Hamilton"s pure time analysis is great if you consider flow as non cyclical. However closed loop flow has it own properties explored under the notions of modularity. Notions of prior, and posterior, before and after, bigger and smaller, inclusion and enclosure all become interrelated.
I think it might be fun to explore these things.
So i listened to a set theoretic description of a metric space and was left feeling empty.
A metric is a measure of distance. Innocuous as that seems there are huge axioms right there: measure(?), distance. and the object of this action(measuring) is a set of "Points"(?), the result is a scalar in the positive reals.
Are the positive reals a measuring line or a number line? or both?
We are given 2 identities and a third rule is a relation. What we are not told is what is the notion of point or the notion of distance.
In cases like this we act like blind geometers, follow the instructions and learn what we can learn. We areexpected to meditate on these axioms and mediate their application.