Tom,
""Does a dimensionless point exist?"
If it doesn't, then neither does dimension."
So do dimensions physically exist, or are they simply conceptual tools?
The same could be asked of any measurement function; Do inches or hours or pounds physically exist? If so, show me one that exists independent of any specific physical medium. Do longitude, latitude and altitude lines physically exist, or are they conceptual tools to describe our reality?
"a trajectory is a vector and the single number which describes the combination of vectors is a scalar."
"All of these have a physical context. that is, they correspond to physical phenomena as boundary points of a measure domain. When we speak of measures we mean that the variables are bound to the maxima and minima of limit and function -- the range within the domain."
These are descriptions and measures. They are conceptual tools.
"There's no ambiguity in physics about the context for existence. It depends on the measurement function, not on a philosophical definition of existence. The question is whether, as in conventional quantum theory, the measurement function is discrete and nonlocal -- or continuous and local, as in classical physics."
Your argument boils down to that we cannot see beyond the limits of our models, our conceptual tools. While this is a highly reasonable and logical argument, it overlooks the fact that we created those tools in order to extend our vision in the first place. So, logically, if we reach a point where we can see no further with those tools, does that mean we stop, or that we need new tools?
If for instance, your tools are made of wood, stone and bone, how do you extend the model? What more is there to carve? Smelting metals required an entirely different way of thinking. So the question now becomes how to rethink the tool box? Can we simply further extend what we have, or is there a way to go back to the drawing board? That requires first the willingness to look at different views and options. You say there are those unwilling to consider Joy's proposals, but then you tell me there is no other way to think of time and space as other than this four dimensional geometry. How can something be disproved when every argument against it, such as time being asymmetrical, is dismissed on the grounds it is not defined by the model. Yes, an hour is a scalar measure of time, but does that really mean time lacks direction? Or that the measure doesn't model that quality of it?
Regards,
John M
