I had thoughts about a second May Mandelbrot post that got a bit deeper into the weeds, but a couple attempts today went nowhere (except the trashcan). But I been having some fun exploring the Mandelbrot with Ultra Fractal, and I thought some pictures might be worth a few words.
Click on any to see bigger versions.
I realized that, if I’m going to do the Mandelbrot in May, I’d better get a move on it. This ties to the main theme of Mind in May only in being about computation — but not about computationalism or consciousness. (Other than in the subjective appreciation of its sheer beauty.)
[click for big]
I’ve heard it called “the most complex” mathematical object, but that’s a hard title to earn, let alone hold. It’s complexity does have attractive and fascinating aspects, though. For most, its visceral visual beauty puts it miles ahead of the cool intellectual poetry of Euler’s Identity (both beauties live on the same block, though).
For me, the cool thing about the Mandelbrot is that it’s a computation that can never be fully computed.
One of those annoying-to-those-who-know-better shortcuts that movies and TV shows sometimes take is the visual trope of throwing a piece of wood (or a rock) at an “electrified fence” and producing an exciting shower of sparks. Typically, one character is just about to touch the fence, only to be pulled back just in time by another character who throws something at the fence to show the first character how they almost bought it.
It looks good — everyone loves a good sparking. In fact, you may have noticed how many action scenes take place in factories that seem mainly to manufacture sparks and steam. You may have noticed how often welders seem to be creating showers of sparks in the background of every action movie.
But this isn’t about our love of sparks.
Tick-Tock, goes the clock…
Last time, in the Determined Thoughts post, I talked about physical determinism, which is the idea that the universe is a machine — like a clock — that is ticking off the minutes of existence. The famous French mathematician, Pierre-Simon Laplace (the “French Newton”), was the first (in 1814) to articulate the idea of causal determinism.
We now know that quantum mechanics makes it impossible to know both the position and motion of particles, so Laplace’s Demon isn’t possible at the sub-atomic level. (It might be possible at the classical or macro level — that’s an open question.) Sometimes the issue of chaos theory is proposed as a counter-argument to determinism, so I thought I’d cover what chaos theory is and how it might apply.
If you want to skip to the punchline, the answer is it doesn’t apply at all.