<Horizontal/Vertical> knowledge.

Few days ago, I realized that the making of knowledge is comprised of two kinds of movement instead of one. When you inquire you aren’t just moving through a tunnel but rather walking the surface and across the levels of a tractricoid-like structure.

This realization shed light on something interesting I choose to briefly expose here. I will start by saying that so far I have been fine with the idea of inquiry as being a journey — a linear path — because nothing seems to be wrong with the idea locally. It is like living with the thought that earth is flat which seems to be a fair claim when we look around and honestly lines are just good enough that we don’t need to consider curves. But as you know flatness can be subsumed under the idea of roundness as a special case of it. Implying that, there is a nontrivial generalization available to use that is not “if it is the case here, then it must be the case everywhere since I can say this everywhere” but more like “there is a bigger picture in which it is possible to say this everywhere while the picture is something entirely different”. This kind of thinking lead me to entertain a similar idea about inquiry.

My idea is to say that as inquirers we are living in a structure that allows two kinds of motion aimed at the making of knowledge. I termed these motions horizontal and vertical to emphasize that they are independent and essentially produce two different kinds of knowledge.

A horizontal movement of the inquirer expands his knowledge without adding something new. It is the act of exhausting the possibilities and reaching the limits of use of that knowledge. It aims at successfully consuming all that there is by combining and arranging the distinctions at the base of our knowledge in all possible ways. When you move horizontally you stay at the same level and cover as much ground as possible. I call this expansion. There is one level in the structure which is the largest and I term it, THE disk.

A vertical movement alters the form of the knowledge the inquirer accesses by adopting or dropping distinctions. That kind of movement takes you from one level to another. The highest level is called the concept-level while the lowest is the instance-level. A downward motion — descend — is associated to the action of specification which implies addition of further distinctions. An upward motion — ascend — is associated with generalization.

It is clear that if we start from a concept-level (highest-level being made of the smallest amount of specifications possible) of understanding and enrich it with further distinctions, we get bigger levels up to the point where there could be no further distinction to be made — THE disk-level— and that anymore specifications will just cause restriction of the levels down to the instance-level (lowest-level being made of the biggest amount of specifications possible). This and the fact that each level is a horizontal expansion outlines the topology of the inquirer’s world.

Familiar intellectual actions like abstraction (the effect of the ascend work) and the range-of-use investigation of a novel science and its interaction with already existing sciences (expansion work) can be fairly explain employing this view of inquiry.

A first utility of the <horizontal/vertical> distinction is to use it to characterize what kind of knowledge one possesses, to better frame his understanding and have a grasp on how to move purposefully within the abstract world. A vertical understanding of something means that you know how it was constructed from instance to concept level. You know what are the minimum relevant distinctions at each level and how they relate across levels to make the spine of the full framework. A horizontal understanding of something means that your knowledge is focused mainly on one level which implies that you will trace lines within the level employing the base distinctions to points of interest — pieces of information. And by doing so, you can generate all what can be possibly known at that level of description.

Now what about a new kind of movement? A combination of both. A diagonal movement is one which moves us across levels and within a given level. A diagonal understanding is one where you are starting at a certain level of understanding and make it to a specific point of interest within the structure by taking the shortest available path (let’s say). You would either ascend or descend to the appropriate level then expand in the direction of your point of interest — the information you are trying to fit in your understanding. A diagonal understanding is what we aim for when we don’t have time to go through the whole framework and we are interested in a very particular thing in it relevant to our use. As you must realize this is just a shortcut and can’t substitute a full (vertical+horizontal) understanding of the framework. Suppose that we are situated somewhere in the structure, there isn’t a unique way leading to some point of interest. There is a multitude of ways which correspond to viable diagonal moves one can perform.

The second utility is revealed within the <problem/solution> distinction. Problems and solutions are just pieces of information that are related to the rest in certain ways. Problems are pieces of information which forward a gap in our comprehension by virtue of lacking connectivity with the rest of our understanding. A solution would be whatever solves the issue of connectivity so that understanding isn’t lacking anymore. Problems that appear at one level can be solved either within the same level or at a different one. If it can be solved within the same level it is a matter of coming up with the right combination to make up a line connecting the problematic point to the rest — or to the base distinctions, since everything in that level is made from the combination of that base. Some problems require us to go to another level where the problem finds origin. The understanding in this case doesn’t perform well vertically even if it is good enough horizontally. Once the right formulation is found at that problematic level, we will have a structure that offers the possibility of a solution at the level of interest. In other words, we will have a scheme of understanding which when lifted up or pushed down will reveal a potential connection between previously unconnected pieces of information.


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