The longer version deals with Newton, Lorentz, Maxwell and Higgs fields as do the books and they accept non-3 dimensional space for their proofs as you know. The books include a solution to Zeno's paradox of Achilles and the Tortoise; but your observations are all valid up to a point and I thank you for them.
Since it is short, I will share the paradox solution from book 6:
This is the solution to the Zeno Achilles Paradox which shows, by way of example, how this works.
As two ct3-ct4 states, Achilles and Turtle, shift position, A does not go to the half way point of T. Instead the number of ct1 solutions between the two decreases to bring them together. The perceived movement is illusory. This idea can be expanded to see what happens if an arrow is fired into a target or if a neutron star collapses into a black hole.
Where our brains begin to hurt is when we think about Achilles passing the turtle because solution order suggests the two cannot pass, but they can change position due to the extra dimensions that define their separation in a two or three dimensional environment.
Solutions can be on opposite edges of the universe and at the same
time be closer together in solution order than those points in between
them. Indeed, that is required by this analysis.
That is one reason
why our existence can only occur in the middle solution space and not at the
edges or center or the universe. This is
indirectly related to the rate of change at the different locations (middle,
edge and center). Existence in the
middle allows our physics to support life where it would not at the other
extremes.
The issue here is entirely different. The problem with Pre-aut analysis is that you are trying to force reality into a 3 dimensional framework. There is overwhelming evidence that space is something (it's there, it must be something). It has no features we associate with dimension because we don't look right. There is good evid. that we experience 3 dimensions and that black holes experience 4 (that's why it shrinks to a point, its stretched out in a 4th dimension). There's fair evidence that time is an effect operating between light speeds (changes in one or two dimensions) and black holes (changes in 4 dimensions). So we have this zero dimensional stuff, 3-d and 4-d stuff. So we're missing 2 dimensional growth. Obviously the wave-particle things suggests itself. We have great evidence that when you go between waves (suggested 2d) and mass (3d) you have an enormous increase/decrease in volume; highly suggestive of a dimensional change. The same is true for a wave to particle transition (line vs page discussion). There is also a model for the transitions that fits (2f(n))^(2^n) which is logically based on geometry and fits observed scales. We see what we want to see, reality screams look!
The focus on time and "empty space" is source of most of the errors in the theories of quantum mechanics even though they all accept at a base level the idea of fewer dimensions, they just fail to recognize that these exist together.
http://www.animations.physics.unsw.edu.au/jw/calculus.htm
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