Extension and Intensity

Greek geometry is a constructive geometry. One constructs figures using only a straightedge and a compass. The fundamental principle is that of length, or extension in space.

So extension is the distance between you and your perimeter, or between you and something else; the stretching out of material and emptiness into space.

Deleuze seems to credit differential calculus with opening us to the thought of intensity. For this reason, he often mentions Leibniz and Riemann.

Euclid’s caclulations only consider one dimension of measurement: length or extension.

Leibniz’s differential equation dy/dx represents the rate of change of one value with respect to the other. This allows us to start thinking about relational intensities. Leibniz applied the notion of differential rates of change to relate space, the position of an object within its surroundings, to time.

Berhard Reimann prompts us to think more deeply about the notion of position. O

Euclidean geometry, as said above, is a straight line construction, conceiving of the world as extended in space. But this construction only makes sense on a flat plane, where the distance between two points is the same wherever one stands in the plane.

But this changes in a curved surface. In a globe, for example, the further you go north or south from the equator, the less distance you have to travel eastwards or westwards to come back around.

What this means is that one’s position within space-time affects the relative forces between yourself and the entities to which one is related. How one positions oneself propagates through variable intensities depending on how one situates oneself.