Noah Topper

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I mean, fair enough, but I can't weigh it up against every other opportunity available to you on your behalf. I did try to compare it to learning other languages. I'll toss into the post that I also think it's comparatively easy to learn.

FWIW I genuinely think ASL is easy to learn with the videos I linked above. Overall I think sign is more worthwhile to learn than most other languages, but yes, not some overwhelming necessity. Just very personally enriching and neat. :)

It's entirely just a neat thing. I think most people should consider learning to sign, and the idea of it becoming a rationalist "thing" just sounded fun to me.  I did try to make that clear, but apologies if it wasn't. And as I said, sorry this is kind of off topic, it's just been a thing bouncing around in my head.

Honestly I found ASL easier to learn than, say, the limited Spanish I tried to learn in high school. Maybe because it doesn't conflict with the current way you communicate. Just from watching the ASL 1 - 4 lectures I linked to, I was surprisingly able to manage once dropped in a one-on-one conversation with a deaf person.

It would definitely be good to learn with a buddy. My wife hasn't explicitly learned it yet, but she's picked up some from me. Israel is a tough choice, I'm not sure what the learning resources are like for it.

...and now I am also feeling like I really should have realized this as well.

I agree that there isn’t an “obvious” set of assumptions for the latter question that yields a unique answer. And granted I didn’t really dig into why entropy is a good measure, but I do think it ultimately yields the unique best guess given the information you have. The fact that it’s not obvious is rather the point! The question has a best answer, even if you don’t know what it is or how to give it.

In any real-life inference problem, nobody is going to tell you: "Here is the exact probability space with a precise, known probability for each outcome." (I literally don't know what such a thing would mean anyway). Is all inference thereby undefined? Like Einstein said, "As far as laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality". If you can't actually fulfill the axioms in real life, what's the point?

If you still want to make inferences anyway, I think you're going to have to adopt the Bayesian view. A probability distribution is never handed to us, and must always be extracted from what we know. And how you update your probabilities in response to new evidence also depends on what you know. If you can formalize exactly how, then you have a totally well-defined mathematical problem, hooray!

My point, then, is that we feel a problem isn't well-defined exactly when we don't know how to convert what we know into clear mathematics. (I'm really not trying to play a semantics game. This was an attempt to dissolve the concept of "well-defined" for probability questions.) But you can see a bit of a paradox when adding more information makes the mathematical problem harder, even though this shouldn't make the problem any less "well-defined".

Would one be allowed to make multiple submissions distilling different posts? I don't know if I would necessarily want to do that, but I'm at least curious about the ruling.

Cool, makes sense. I was planning on making various inquiries along these lines starting in a few weeks, so I may reach out to you then. Would there be a best way to do that?

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