Thumbnail
Access Restriction
Open

Author Smadja, Ivahn
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Variational Derivative ♦ Early Twenty Case ♦ Mind Pattern ♦ Mathematical Theory ♦ Mind Collusion ♦ Later Stage ♦ Structural Knowledge ♦ Actual World ♦ Hamiltonian Differentiation ♦ Mere Heuristic Device ♦ Affine Field Theory ♦ Objectivity Towards Selective Subjectivism ♦ So-called Hamiltonian Derivative ♦ Available Variational Method ♦ Action Principle ♦ Eddington Train ♦ Theoretical Function ♦ Derive Gravitational Field Equation ♦ Consistent Shift ♦ Dual Role Requiring
Abstract This paper sets out to show how Eddington’s early twenties case for variational derivatives significantly bears witness to a steady and consistent shift in focus from a resolute striving for objectivity towards “selective subjectivism ” and structuralism. While framing his so-called “Hamiltonian derivatives ” along the lines of previously available variational methods allowing to derive gravitational field equations from an action principle, Eddington assigned them a theoretical function of his own devising in The Mathematical Theory of Relativity (1923). I make clear that two stages should be marked out in Eddington’s train of thought if the meaning of such variational derivatives is to be adequately assessed. As far as they were originally intended to embody the mind’s collusion with nature by linking atomicity of matter with atomicity of action, variational derivatives were at first assigned a dual role requiring of them not only to express mind’s craving for permanence but also to tune up mind’s privileged pattern to “Nature’s own idea”. Whereas at a later stage, as affine field theory would provide a framework for world-building, such “Hamiltonian differentiation ” would grow out of tune through gauge-invariance and, by disregarding how mathematical theory might precisely come into contact with actual world, would be turned into a mere heuristic device for structural knowledge.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 2010-01-01