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Extra info for Dogma of the Continuum and the Calculus of Finite Differences in Quantum Physics
Besides the concept of the continuum our usual g e o m e t r y assumes t h a t we can took 'from outside' on geometric structures drawn on p a p e r or c o n s t r u c t e d in physical space. This is quite a d e q u a t e except if we s t a r t thinking a b o u t the universe. We c a n n o t look at the universe from the outside since we are 'in it' or p a r t of it. 5-1. Two equilateral triangles. 5-1a. It has three vertices 1, 2, 3 and three equally long edges 1. 5-1b shows again three vertices and three equally long edges.
For a simple example of what finite differences Ax, At rather than differentials dx, dt can do for us consider the cases of infinite energy that currently are resolved by renormalization. It has been pointed out before that some of these cases are caused by a problem of Maxwell's equations with the causality law (Harmuth et al. 5). nden: daft er ein dreidimensionales Kontinuum/st. 1 . 4 D O G M A OF T H E C O N T I N U U M IN PHYSICS 29 by being able to account for the magnetic dipole currents p r o d u c e d by r o t a t i n g m a g n e t i c dipoles.
5-1b shows again three vertices and three equally long edges. We have no difficulty seeing a difference between the two triangles. 5-1a if we look from above at the paper plane and see the curved edges projected onto the paper plane. We can see different things if we can look from different directions. This is geometry viewed from outside. 5-1 be implemented 'in space' by three rods or thick wires and make them very long. If we put an ant schooled in mathematics and physics on these structures it is 'in the structure' or part of the structure.