I am now developing (when I can steal some time), the field of DK dimensions, DK spaces, DK languages in the form of "programmable language". One can view mathematics as a language, but in the past it was hard to incorporate "semantics" (meaning) in a precise and disciplined way. Mathematicians have used "semantics" (in the form of physics and geometry) as a primary driver, like Archimedes, Newton, and Gauss. But in the recent centuries, they more and more relied on syntactical "patterns" in the form of "numbers" to get insight, such as the work of Cantor, Hilbert, and Grothendieck. I too, started out that way of Grothendieck, because of new math, but my father always argued with me in this regard. More recently, I tried to start from the most simple elements (boolean logic or things like Heyting algebras, in some sense the most syntactic), and using Robert Rosen ideas an important elaboration of my father's approach, as my basis and my "words."
We can’t solve problems by using the same kind of thinking we used when we created them.
-- Albert Einstein
I progressed learning a lot of mathematics, physics, chemistry, biology, economics, yada yada. But, only when I, instead of fabricating (analysis and synthesis) "bottom up -- e.g., boolean," and I started fabricating (analysis and synthesis) "top down" did I realize the key. The following encapsulates mathematics, with essentially five SEMANTIC symbols. The task is to expand from those five semantic symbols, creating other languages with more symbols derived from this foundation, and not violating semantics or syntax, or being arbitrary in one's assignments (and creation) with other semantic symbols (and not overloading them either). With those five symbols one can fabricate mathematics (and new mathematics) and maybe even, the universe in the abstract.
Not showing the operator (i.e., ^: the power of), one can get the repeating string: eπi101iπe
The point being the "value" of this circular (and "recursive" in a way) string has a SEMANTIC FIXED POINT.
eπi101iπeπi101iπeπi101iπeπi101iπe ... <=> 1
That is, eπi101iπe = 1, moreover, eπi1 = -1, 00 = 1, 01iπe = 1, {so one can create the string [-1,1,-1,1,-1, ....]}
Another point is 01iπe = 0abcd for all a,b,c,d in otherwords, the only SEMANTIC FIXED POINT IN THIS VERY SPECIFIC STRING (01iπe) is zero.
Regarding an infinite number of connected spaces.
Regarding the growth of good/bad ideas
Regarding the birth and death of bad/good ideas.
