Status Updates From Where Mathematics Comes Fro...

using a suite of metaphors, Lakoff and Nunez intuitively explain Euler's magic formula and how an exponential e raised to an imaginary power i times Pi equals negative one. It is amazing that with normal human brains, we can grasp something so abstract and amazing.

going over the metaphors to Euler's magic formula e^i(pi)-1=0

I agree that embodied cognition is a good gateway to math, but I still think Math exists independently of the mind. These concepts kick back like when you kick tires. So, l like embodied cognition for pedagogical purposes. I still think math is discovered, not just metaphor play.

Dedekind cuts and metaphors for the continuum, and Weierstrass and taming monster functions.

Points and the continuum and space-filling curves, and the way we build them from the concrete.

Transfinite diagonalization arguments and the specks or dots of infinitesimals.

extending this infinity to infinite numbers, polynomials, and sequences. And the concept of a least upper bound to get Dedekind cuts and the real numbers filling the number line.

Infinity and indefinite iterative processes like breathing and day-night cycles. Iterative processes happen all over the place, and many have no definite end and are good metaphors for the infinity of natural numbers.

ordered pairs and the metaphor of set theory in terms of ordinality and Cardinality.