Let us use Lacan’s chain rule  to take the derivative of the signifying function and obtain the meaningless signification of the true truth . Here is the standard mathematical way of taking the derivative of a function:
Here f indicates the signifying function that bears an opacity of meaning; t indicates time or any other variable that our analysis is concerned with; x, y, z indicate the dimensions (dit-mensions) or the multiple discernible variables that reside within the opacity of the signifying function, i.e. they are what the signifying function is about, they constitute its symbolic topic; d indicates derivative or the analysis of a variable; ∂ indicates partial derivative or the analysis of a partial variable.
First of all, the whole operation df/dt has the form of a metaphor:
1) The equation formulates the substitution of f for t: It articulates how the signifying function f covers our point of concern t. Here t is not only time that can be read on a clock, but also our steady march towards death, which invariably becomes our central concern as a living being; moreover, t is also loaded sexually because human individuals are sacrificed for the continuation of the human species . The metaphorical function of signification is how it covers our concerns about time, death, sex by being substituted for it. This primarily refers to the paternal metaphor as the coverage of the Name-of-the-Father.
2) The variables (x, y, z) serve as the intermediate terms that symbolically ground the signifying metaphor df/dt. They are used for determining the location of the signifying function and they lend some partial transparency to the opacity of its meaning. There is a compulsion to multiply these variables because their partiality implies insufficiency. Each new variable compensates and covers for the insufficiency of the earlier ones, and their multiplicity compensates for the failure of the One signifying function (Name-of-the-Father). In the case of the spatial world, three orthogonal variables x, y, z sufficiently cover the function. In the case of the combinatorial unworld, however, the variables are never enough since it is impossible to establish the sexual relationship .
The partiality of each variable should be taken not as the index of its insufficiency, but the index of its reality. We will examine just one of the three components of the signifying metaphor since logically they are all equivalent.
Take ∂f/∂x dx/dt. Here x indicates any intermediate term that symbolically helps the Name-of-the-Father to metaphorically cover the inescapable problematic of time, death, sex. Recall Lacan’s example intermediate terms: mother’s desire and the foreign word “Signor” (see ). The primary character of the intermediate term x is its self-cancelling quality. It becomes invisible (it gets forgotten) from the perspective of the established metaphor df/dt.
The variable x is common to the two terms ∂f/∂x and dx/dt, it is what connects them but it’s also what divides them. When we examine partial variables like x, the division between ∂f/∂x and dx/dt becomes visible, and we leave the dashing domain of metaphor and enter the more refined domain of metonymy. This is the famous division of the subject of the unconscious.
The variable x functions like a place where these two terms are gathered or collected together. But the terms themselves ground the place of x in different ways:
1) ∂f/∂x means that our variable x is a partial aspect of the paternal signifying function f. In other words, x takes part in f. This is the symbolic role that represents the subject for other signifiers. This term indicates the subject’s symbolic ground.
2) dx/dt means that our variable x is implicated in the problematic of time, death, sex indicated by t. This is the symptomatic knot that the subject dwells in. This term indicates the subject’s real ground.
Symbolic ground is indicated by the partial derivative symbol ∂ because mathematics officially acknowledges that the three variables x, y, z are symbolically entangled through the function f by the following notation: f(x(t), y(t), z(t)).
However, real ground is indicated by the full derivative symbol d because mathematics can never acknowledge the real entanglement among the variables x, y, z through the problematic of time, death, sex indicated by t. This is why the “full” derivative df/dt only works in the spatial world; the combinatorial unworld reduces it to a metaphorical imposture. The subject’s real entanglement is preferably foreclosed but often simply disavowed by science in general and statistics in particular. This is why I invented dynamistics as a science that acknowledges the real entanglement of the subject .
Thanks to Martin Zika for helping with the LaTeX equation code.
To learn more about the mathematics of the equation, visit this link.