I’m an artist, writer, and human being.
To be a little more precise: I make video games, edit Wikipedia, and write here on LessWrong!
Yitz
Karma: 2,489
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.
An Introduction To The Mandelbrot Set That Doesn’t Mention Complex Numbers
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.
Do you mean that after your personal growth, your social circle expanded and you started to regularly meet trans people? I’ve no problem believing that, but I would be really really surprised to hear that no, lots of your longterm friends were actually trans all along and you failed to notice for years.
Both! I met a number of new irl trans friends, but I also found out that quite a few people I had known for a few years (mostly online, though I had seen their face/talked before) were trans all along.
Nobody I’m aware of in the local Orthodox Jewish community I grew up in though.(edit: I take that back, there is at least one person in that community who would probably identify as genderqueer though I’ve never asked outright) The thing is, many people don’t center their personal sense of self around gender identity (though it is a part of one’s identity), so its not like it comes up immediately in casual conversation, and there is very good reason to be “stealth” if you are trans, considering there’s a whole lot that can go horribly wrong if you come out to the wrong person.
Strong agree here, I don’t want the author to feel discouraged from posting stuff like this, it was genuinely helpful in at the very least advancing my knowledge base!
I notice confusion in myself over the swiftly emergent complexity of mathematics. How the heck does the concept of multiplication lead so quickly into the Ulam spiral? Knowing how to take the square root of a negative number (though you don’t even need that—complex multiplication can be thought of completely geometrically) easily lets you construct the Mandelbrot set, etc. It feels impossible or magical that something so infinitely complex can just exist inherent in the basic rules of grade-school math, and so “close to the surface.” I would be less surprised if something with Mandelbrot-level complexity only showed up when doing extremely complex calculations (or otherwise highly detailed “starting rules”), but something like the 3x+1 problem shows this sort of thing happening in the freaking number line!
I’m confused not only at how or why this happens, but also at why I find this so mysterious (or even disturbing).
Base rates seem to imply that there should be dozens of trans people in my town, but I’ve never seen one, and I don’t know of anyone who has.
I had the interesting experience of while living in the same smallish city, going from [thinking I had] never met a trans person to having a large percentage of my friend group be trans, and coming across many trans folk incidentally. This coincided with internal growth (don’t want to get into details here), not a change in the town’s population or anything. Meanwhile, I have a religious friend who recently told me he’s never met a trans person [who has undergone hormone therapy] he couldn’t identify as [their gender assigned at birth], not realizing that I had introduced a trans friend to him as her chosen gender and he hadn’t realized at all.
Could you give a real-world example of this (or a place where you suspect this may be happening)?
Can I write a retrospective review of my own post(s)?
Shower thought which might contain a useful insight: An LLM with RLHF probably engages in tacit coordination with its future “self.” By this I mean it may give as the next token something that isn’t necessarily the most likely [to be approved by human feedback] token if the sequence ended there, but which gives future plausible token predictions a better chance of scoring highly. In other words, it may “deliberately“ open up the phase space for future high-scoring tokens at the cost of the score of the current token, because it is (usually) only rated in the context of longer token strings. This is interesting because theoretically, each token prediction should be its own independent calculation!
I’d be curious to know what AI people here think about this thought. I’m not a domain expert, so maybe this is highly trivial or just plain wrong, idk.
Anyone here following the situation in Israel & Gaza? I’m curious what y’all think about the risk of this devolving into a larger regional (or even world) war. I know (from a private source) that the US military is briefing religious leaders who contract for them on what to do if all Navy chaplains are deployed offshore at once, which seems an ominous signal if nothing else.
(Note: please don’t get into any sort of moral/ethical debate here, this isn’t a thread for that)
I think this would be worth doing even if the lawsuit fails. It would send a very strong signal to large companies working in this space regardless of outcome (though a successful lawsuit would be even better).Edit: I assumed someone had verifiably already come to harm as a result of the chatbot, which doesn’t seem to have happened… yet. I’d (sadly) suggest waiting until someone has been measurably harmed by it, as frustrating as that is to not take prophylactic measures.
Thanks, this is great! I’ll print it up and give it a read over the weekend. Any other literature (especially from competing viewpoints) you’d recommend?
[Question] Literature On Existential Risk From Atmospheric Contamination?
I might have some time tomorrow to test this out on a small scale, will try to remember to update here if I do.
Thoughts on DALL-E-3?
Any recommendations for smartphone games with similar properties? I’m on a trip without easy access to my computer right now, and it would be nice to have some more intellectually challenging games available
Thanks for the great review! Definitely made me hungry though… :)