ABSTRACT
Key Concepts: significance, absolute and relative space, the double torus, knotting and ‘naught-ing’.
With topology, we have significance (signifiance) rather than signification in language. One can flatten out a knot, even though it has three dimensions; one can flatten it out so that it just looks like two dimensions. Then, “this line or string is something other than the line I defined earlier with respect to space as a cut and which constitutes a hole”. Now the surface of a circle, which was the concern of the early Greek mathematicians, is understood to be a hole. This raises the question of whether space is relative or absolute because the idea of absolute space implies there being a container as opposed to relative space, which is always defined by a point, a line, or matter.
The concept of absolute space is illustrated by the double torus – the torus is like a donut: you make a knot by putting the string through a hole or putting a line through a hole (and then you create another circle). But, for a torus, it has the distinction of having two holes – the hole that is circumscribed by the tube and the hole that is inside the tube. There are two voids there, two holes. While in a bubble, you have only one hole, only one space inside the bubble.
The torus is reason, in that reason articulates positive and negative propositions or affirmations and negations, functioning according to a ‘knotting’ among universals and particulars, positives and negatives, affirmations and negations, and so on.
The idea of having a demarcation is not only that of ‘making the cut’ somewhere between particularity and universality, but the relation between the two is also maintained. Any time a demarcation is made, a stich and a knot are formed. This is what reason does.
When you have integers, and you have zero and a unit that creates a ‘one’, and a ‘one two’, a ‘two three’, a ‘three four’ – it’s the same unit repeated, instantiated each time. Then you have the system of marks that evolved from the unary system, but they are now all discrete marks. Within the Symbolic, meaning cannot be defined in isolation, and it is a function of the relative relations between signifiers.
