One of my favorite discoveries in life is the Mandelbrot set. Considering it gives me a strong sense of the numinous. I’ve been enthralled by it ever since Fractint, an MS-DOS program that generated fractals. I’ve posted about it a lot here; today I want to take you into the heart of its chaotic behavior.
The Mandelbrot set has a number of properties that make it such a fascinating study: Firstly, it demonstrates chaos theory. Secondly, it demonstrates how complex patterns can arise from simple beginnings. Thirdly, it reveals a problem concerning real numbers. Fourthly, every pixel is a demonstration of Turing’s Halting Problem. It’s also infinitely complex and incredibly beautiful.
Today we’re going to explore the shore of the Mandelbrot lake.
6 Comments | tags: chaos, chaos theory, fractals, Mandelbrot, Mandelbrot fractal | posted in Science
Lately I’ve been reading about compatibilism with regard to free will. While I’ve considered free will before, especially in the context of determinism, I’ve never explored compatibilism, and I decided it was time I got around to checking it out.
What triggered my renewed interest was, firstly, the movie Arrival (and the short story on which it’s based), and secondly, the HBO series, Westworld. Both have thoughtful science fiction with themes concerning free will (or its lack).
When one of my favorite physics bloggers, Sabine Hossenfelder, wrote a post about free will, it inspired me to write one, too. Monkey see, monkey do!
103 Comments | tags: causal determinism, chaos, chaos theory, determinism, free will, physical determinism | posted in Opinion, Philosophy
It seems fitting to take this opportunity to write a Sideband post the way I had originally intended when I began them. That intent goes back to the beginning; the first Sideband post was my second post here. For better or worse, the original intent didn’t last long.
In fact, it’s hard to see much difference between the Sideband posts and the other posts. That probably reflects a lack of focus on the main topics. Sidebands were intended for stuff that was off topic. But I’ve been so all over the map on topic that at least one blogger asked if I had a short attention span. [insert here one of the short attention span jokes you’ve heard before]
That’s not going to change. I’m eclectic; so is my blog. Sidebands will evolve. For now, here’s a Sideband on yesterday’s post, just like Blogger originally intended.
2 Comments | tags: chaos, chaos theory, fractals | posted in Math, Physics, Sideband