Black cat in Hotel Lafayette, The Matrix Trilogy.

It is the first Friday of winter holidays. My writing on “Informational Transducers” is going out of hand. It wasn’t in my plans to write off-series. It came out of necessity. The ideas deserved their own piece.

My thoughts penetrated the topic deeper than expected. I almost sank without reaching of bottom of it. I intended to build a bridge for sake of one passage in the above mentioned article. Yet, I find myself opening a door that I will probably keep open for now.

For the span of this text, you will be taken through an unusual exposition. Its conduct follows my rhythm and paints my intuitions.

Just as any creation, the world is an expression. The biggest and most encompassing of all. Just as any design, it is the manifestation of a constraint whose satisfaction seeks equilibrium and the dynamic of which maintains reality.

Only then, the omnipresent change we observe in everything takes a interesting meaning. It is no random process; it is a purposeful one. The world’s way of balancing its variables, which once evened out, everything will cease to become. And just as we go through steps to solve an equation. Reality is nothing but the by-product of a solving process whose steps are recorded as, the history of all creation.

In all of what I expressed so far, variance is the theme; the key to understand “how”.

The ever changing aspect of things makes control a desirable thing to possess. To effect and to predict become the most powerful acts one can perform. However, all of this cannot be attained without deep understanding of the mechanisms and interactions. Comprehension is then, control.

In any study, it is always possible to define a space. Such construction serves two purposes, (1) selecting the object of interest and (2) isolating its dynamic from external noise.

The formulation of observations becomes possible with the adoption of a basis — an ontology of sorts. Such act is akin to the choice of a point-of-view; an approach to describe what is possible within our space.

The choice of a basis is a choice of an emphasis. As a consequence, there exist no unique description of things; only relative ones.

The emphasis flows from the motivation behind study. We are curious about something and so, all we do is centered around explaining it. Yet it can happen, that further understanding requires a shift. Looking at the same things but from a different point of view. Such shift can be effected by a change of basis within the same space. The result of which, are new descriptions generated by the new basis.

During transformations of this sort, the objects of our space exhibit invariance. The descriptions change but not what they are about. The same way, everything shifts during a rotation except for the center.

Invariance is a core thing to transformations as it defines them negatively. This way, we understand variance through what is constant rather than what does change.

If we model each object in our space as a circle and its variance as a rotation, then its center would represent the invariant — that is, the object in-itself. The area of the circle would be the layer of description generated by the basis we chose. And anything outside the circle would be the layer of perception, that is, how the object is seen by the rest of the system.

During transformations, the description layer exhibits covariance — it rotates along. And so, if our object attempts to communicate with the rest of the system, its output is encoded in the updated basis. The perception layer has to adjust by rotating in the opposite direction — it contra-varies. Both actions cancel out so that the rest of the system recognizes the transforming object and manages to establish proper interaction with it.

Covariance and contravariance are two complementary processes which regulate the channels of exchange between both description and perception layers. That is, while the output of a transforming object covaries, its input contra-varies.

What about just regular objects? you must be asking. Not all object are necessarily transforming. Well, all objects are transforming at least in one way; into themselves.

If you are confused, read along.

No one would oppose the fact that we can find a system in anything, even the objects of a bigger system. We can — just like we attempt to describe the universe — define a space and apply the previous recipe of study. That is how we try to explain how something works and how it maintains itself.

The underlying dynamic of an object is what empowers us with an answer. Such dynamic will be laid just as stated before in term of the transformation of its components from one state to another and the result of which is, the transformation of the object into itself.

The universe is no exception. The constant variation of its parts makes for its persisting and self-altering aspects. A singular behavior which requires both description and the ability of self-perception.

To be within and without.

Knowledge Representationalist | «Seek power through nonother than beauty of expression.»