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.
On the one hand, a main theme here is theories of consciousness. On the other hand, it’s been almost eight years blogging, and I’ve covered my views pretty well in numerous posts and comment threads. Our understanding of consciousness currently seems stuck pending new discoveries, either in answering hard questions, or in providing entirely new paths.
A while back I determined to step away from debates (even blogs) that center on topics with no resolution. Religion is a big one, but theories of mind is another. Your view depends on your axioms. Unless (or until) science provides objective answers, everyone is just guessing.
But it’s been three-and-a-half years, and, well,… I have some notes…
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!
Over the last few weeks I’ve written a series of posts leading up to the idea of human consciousness in a machine. In particular, I focused on the difference between a physical model and a software model, and especially on the requirements of the software model.
The series is over, I have nothing particularly new to add, but I’d like to try to summarize my points and provide an index to the posts in this series. It seems I may have given readers a bit of information overload — too much information to process.
Hopefully I can achieve better clarity and brevity here!
I’ve written here before about chaos theory and how it prevents us from calculating certain physical models effectively. It’s not that these models don’t accurately reflect the physics involved; it’s that any attempt to use actual numbers introduces tiny errors into the process. These cause the result to drift more and more as the calculation extends into the future.
This is why tomorrow’s weather prediction is fairly accurate but a prediction for a year from now is entirely guesswork. (We could make a rough guess based on past seasons.) Yet the Earth itself is a computer — an analog computer — that tells us exactly what the weather is a year from now.
The thing is: it runs in real-time and takes a year to give us an answer!
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.
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.