#57 Extremely complex behavior from extremely simple systems

The Cybernetic Brain: Sketches of Another Future by Andrew Pickering

“The motto of Wolfram’s New Kind of Science (2002) is ‘extremely complex behaviour from extremely simple systems,’ and this is precisely the phrase that goes with the earlier cybernetic discovery of complexity. Whereas the cyberneticians built machines, Wolfram’s work derives from experimentation with very simple formal mathematical systems called cellular automata (CAs). And Wolfram’s discovery has been that under the simplest of rules, the time evolution of CAs can be ungraspably complex—the only way to know what such a system will do is set it in motion and watch” (Pickering, 2010, 30).

I’m reading Pickering’s Cybernetic Brain at the moment and came across a so-called genius whom I’ve never heard of before. His name is Stephen Wolfram and is known in part for his research in cellular automata. As the quote says above, complex behavior from cellular automata comes from simple systems. The computation starts at time 0 with a number of different looking cells, and over time these cells begin to form a grid-like composite. The only way to find out what the image will look like is to let the system run and see what happens.

Computations can happen in different dimensions. What troubles me the most, or the computation that gives me the most angst, is the Sierpiński triangle. Imagine one large triangle and then theoretically infinite smaller triangles within triangles. If you click on the Wiki link to cellular automata above, you’ll see the image of a two-dimensional Sierpiński triangle. The 2D version of this triangle makes me anxious once it becomes three-dimensional, as if it were a space I’ve been to before, a remembering of something, or perhaps experienced something like it during one of my previous psychedelic voyages. This kind of Mandelbrotian geometry gives me the goosebumps.

To give you an idea of what I’m talking about, here is a YouTube video of a 3D Sierpiński triangle. The idea of going infinitely deeper into the image that is determined by pure mathematics is mind-boggling. Is it the fact that it never ends that makes me nervous? I suppose infinity can unsettle the finiteness of one’s human condition, unlike the infinity of math sets. Further, we can only dive as deep into the fractal triangle depending on the computation power of our computer. If infinity is infinite, then, no matter how AI-ed our systems, those too will never reach an end point. We can dig as deep as possible and likely find nothing or merely repetition ad infinitum.

What interests me is what we could find by going ever deeper down the fractalized rabbit hole in our computer. Might we find artificial life? Might we find the spark of some kind of digital life form, perhaps an advanced civilization of conscious beings that took eons to evolve and mature, yet only seconds for our quantum computer to generate in our realm. I’m reminded of the film Tron: Legacy (2010), the second installment of the Tron film franchise, wherein the main character from the first film, Kevin Flynn, discovers “isomorphic algorithms (ISOs)”, a kind of spontaneously occurring artificial life form within the limits set in the computer’s software and/or hardware. What could we find apart from beautiful mathematically constructed latticed architecture?

Another reason these Mandelbrotian fractal geometry sets give me the creeps is because they don’t resemble anything human (at least at present-day). It’s alien; as alien to me as a hornet’s nest looks on the outside or a termite or ant colony might look on the inside. The thought I can’t get away from is this: considering these Mandelbrotian sets and psychedelics produce similar patterns, will human architecture and the human’s world evolve into precise, mathematical configurations as we begin to understand more about psychedelics, artificial intelligence, quantum mechanics, and subsequent scientific revolutions in mathematics and physics? Or, might we have two worlds in the future: one baseline, biological and physical, and the second, virtual, silicon, and perhaps nonphysical?

Back to the quote at the top, I wonder whether there is a connection between Wolfram’s motto—“extremely complex behavior from extremely simple systems”—and Occam’s razor. Does the simplicity of Wolfram’s claims about cellular automata suggest something important that we should be looking into or that we’ll discover in both carbon- and silicon-based substrates/universes? I won’t delve too deep into transhumanism here, but it makes me wonder whether humans will eventually merge with their technology, able to navigate both physical and virtual worlds at their discretion, and will the virtual seem as physical as the baseline physical world? Personally, I think moving between worlds with different experiences of time would drive one to insanity, because getting lost in or convinced of the reality of the virtual would produce a shock to that person who returns to the physical world. Derealization would set in. Similarly, temporary or permanent derealization is a common side effect from taking psychedelics.

In sum, there are many connections between psychedelics and Mandelbrotian fractal geometry, especially this new concept I’d never heard of called cellular automata. I must look into this more and I want to read Wolfram’s mammoth 1000-plus-page book, A New Kind of Science (2002).

Pickering, A. (2010). The Cybernetic Brain: Sketches of Another Future. The University of Chicago Press.

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