[Top][All Lists]

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
## Re: [Axiom-developer] categorical design

**From**: |
root |

**Subject**: |
Re: [Axiom-developer] categorical design |

**Date**: |
Thu, 9 Oct 2003 23:47:27 -0400 |

Bill,
re: categorical redesign.
My view of this is to think of Axiom's mathematics as a general
graph rather than as a lattice with loops. Think of drawing the
whole of the algebra on the surface of a sphere. Picking one of
several defined starting points (sets, categories) in the algebra
would be like rotating the ball until the chosen point is at the
north pole. Everything else is defined in terms of that pole.
Choosing a new point would be like rotating the sphere to
adjust it to the new "north pole" and everything in the graph
now flows from that point. A loop in the algebra goes all the
way around the sphere and you can choose any point in the loop
as fundamental. The choices I made to "break the loop" were
arbitrary.
I'm not sure if the graph-mapped-onto-a-surface resonates with
you but that's how I think about it. (The surface need not be a
sphere, of course).
Tim