Thursday, August 25, 2016

Getting At the Collapsed Dimension

aka Disembodied Navigation of High Dimensional Reality

Alex Grey – Sacred Mirrors

Oops. I just dropped a clear thumbtack on a white floor. I used to hate that, until I learned the trick. You have to collapse the dimension.

Without hesitation, I drop to the ground, lowering my plane of vision until I’m sideways, eyesight scooting across the surface of the floor, until – there it is; I found my thumbtack.

From above, the visual information of the tack is similar to that of the floor. There’s no edges to be distinguished. Viewing the floor as a one-dimensional line (once your head is level with the floor) instead of a two-dimensional plane (as seen from above) makes the thumbtack plain-as-day. The thumbtack is then the only thing that penetrates into the second dimension – it is the only thing that raises above the floor.

If what you’re trying to do is disentangle the information of the tack from the information of the floor, then reducing the information of one make the remaining asymmetry obvious. A floor is essentially 2-D, and a tack is 3-D. And by “collapsing” your visual field to 1-D (by now seeing it as a line stretching above and below you, with the floor on one side and everything else on the other), the “leftover dimension” of the tack becomes immediately apparent. This is not so much about science-fiction space-folding dimensionality, but about information in general.

In the highly abstract, “disembodied” discipline of information science, dimensionality is not about space, or what I like to call body space. Body space is the three dimensions we are so familiar with, it is a volume and we are in it. But this is only one way of using dimensionality. (The imaginings of Flatland will only get us so far.) In essence, a dimension is a line of potential measurements. It doesn’t have to be about direction like NSEW. It can be in lightness or darkness, as in the one-dimensional measurement of the rods in our eyes. The spectrum of colors is another one-dimensional measurement used for seeing. Together, these two dimensions can generate a third piece of information which is the point in-between the two (and is the difference between pink and navy blue). This is now a measurement of the two measurements. The very idea of dimensionality is for creating this information space as a way for recognizing and manipulating complex patterns in our environment.

Color uses three dimensions, which are lightness/darkness, red-blue (rainbow spectrum), and brightness/dullness (similar to but not the same as light/dark). So “color” is (according to art academia) a piece of 3-D information; it is a measure of the three measurements. And vision in general is not dependent on color alone, but other things, particularly spatial positioning. But let’s stick to color.

What happens when we compare color to smell? Things get different. Smells only have two dimensions, “good” and “bad”. Then again, and just as valid, smells can have infinite dimensions. Recognizing a smell as “good” or “bad” is the highly subjective alternative, and shows more about culture and the individual than it does the smell itself. There must be another way.

To date, there is no comprehensive, universal organizing principle for odors. Some attempts use a multidimensional odorspace, such as Henning’s prism. Theoretically, any smell can be categorized, or identified, as a point in a prism. The vertices of the prism are Flowery, Foul, Fruity, Spicy, Burnt, and Resinous. Something called “Fruity” will sit right in the corner of the prism. Other odors can be in-between two or more odors, so that “Citrus” might be somewhere between Fruity and Flowery (and just a bit towards Foul?).  This is how odors start to drift away from the vertices, and then the edges, and then from the planes themselves into the middle space of the prism. Again, each point, or odor, is now in-between all the odor-classifying vertices. Technically this is a hybrid model, because there are 6 primaries, but the corresponding odor-points are represented inside a 3-D form. (Please note that the original Henning’s odor prism was meant to deliver information on the edges and between the vertices; the smells were not meant to be read inside the prism but on its surface, making it only a 3- or 4-dimensional odor space.) [By the way, check out this Cabinet article on other ways of organizing scents.]

Hennings Odor Prism

There is another way one can imagine a wheel with 6 spokes, where the points at the end of the spokes are primary odors (popcorn, mint, lemon, etc.).  Every identifiable smell looks like a misshapen, spiderwebbed splat reaching further outwards towards the smells it is similar to, and sinking down to the middle where it isn’t. This is a hybrid also, for the final piece of information is a 2-D shape, based on 6 dimensions.

Let us try one more. Imagine a ball with spikes sticking out in hundreds of directions, each one a primary odor. Any given odor is understood as being “between” these hundreds of primaries, as a measurement of the hundreds of measurements.

Here’s an example of a Radar Chart.

This is the idea of a high dimensional information space. It’s a pretty alien idea to us body-users, but not to the algorithms that run our lives, and apparently not to the nose on our face. Thinking about how we categorize smells is perhaps a step in the direction of making ourselves more at home in high-d reality.

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