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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.

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.

I’ve been trying to post this as a separate thread

I will expand this later, but the basic idea of time seems to be similar to a Fourier analysis. This would come from Bergson and Husserl, both of whom were mathematicians, as well as from Poincare and Einstein.

Each incident is an event at a point of space-time. An incident is defined by thee cohesion of a certain set of states at a certain point.

A space-time event sents out waves through the fabric of space-time.

The snapshot of any moment is the sum of these prior wave functions. Apparent stability is a product of wave functions, a temporary “standing wave”.
https://en.wikipedia.org/wiki/Fourier_analysis

This is where the term “non-localizable” comes from, for example.

Because space-time events emerge from a sum of waves, it creates some issues for questions of generality and particularity.

Namely, the problem of noise arises inevitaly for any stable construction — stability and noise are two aspects of the same process

https://www.wbur.org/onpoint/2024/03/30/archive-and-in-the-news-noise-hinders-human-judgement