Wednesday, November 30, 2005

Scales and Perception

Character is like a tree and reputation like its shadow. The shadow is what we think of it; the tree is the real thing. --Lincoln

This painting is Lavender Mist by Jackson Pollock. One approach to understanding it is given by Harley Hahn who describes how Lavender Mist leverages our subconscious to inspire a range of feelings and thoughts that spring from its suggestive colors and composition.

If we saw this very same painting on the floor-covering canvas of a room in the process of being repainted, we would think not much of it. Instead, it is thrust upon us by Pollock and so we focus our attention on it. Like walking past a dull mirror, we are allowed to see in it what we might see. We stop and we are transfixed. Perhaps the colors and patterns bring to mind struggle and hope, potential and confusion, or some other complex combination of feelings and thoughts. Whatever meaning Lavender Mist has, it is clearly subjective.

If we hadn't known that Pollock was an established artist we would not have been able to guess so from this painting. There is no critical agreement by experts or any other significant subset of viewers as to the meaning of Lavender Mist, but one thing is clear: when viewed from less than five inches or beyond 50 feet, it is nondescript. Whatever structure it has, Lavender Mist is meaningful only within a small slice of a distance dimension. Even abstract projections of the visual information of the painting at cognitive distances outside a limited range end in the amorphous. No matter how moved we may feel by Lavender Mist when seen from five feet, the range of meaning of this painting is strictly bounded. Sometimes a drip is just a drip. Yet, there is something that we recognize as "truth" in our consideration of the painting. It can be evocative as well as provocative.

But people think and feel characteristically in different ways. Freud suggested a psychoanalytic model that seems to be of some applicability here. The Id type of thinking was recognized by R-Doh who observes the debate and remarks:
How disgusting. Obviously, Bitch can't think:

“What’s interesting is that you’re trying to frame this debate around the ‘personhood’ of a fetus, while completely overlooking the personhood of women.”

Let's see. I know I've analyzed this kind of behavior before. What could it be? Where could it be?


Oh, yeah! Limbic dominated thinking.
Perception on this scale is instinctual, not factual.

Now consider an image of the Mandlebrot set generated by the program WinCIG. We can recognize self-similar structures at different scales and amazing meta relations. While we can use the program to infinitely explore scales and discover an amazing variety of apparent complexity, the information throughout the entire range of scales is finite. In fact, the essential information can be related in a single mathematical formula. There seems to be "truth" in this graphic as well. This truth is objective.

These two graphics are related in that they are presented on a computer screen with a finite number of bits per pixel and a finite number of pixels. The information of both is compatible, appreciable, and quantifiable. The information from one can be communicated to the other by a bijective mapping of pixels--a set of rules for communication within limits of modern technology. Rather than a bit to bit mapping, we communicate information using encodings that are lossy, of certain robustness to transmission errors, and may or may not be decoded faithfully. In both cases we choose the source encoding and ultimate embedding of the information at the receiver. This ability to choose is the shared mystery of Pollock and Mandlebrot.