified random mechanism and suppose that N (∊) of the resulting triads form triangles with largest angle ≧ π – ∊. The main object of the paper is to obtain asymptotic formulae for and Var ( N (∊)) when ∊ ↓ 0, and to solve the associated data-analytic problem of testing whether an empirical set of n points should be considered to contain too many such ∊-blunt triads in the situation where the generating mechanism is unknown and where all that can be said about the tolerance ∊ is that it must be allowed to take values anywhere in a given interval ( T 0 , T 1 ) (0 < T 0 < T 1 ). This problem is solved by the introduction of a plot to be called the pontogram and by the introduction of simulation-based significance tests constructed by random lateral perturbations of the data.
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            Introduction

            D.G. Kendall (1977)
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              Publication date Created: 07 July 2013
              Publication date Updated: 2015-05-27
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              ArXiV ID: 1307.1923
              SO-VID: f5e0268a-5e21-41f8-9487-b3d272567c35
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              http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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              Journal reference Stud. Hist. Phil. Mod. Phys. 51 (2015) 1-8
              Comments 11 pages with 5 figures. Improved text, as Accepted by SHPMP (Studies in History and Philosophy of Modern Physics) with some new explanations, minor corrections and updated references
              Categories gr-qc

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