I agree with you when it comes to humans that an approximation is totally fine for [almost] all purposes. I'm not sure that this holds when it comes to thinking about potential superintelligent AI, however. If it turns out that even in a super high-fidelity multidimensional ethical model there are still inherent self-contradictions, how/would that impact the Alignment problem, for instance?

What would a better way look like?

imagine an AI system which wipes out humans in order to secure its own power, and later on reflection wishes it hadn't; a wiser system might have avoided taking that action in the first place

I’m not confident this couldn’t swing just as easily (if not more so) in the opposite direction—a wiser system with unaligned goals would be more dangerous, not less. I feel moderately confident that wisdom and human-centered ethics are orthogonal categories, and being wiser therefore does not necessitate greater alignment.

On the topic of the competition itself, are contestants allowed to submit multiple entries?

I remember a while back there was a prize out there (funded by FTX I think, with Yudkowsky on the board) for people who did important things which couldn't be shared publicly. Does anyone remember that, and is it still going on, or was it just another post-FTX casualty?

Thanks for the great review! Definitely made me hungry though… :)

For a wonderful visualization of complex math, see https://acko.net/blog/how-to-fold-a-julia-fractal/

This is a great read!! I actually stumbled across it halfway through writing this article, and kind of considered giving up at that point, since he already explained things so well. Ended up deciding it was worth publishing my own take as well, since the concept might click differently with different people.

with the advantage that you can smoothly fold in reverse to find the set that doesn't escape.

You can actually do this with the Mandelbrot Waltz as well! Of course you still need to know each point's starting position in order to subtract that for Step 3, but assuming you know that, you can do exactly the same thing, I believe.

Thanks for the kind words! It’s always fascinating to see how mathematicians of the past actually worked out their results, since it’s so often different from our current habits of thinking. Thinking about it, I could probably have also tried to make this accessible to the ancient Greeks by only using a ruler and compass—tools familiar to the ancients due to their practical use in, e.g. laying fences to keep horses within a property, etc.—to construct the Mandelbrot set, but ultimately…. I decided to put Descartes before the horse.

(I’m so sorry)

By the way, if any actual mathematicians are reading this, I’d be really curious to know if this way of thinking about the Mandelbrot Set would be of any practical benefit (besides educational and aesthetic value of course). For example, I could imagine a formalization of this being used to pose non-trivial questions which wouldn’t have made much sense to talk about previously, but I’m not sure if that would actually be the case for a trained mathematician.

Do you recognize this fractal?

If so, please let me know! I made this while experimenting with some basic variations on the Mandelbrot set, and want to know if this fractal (or something similar) has been discovered before. If more information is needed, I'd be happy to provide further details.