I agree with you about the threshold 100%. It’s crossing over and it’s turning into a religion by fighting with religions. There’s no difference between, “Let’s fight to remove religion from the world” and “Let’s turn the world into our religion”. It works out to being the same thing, imho. Neighborhood kids from neighboring towns fighting before the big football game. Silliness and it tarnishes a portion of the scientific community for me. When I find scientists who stay out of the rumble altogether, or are extremely careful to only point out the excesses (of bad science and bad religion equally, like Carl Sagan did) – they have my undying respect.
I find myself going to geometry sometimes myself. But then I get into the cognitive processes behind line generation and the whole question of symbolic representation and the whole map vs territory question.
Still hard not to go into the geometry.
I can’t place my full trust in mathematics as a system-of-pure-truth because… I suppose… I’m a realist of an annoying sort: I see things as analogies for analogies, all the way down the line.
I analogize thought processes as machines that have both internal and external impetus – the engines work anywhere there is change; but I don’t think imagination/ideas are in a separate realm. They’re a part of us biologically, historically, culturally, etc and it’s because we’re using them that they have existence. A lost book that no one knows about has no meaning. It’s in the participation – the activation of the mental machines (or physical machines if one uses worldly elements to make things rather than the line-generation mechanisms of the brain).
Anyway… this is a ramble. I could go on about this subject ad infinitum… if I believed in infinity