Notes on operationalization

You may not be able to describe a thing if you are using that thing to describe itself. You may be able to describe what it does but not what it is.

Persistent controlled processes breaking down tend to produce more fallout compared to short-lived ones. If the methods of designing such processes are not considered, the accumulation-breakdown cycle is bound to continue indefinitely.

It is worth first admitting the logical convenience in criticisms of operationalization and of its offspring that will follow. However, there are good reasons for them to exist, because a model can be said to be unfalsifiable until enough time or operations pass for it to break or persist, depending on the requirements and fault tolerance. Unlike models, the criticisms of operationalization themselves are falsifiable and may not even require experiment; it only takes to misassign or misrepresent a variable, operator, definition for a system to collapse or cascade into something different.

The first section, not much unlike the others, is effectively an interpretation of Goodhart’s law that uses Alfred Korzybski’s terminology to make its points. The text is semiformal and could see amendment or removal of parts in the future.

1

Concerning models and reality, it is likely that the meaning of their divergence is not the same in all scenarios, where the same mistake makes for different implications that do not necessarily have to follow the same story.

In each of them, reality can become a parody of itself if the descriptions and treatment continuously misrepresent it. One may use X but call it and treat it as Y which only in some cases is X-like. The parameters picked for the model end up making the measurements a user’s reality.

Starting Propositions

I. The map may already be the territory. Standard recommendation implies there is a map-less position available, but in this context mapmaking as an a priori does not exist and the map is already complete and in use. Scenario: decisions can only be made based on the territory’s description where further inquiry into the territory is either disallowed or no longer possible.

II. The map in use changes the territory. Scenario: decisions made based on the map result in the perversion of the territory. Further divergence between the map and the territory may follow.

III. The map can become the territory. Scenario: decisions made based on the map produce such results that the map starts matching the territory in a literal sense.

Secondary Propositions

– Initial territory may be unchangeable, in which case it would be fundamental. Example: the new version references the initial territory but certain behaviors differ. The fundamental behaviors can still prevail in the end.

– Where the notion of fundamental territory (such as certain laws) does not exist, the initial territory is completely replaced by the new territory. There is no foundation to remain.

2

A decision-maker must operationalize both the system and himself as the interactor with all his extensions.

The model that includes the interactor, and the model that does not, may not be the same model. A system that responds to the interactor’s input and presents outputs to his “control centre” is different from that system’s model.

Attempting to specify further and make a distinction from the observer effect in physics, we say that the act of taking a position in the modelled system must change the model.

To be completed, the model without the interactor can be assigned and tolerate uncertainties. It is tempting to speculate that the model including the interactor cannot tolerate uncertainties to the same degree.

The statements turn out to be parallel also to Stafford Beer’s work in management cybernetics.

3

We introduce the uncertainty of what a parameter is, and can assign a probability to its value or definition.

A number of possible values of a parameter can be assigned probabilities. One may go as far as necessary in terms of the increments of possible values, in case it is useful to have such a scale.

This would produce a kind of probability distribution. Given many guesses of a value’s probabilities, many overlapping distributions may be produced. Multiple values in a problem can be uncertain, which in this context would produce a joint distribution.

The definition of a parameter can be questioned in its entirety, and probabilities can be assigned to that as well. In a given equation, this can manifest as the probability of the parameter being measured in one unit as opposed to another.

4

In order to describe operationalization, it must first be operationalized. Starting with a broad measure, we can specify system-dependent degrees of freedom that allow things to exist within it.

Parameters have degrees of freedom to their changes. There is some form of control given that this freedom is usually constrained by limits. The concern being that in many cases, its complete dynamics may be assumed to be under control when they are not. Not only is the function in force, the dynamics of the function itself might not be fully captured.

The function dynamics can be described as compact or noncompact. Closing things as either direction is traversed results in a negative description of freedom. This would be a definition of the parameter space bounds at the lowest level. Another subject is what to do with known bounds. Finite, unchecked, or infinite data point notation can be used for nodes in a graph or other relational structure.

Having obtained incomplete data may not allow the specification of bounds. Generalizing the sufficiency of the data required to specify bounds in any system may be impossible.

Accepting bounds as unknown in such a case might still allow the decision maker to use the model, where the system gets treated as being under sustained exploration. The acceptance of unknown bounds would still likely require the ability to recognize system-dependent infinities or explosions.

Available data might be sufficient to establish that the parameter or a region of the parameter space takes a particular value and provably not something else, which would be a positive description of freedom.

5

Beyond functional terms, a dependency metric can be used to describe parameter constraints. This may come in the form of sets, directed graphs, and other structures, depending on the interpretation.

An element can belong to many sets, or a set can contain many elements, making for two control directions. A directed weighted graph node can be pointing to many others, or many others can be pointing to it, also making for two control directions. The principle is one-to-many versus many-to-one as a form of control where the individual node (parameter) is in focus.

It generally follows that a large number of connections make for higher collective weight or less concentrated pull. A small number of connections with high concentration of weights produces its own respective control.