“You start to unavoidably wonder: are we alone in the universe?”
— Chris Hadfield, astronaut, formerly commander of the International Space Station
The Mandelbrot set knows us — may be another way of asserting the same mystery.
The Mandelbrot set renders everything infinite — and we have not thought about the space around the Mandelbrot elements. Mathematical space — how numbers carve themselves out, or cast a shadow, in mathematical space. Mandelbrot himself pointed out that when he started to see the pattern, he began to understand the “set.”
By “set,” he meant the mathematics that were concealed in apparently rough, unordered textures, but which concealed an underlying order progression.
Mathematics and consciousness of form
By pattern, he meant the shape, a geometry between numbers, operations, procedure steps, in equations. Wikipedia’s article on the Mandelbrot set shares the following:
The equation expresses how the shape referred to as “the main cartioid” is the seed of all the shapes that flow from it, and is itself the coordination of detail just “below it” or within it, on smaller and smaller scales of reference.
In the study of consciousness — cognition — we call this conversion of one motion and calculation into another, “synesthesia.” To feel together. Sound as visible. Color as having sound, shape, form, pattern. Mathematical space is not shapeless — though it may seem axiomatic to insist that it is.
— Gifts Delight Laminated 44×16 Poster: Functional Fractals Mandelbrot Set in F – Michael Heasell —
The more you know, the smaller you are
Our notion of exactitude is related to detail. You cannot have an accurate representation of anything, if there is no detail in it. But, now the units of how that detail is rendered, become relevant. The more exact we become, the more detailed our representation of anything — say, the coastline of England — the vaster it is.
The coastline of England, where the universe vanished
The coastline of England, said Mandelbrot, becomes longer as we make it more and more exact. We measure a cove that is a mile wide, then little wobbles and irregularities in the shape of the cove. As we move to individual rocks, grains of sand — as we get more exact about the length of something — the more texture and detail emerges Individual pebbles. Soon, we get more and more detail: we plunge into the atomic level and now it is vast — and it is soon infinite.
The Mandelbrot set knows us — in expanded and detailed versions. By the way, we mentioned Benoit Mandelbrot, who referred to himself as a “fractalist,” in our article Are UFOs changing our consciousness?
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