Doug thank you for your comments.
I have read your essay and can understand your reaction relative to your inability to relate to it in a way that would advance your knowledge. I do not mean this in a derogatory way. I found your essay to be well written and to the "point". In writing my essay and trying to link art theory to science, definition of a point was the first thing that I needed to do. Like you point out in your essay, understanding the nature of a point is really what lies at the heart of understanding everything.
Science uses mathematics as a tool in modeling. As a result, scientific modeling has the same limitations that mathematics does and the same characteristics. Mathemematics evolved from counting, to geometry to trigonometry etc... and types of numbers evolved to include zero, and negative numbers and real numbers and imaginary numbers etc.. Just like in science, this evolution did not evolve from a framework of understanding what the whole picture looks like. These limitations do not exist in art.
Which brings us to a "point". A point is a purely imaginary construct. Counting points or arranging points relative to each other in various defined groupings, and using numbers to represent them and their relationship to each other, can be very confusing because number usage is ill defined. The concept behind a number used in counting, and that same number used as an exponent, or a subscript denoting dimensional characteristics are fundamentally different.
What I had hoped a mathematician would get out of my essay is that there is both a real and imaginary component to all numbers. All numbers are complex. All points are complex. Real numbers are a subset of imaginary numbers such that the imaginary component assumes a value of zero. If you view this geometrically, a countable point of real zero dimension requires eight imaginary points to define it.
I could go on but the thing I liked about your essay is that it recognizes the fundamental shortcomings of mathematics and that understanding the nature of a point is critical to understanding anything and everything.
Pete