Pt3.Ch6.Sb2 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘The Calculus’. summary

by Corry Shores
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[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]

 

Henry Somers-Hall

 

Hegel, Deleuze, and the Critique of Representation.

Dialectics of Negation and Difference

 

Part 3: Beyond Representation

Chapter 6: Hegel and Deleuze on Ontology and the Calculus

Subdivision 1: The Calculus

Brief Summary:

Deleuze’s and Hegel’s anti-representationalist philosophies can be compared on the basis of their different interpretations of differential calculus and Kant’s antinomies.

Summary

Calculus deals with “quantities whose relations to one another vary.” (162) Somers-Hall deals mostly with speed, the relation of time to distance. Early developments in the study of rates of change come from Oresme. To find velocity, draw a graph with time as one axis and distance traveled as the other. To determine the speed we look at change in distance over change in time, which also gives us a diagonal between those time-space coordinates on the graph. This only gives us average velocity. If we wanted to know the velocity at any moment, it would have to be at constant speed. But for motion with inconstant velocity, we cannot use this method. Instead we need to draw a tangent to the curve to determine the velocity at that moment. But a point cannot have a direction. Leibniz’s solution is to begin with the diagonal between the point in question and some other arbitrarily selected point (which gives the average velocity within the bounds of that time frame), and then bring the arbitrary point infinite close to the one in question. This slides the diagonal to indicate the velocity at that point. In fact, we can do this merely working with the graph’s functions in their numerical form. (163d)

For Hegel, calculus’ method is expressed in the formula [see §608 of this entry]

or

The second one is the gradient function for a curve, change in x over change in y. Let’s first examine

(Thanks Dr. Siddique / faculty.uncfsu.edu)

So the i  on the bottom is the x value. And our function gives us y = f(x). So we will find the y values by using the function formula. On the top, we have two applications of the function. The second one tells us what point along the y axis is right above the first x value.

 

Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.