As you may have noticed, the crank behind the "Inverse 19" rubbish in my Loony Toony Tangents post has shown up in the comments. And of course, he's also peppering me with private mail.
Anyway... I don't want to belabor his lunacy, but there is one thing that I realized that I didn't mention in the original post, and which is a common error among cranks. Let me focus on a particular quote. From his original email (with punctuation and spacing corrected; it's too hard to preserve his idiosyncratic lunacy in HTML), focus on the part that I've highlighted in italics:
I feel that with our -1 tangent mathematics, and the -1 tangent configuration, with proper computer language it will be possible to detect even the tiniest leak of nuclear energy from space because this mathematics has two planes. I can show you the -1 configuration, it is a inverse curve
Or from his latest missive:
thus there are two planes in mathematics , one divergent at value 4 and one convergent at value 3 both at -1 tangent(3:4 equalization). So when you see our prime numbers , they are the first in history to be segregated by divergence in one plane , and convergence in the other plane. A circle is the convergence of an open square at 8 points, 4/3 at 8Pi
One of the things that crackpots commonly believe is that all of mathematics is one thing. That there's one theory of numbers, one geometry, one unified concept of these things that underlies all of mathematics. As he says repeatedly, what makes his math correct where our math is wrong is that there are two planes for his numbers, where there's one for ours.
The fundamental error in there is the assumption that there is just one math. That all of math is euclidian geometry, or that all of math is real number theory, or that real number theory and euclidian geometry are really one and the same thing.