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Well, now I'm wondering - is neural network training chaotic?
This is awesome, I would love more posts like this. Out of curiosity, how many hours have you and your colleague spent on this research.
1In my personal experience, exposure therapy did help me with the fear of such "extreme" risks.
In the very beginning of the post, I read: "Quick psychology experiment". Then, I read: "Right now, if I offered you a bet ...". Because of this, I thought about a potential real life situation, not a platonic ideal situation, that the author is offering me this bet. I declined both bets. Not because they are bad bets in an abstract world, but because I don't trust the author in the first bet and I trust them even less in the second bet.
If you rejected the first bet and accepted the second bet, just that is enough to rule you out from having any utility function consistent with your decisions.
Under this interpretation, no it doesn't.
Could you, the author, please modify the thought experiment to indicate that it is assumed that I completely trust the one who is proposing the bet to me? And, maybe discuss other caveats too. Or just say that it's Omega who's offering me the bet.
So you say humans don't reason about the space and objects around them by keeping 3d representations. You think that instead the human brain collects a bunch of heuristics what the response should be to a 2d projection of 3d space, given different angles - an incomprehhensible mishmash of neurons like in an artificial neural network that doesn't have any CNN layers for identifying the digit by image, and just memorizes all rules for all types of pictures with all types of angle like a fully connected layer.
I guess I was not clear enough. In your original post, you wrote "On one hand, there are countably many definitions ..." and "On the other hand, Cantor's diagonal argument applies here, too. ...". So, you talked about two statements - "On one hand, (1)", "On the other hand, (2)". I would expect that when someone says "One one hand, ..., but on the other hand, ...", what they say in those ellipses should contradict each other. So, in my previous comment, I just wanted to point out that (2) does not contradict (1) because countable infinity + 1 is still countable infinity.
take all the iterations you need, even infinitely many of them
Could you clarify how I would construct that?
For example, what is the "next cardinality" after countable?
I didn't say "the next cardinality". I said "a higher cardinality".
Ok, so let's say you've been able to find a countably infinite amount of real numbers and you now call them "definable". You apply the Cantor's argument to generate one more number that's not in this set (and you go from the language to the meta language when doing this). Countably infinite + 1 is still only countably infinite. How would you go to a higher cardinality of "definable" objects? I don't see an easy way.
To check if A causes B, you can check what happens when you intervene and modify A, and also what happens when you intervene and modify B. That's not always possible though. You can consult "Causality: Models, Reasoning, and Inference" by Pearl for more details.
They commit to not using your data to train their models without explicit permission.
I've just registered on their website because of this article. During registration, I was told that conversations marked by their automated system that overlooks if you are following their terms of use are regularly overlooked by humans and used to train their models.
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Instead of inspecting all programs in the UP, just inspect all programs with length less than n. As n becomes larger and larger, this covers more and more of the total probability mass in the up and the total probability mass covered this way approaches 1. What to do about the non-halting programs? Well, just run all the programs for m steps, I guess. I think this is the approximation of UP that is implied.