For Pythagorean triples, the geometric object is a circle;
, and the area is transcendental, and thus the one-dimensional circumference.
The Special Theory of Relativity is actually a case of generating real numbers for the basic concepts of independence of (c,v) (where the relation is complete because they are related by scaling - i.e.
) and continuity, where the "energy" and "momentum" are independent (ct,vt'). However, it shows that if there is only one positive particle (conceived of as a real number), then
(the ultimate "Black Hole", since there is no additional v/c where v > c. "Black Holes have no hair.
Philosophically, it means there is only The One... that is, me (the "wow" of physics).
Quantum mechanics assumes that one can't be sure about that, since one occasionally gets a sunburn (the "ow" of physics), so it is a statement ("There is me and thee, but I'm not absolutely sure of thee, especially if I am wearing sun-tan lotion
(The Egyptians may have been right about the sun god...
Wittgenstein declares there is no possibility of talking only to one's self, which is equivalent to asking "what language did you speak before you were born?"...
Goedel (and Einstein) assumes there are two observers, but if one says his language is complete, the other guy just adds an integer to the conversation ....