In a previous text, I took a standard differential equation and put it to a use that was never intended by the mathematicians themselves, and interpreted its psychoanalytic significance . As a result, some people familiar to the standard practices in mathematics protested that they viewed my interpretation of the equation as “nonsense” and therefore “invalid”. Here I would like to explain what their protest means.
In the definition of space-time as a mathematical object, time is the fourth dimension (t) that is orthogonal to the three dimensions (x, y, z) of space. So we can simply say: What is orthogonal to space is time.
The orthogonality of time to space makes sense in that time is something entirely different from space and they have “nothing in common” in the sense that their projections onto each other yield zero vectors.
But the orthogonality of time to space also means that time is being modeled as a spatial dimension (t) just like the other three spatial dimensions (x, y, z). Space-time is often called a spatio-temporal field but it is really just a spatial field, because the so-called temporality is structurally indistinguishable from spatiality. As a symbolic gesture we call t “time” but really there is nothing temporal about its structure. So where has time really gone?
Symbolic temporality (t) is a simple extension of the spatial field, reducible to it, just making it 4D instead of 3D.
Real temporality, on the other hand, is orthogonal to the whole spatial field, not merely to its individual dimensions. I call this field, the combinatorial field . Since the combinatorial field of real time is also orthogonal to the symbolic representation of time (t), it may be appropriate to call it the “fifth dimension” , although keeping in mind that this is not a regular spatial dimension intended by the standard practices of mathematicians, but rather a dit-mansion (house of speech) unintended by them. Let’s label this fifth dit-mansion, w.
It is said that symbolic temporality (t) has “nothing in common” with space (x, y, z) in the sense that their projections onto each other yield zero vectors. In fact, x, y, z and t have plenty in common, they are exactly the same except their names.
In contrast, real temporality really has nothing in common with spatiality in the sense that the combinatorial field makes no sense from the perspective of spatiality: w is not spatially representable.
This fifth dit-mansion w is the topic of psychoanalysis . I chose the letter w for a few reasons:
1) Real temporality is founded on the pinging of interlocution between the double-you: “You?” “You!”
2) Real temporality is what distinguishes the whole of meaning from the hole of nonmeaning by virtue of the interlocutor’s recognition: w-.
3) Real temporality dwells in waves of resonating voices that can get waived at any time.
4) Real temporality asks the questions: what, where, when, who, how?
5) Real temporality is suspended at the dilemma between “woe!”, “whoa!” and “wow!”
As a result, it makes perfect sense that w “makes no sense” from the perspective of x, y, z and t, since it is orthogonal to the whole of them. But in contrast to the zero vector that can never have a direction, this “making no sense” does have a direction albeit an unconscious one.
 See “Spatial and Combinatorial”