Behold the
Mandelbrot Set, a world-renowned image and a powerful symbol of infinity. The mathematical concept it illustrates is one of the most intuitive --it describes self-similarity-- and yet it remained unknown, even unbeckoned and unsought-after, until the advent of the modern computer. This dormant formula only came to life after iterations so numerous as to be considered infinite were the human hand the one computing. The computer showed us what a simple formula could do, if you scale it up. It shows us a behavior, not of things, but of space-time itself.
I wake up to the sound of rain, splattering. Then I wake up some more, and realize it's not rain.
It's coming from the ceiling. The plumbing. One hundred years of building and habitating and changing and changing has left me with an unfortunate design that is now leaking water from a ruptured pipe above the kitchen ceiling, and into my pantry closet.
Now I am fully awake, and fully out of bed, and pulling out all my things from the closet. I am transporting a 3x3' closet's worth of possessions to a 10x10' back room, and hastily.
The plumber has come and gone, and the handyman who repaired the closet. It's time to replace my things, to fill the closet again. But all I can do is stare at the sprawling piles of stuff, that was once compacted, compressed into a 3x3' closet. How did all this stuff possibly fit in that little closet. And it occurs to me -- this is fractals.
We are all familiar with the general idea of fractals, the Mandelbrot set, the self-similarity, the LSD. But that intuitively recognizable feature is an outcome of an underlying objective. The reason a fractal looks the way it does is because of its space-filling behavior, which itself is a function of growth limited by space. In order to keep jamming more and more stuff into that space, you have to follow the fractal formula.
A better example of fractals is not a tie-dye t-shirt but the coast of England. If you were to measure the coastline of England with a one-mile long measuring stick, it would be a pretty vague approximation of the coastline, but with a defined length.
Then if you were to measure with a one-foot stick (which would be ironic), you would get a much better approximation, but also a much larger coastline, because now that your shorter imperial stick can reach into all the nooks and crannies, it makes the total length that much longer. In fact, the smaller your measuring stick, the longer the coastline.
By this reasoning, the length of the coastline is infinite. In other words, it is not a 1-D line at all. Yet neither is it 2-D. It is 1.456-D, or maybe 1.879-D; it is a fraction of a dimension.
When you fill a closet with things, it doesn't just happen all at once. Sure, you start by "filling" the closet. But over time, as you use the things and remove things, add more things, and rearrange, you are filling the space more and more. But you're not just filling it with things now, you're filling it with intelligence.
The more time goes by, and the more you use things, remove, add and rearrange, you are going to fill all the nooks and crannies of that 3-D space until it is no longer 3-D. It becomes a fraction of a dimension.
Then, when you take everything back out, you collapse the extra fraction that you helped to create. When the things come back into normal 3-D space, they seem bigger in aggregate, they seem to have
gained size in the process. The closet is now sprawling across an entire room. That difference is fractals. (It's also because the 3-D closet is now spread across a 2-D floor; but that doesn't account for all of it's 'enlargement', as the same phenomenon is experienced with filling a box truck on moving day).
If we could extrapolate this to the 4th dimension, what would we be talking about? Or do I need to be on acid to have that conversation. Maybe an easier question would be -- what does the airtight Tetris block have that the jumbled pile of pieces does not? (Well, it doesn't have air, obviously.) But besides that, it's the entropy. The block is ordered, and the pile disordered. The pile is a random mess, and the block an intelligent artifact.
I hadn't thought of my catch-all pantry closet as an intelligent artifact, yet here it is, an entropy-reversing portal that uses intelligence to loop out of it's limited dimensions.
Post Script:
It is still hard to see the pantry closet as having something to do with intelligence. Try taking it out and putting it all back so it fits. Then you'll see how much "intelligence" went into its arrangement. The difference is that in its natural state, the closet possesses an accumulated intelligence. Over time, as you use all the things in the closet, your intelligent behavior leaves its residue on the things in it. It is a storage depot, not of things, but of an arrangement.
Post Post Script:
[I start looking up these deepdream images and I have to post them all.]
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[can't find source bc pinterest; thanks obama]
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| Style Transfer, which is not the same as DeepDream, but does use neural nets, i.e., robot brains. Link. |
