Well it would seem that his thinking is predominantly singular, and not just in that it is his thinking. He considers his “point” to be his ultimate “finite” interpretation and his “line” to be his ultimate “infinite” interpretation. By his own assertions they derive from what he calls “singularity”, attesting only to his own singular predilection. By combining them into what he refers to as a “complex” he comes to his ‘multiple’ (more than his point but less than his line). So yes he has looked for a point and a line and has found only one of each, but then just stopped looking. Which has restricted him to that rather bizarre “singularity” of his own thinking.
It's hard to clue Doron to spark up his vision generator funny, coz he is not fond of math of the college kind. That's why he misinterprets some descriptions, which may not be the best, but are used informally anyway, coz the listeners are familiar with the real deal. Take this "point coverage," for example. I'm positive that Doron never came across the concept of limits. Suppose that you have a line segment 6 units long and you divided the length by 3. The result is a line with 3 "sub-segments" each of them 2 units long. That's neat, but hardly enough to accommodate the needs of calculus, for example, where the x-axis is in
R and needs to be divided into the smallest possible segments. To accomplish that, the domain line
a is divided by
n, such as
n → ∞. The result is identical wherever limits are mentioned:
[lim n→ ∞] a/n = 0
Without knowing what is really going in there, a person suffering from math phobia may come to the conclusion that the domain line
a has been divided into infinitely many line segments each of them having its length equal to zero and therefore
a is "entirely covered by points." This is not so, otherwise it would be impossible to compute the area under any curve. But the term is used with no problems, coz the real meaning is pretty much understood by everyone hanging around math except by Doron. Even though he may accept the presence of "all points in the line," he insists on some space between them, as if his discovery was hotly contested by the views of the traditional math.
There is no way to learn to swim without getting into water, and that's exactly what Doron think is possible. He never poked the concept of infinity with his pencil, so he is not aware of certain realities that govern over the x-axis populated by points whose job is nothing else but to feed a function, and so fancy points need not apply there. Of course, there is only one set
R, but Doron thinks that the angels will carry him to that set, so his fine Nike shoes wouldn't get dirty by stepping into the limits and other assorted tools of "mental exercise" used in Torture Chamber High.
Maybe he is not that good in the perpendicular reasoning, as opposed to his often-mentioned parallel reasoning. That's why he stays away from the Cartesian coordinates and all that high school math for commoners. Or maybe he doesn't want to get bothered by anything like that in his serene ascend to the Doronian metric space (formerly the ionosphere) of mathematical knowledge.
