The concepts of Euclidean distance, or a geodesic, are of course suitable models for the practical application of measurement at classical scale. However, it will be argued here that the complete picture of the abstract geometry that intervenes two points necessarily involves a dynamical network of discrete intervals. Then measurement concepts that aim to remain valid at microscopic length scales must take account of dynamical update in that network. The abstract model developed on that basis displays characteristics analogous to quantum mechanical features; then it is proposed for consideration as the ‘very general model’ of interest to quantum gravity programs. This model suggests that the current formulation of classical mathematics is antithetical to the unification program of quantum gravity.
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