From Osher Doctorow
Elliptic curves are very important in algebraic geometry and are a type
of abelian (commutative) variety, which in turn (variety) is defined in
terms of sheaves and schemes. For elliptic curves over a field with
field characteristic other than 2 or 3, the general equation of an
elliptic curve is expressible with change of variables as:
1) y^2 = x^3 + ax + b
or in Legendre normal form:
2) y^2 = x(x - 1)(x - k)
for constants a, b, k.
Since the only known (probable) causal/correlational expressions are 1
+ y - x and y/x based respectively on Probable Influence/Causation and
conditional probability, the elliptic curves represented by (1) or (2)
are already too complicated for causal/correlational expressions.
This is a special illustration of the fact that Category Theory's
"composition of functions" is far too general but also far too
different to be of causal/correlational use. Category Theory is
heavily used with Algebraic Topology, Algebraic Geometry, and K-Theory.
Osher Doctorow
.
|
