Knot Theory
knot theory
some formalization of math, makes it wholly unnatural and hard to work with. i think knot defined in topology is such a example.
- it drags in a whole def of topological space machinery.
- similar situation is the epsilon delta definition of limit, vs non-standard analysis.
- and similar situation is set theory logic axiomatic basis vs computational basis e.g. homotopy type theory.
- The question is, can a knot be defined more simply and allow easier methods to work with... i presume so, just that u got other issues.
- knot theory seems interesting, in that it's a weird beast. it's not topology in the traditional sense, not algebra, not finite nor discrete thing, not analysis, and not geometry in the traditional sense, and not combinatorics, ah maybe it is.
- at least, graph theory is finite and discrete and concrete.
- but knot theory in higher dimensions, and knot complements, seems become proper topology. Something homology...
- is knot theory of higher dimensions still the same nature as knot theory?
- a wild knot! untame! pretty wild. math, geometry.
