Paul,
I sort of went into this in one of your previous posts;
One way to consider this is to ask what math does and I would simply say it describes, defines. The issue than becomes is to whether there is anything which can’t be defined. As the position of some seems to be that if it can’t be described, it doesn’t exist and that it only exists as its description. Which seems to be the platonic math position.
Such as that space is the three dimensions of the xyz coordinate system, as that is what is measured, or that time is a dimension, measured as duration.
What seems to me is that squishy element that seems to slip around these measurements is “energy.” Think of a wave; You can only really measure things like amplitude, or frequency, possibly kinetic energy.
Yet these measurements confine, as they define. Amplitude and frequency only come about as the energy of the wave peaks, or is otherwise interfered.
Then look at what physics mostly prefers studying, in the very large and the very small, where the forms and definitions are most clear and the actions are most regular. This is where the energy is most quantized and inertial.
Meanwhile “energy” in the middle ground is fuzzing all the measurements.
So what if we compare these two? Energy pushes, while form defines. Galaxies are energy radiating out, as form coalesces in. We have the digestive, respiratory and circulatory systems to process the energy driving us on, along with a central nervous system to perceive, order and judge all the somewhat static forms this energy expresses.
Note that mathematicians and physicists are very intellectually inclined, so they might naturally prefer the ordered form that the brain is designed to perceive.
Then look at the rest of us, with both the gut/heart/appetite/desire driving us on, along with the head to judge and order our actions.
Society is that raw social energy bubbling up, as civil and cultural forms coalesce in. Youth and age, liberal and conservative.
The anarchy of desire, versus the tyranny of judgement.
As well as the forementioned galaxies.
So it would seem that while mathematicians only see order versus chaos, for the rest of us, it seems to be energy versus form.
How might this relate to the conundrum of quantum mechanics, where there always seems to be another layer of structure however deep they look, it still gets that much more fuzzy and statistical? Might it be an issue of trying to digitize what is still ultimately analog? What really holds everything together, if it isn’t already connected?
Not that you will ever penetrate the professional bubble, as they would put the fantasy world of any religion to shame, but just some thoughts on the reality we have to navigate.