I think I understand a bit more why you tried to tell me the importance of teaching math with gears (Geometry vs Set Theory). Which mathematical universes deal with magic (infinite series, Cantor’s works [leading to his insanity])? I think I see how you arrived at the conclusion to teach with something tangible and real, and don’t act like you do magic when you do not. People who love to deceive and simply use logic games and fantasize about a concept that has no existential meaning (like infinity) only hurt people in the end with their dishonesty. One of my math teachers in college, the hippy type, acted like with infinite series he was “doing magic” by adding up infinities to infinity to reach a finite sum (based on a purposeful ignorance of time). Which I think he mentioned we ignore time, but the implications of that should make us realize if one ignores a real dimension, then how can one speak of anything real, at all? So when we ignore time, we deal with the ideal and not the real.
Good job mate. I learnt a lot of these ideas from Professor N.J. Wildberger. If you haven’t already checked out his channel, he breaks down this topic the best I’ve seen.
This is awesome. Thank you for introducing me to this guy.
Cantor screwed up math for “reals”. (Lolz)
Looks like NJ thinks mathematics foundations should be based on arithmetic and not geometry.
Curious, if universal commensurable grammar uses geometry in a different sense than in mathematics, I feel like Curt’s usage of geometry refers to something other than Euclidean geometry.
Unless I’m off base. Please correct me if I’m not understanding.
Will check it out, thanks.
—“the importance of teaching math with gears (Geometry vs Set Theory). “—
Awesome! Well you get operationalism. 😉 Real vs Ideal.
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