Modelling Uncertainty

When I was a child, I didn't live in space. Adolescence was a time of unpleasant and sudden captivity to Euclidean space. "Normal" sizes. Fat redistribution. Occupying space in general. Adulthood, hopefully, is realizing that Euclidean space is a metaphor for Being, and not the other way around. The primacy of the flesh, in other words, comes to a gradual end in adulthood, if you ever get there.

Being is about minimizing distances, or maximizing probabilities. Definitions, distinctions, are classifications and conjectures. Classification or hypothesis seeks to capture the essence of the thing. And the essence is may not be a spatial boundary. If awakening is coming to Being as it is, awakening is about learning to think in the logos itself, and not in a simile of it. But coming out of adolescence, it feels more like the simile is the thing itself, and that the logos is the derivative.

Non parametric models are about thinking non-spatially. You're still identifying an object, you're still looking to make an objective case of some sort, but the objects are no longer balls in the air. They have no theater image at all. Their essence is not something you can "picture." The systems of equations, which find the line between thing-we-are-seeking and no-cigar, is still there, but the gravitational pull is no longer about falling to a minimum in a straight line.

The line should not be underestimate. I am not here to disparage straight lines. There really are straight lines, even if surfaces are never truly straight. The model still comes first. Whether the model captures the essence of a thing, being the question, makes it seem ever more trite and precious that a line might ever serve as a model for any boundary, however. The line between A and B, thing and not thing, theta and error, must be something much more like a surface. Under the electron microscope, no less.

Not a surface inside of a given space, however. A surface that is instead the grounds of the space, where the space and the qualitative proximity are defined in one divine flick of the light switch. And then there was always light. And of course there's the moment you realize that you have always been in a universe of symbols, and living in space was always secondary. Sometimes the linear regression has an r squared of -6,000,000. And yet there must be truth in every phenomena. There must be a something that is happening.

But probability is not distance. When I try to think of it as something like a proximity, I cannot. But I can think it through, as a qualitative proximity. A qualitative proximity that has a feeling of proximity. A magnetism, a gravity. Something more like a bunch of black holes in spacetime, whose qualitative proximity is based on the gravitational pull of of the coefficient, which brings the model "closer" to the posterior at that data point.

And yet proximity is still, for all of its objectivity, is still parametric. There is still a hint of the metaphor of Euclidean space there, yet wobbling like ear drums. You still have to push past that. There are so many ways to triangulate on the essence of a thing. Think of the heptapods. Raspberry and Flapper. Sentences do not need to unfold in this awkward unraveling. The logos can be captured in a symbol, with cues for grammatical cases. Who did what to whom is not a sequential answer.

These days the execution is out of the box. Random forest is the pen tool of cutting out a phenomenon around the edges. Gradient descent is the magic wand. Really whatever works, though, right? I can see how you might model with a million other kinds of proximity. And still the world is our home, giving language to the metaphors that might speak to our flesh. Proximity is not any less real, it's just another version.