As promised, here is the "Q" part of the Less Wrong Video Q&A with Eliezer Yudkowsky.
The Rules
1) One question per comment (to allow voting to carry more information about people's preferences).
2) Try to be as clear and concise as possible. If your question can't be condensed to a few paragraphs, you should probably ask in a separate post. Make sure you have an actual question somewhere in there (you can bold it to make it easier to scan).
3) Eliezer hasn't been subpoenaed. He will simply ignore the questions he doesn't want to answer, even if they somehow received 3^^^3 votes.
4) If you reference certain things that are online in your question, provide a link.
5) This thread will be open to questions and votes for at least 7 days. After that, it is up to Eliezer to decide when the best time to film his answers will be. [Update: Today, November 18, marks the 7th day since this thread was posted. If you haven't already done so, now would be a good time to review the questions and vote for your favorites.]
Suggestions
Don't limit yourself to things that have been mentioned on OB/LW. I expect that this will be the majority of questions, but you shouldn't feel limited to these topics. I've always found that a wide variety of topics makes a Q&A more interesting. If you're uncertain, ask anyway and let the voting sort out the wheat from the chaff.
It's okay to attempt humor (but good luck, it's a tough crowd).
If a discussion breaks out about a question (f.ex. to ask for clarifications) and the original poster decides to modify the question, the top level comment should be updated with the modified question (make it easy to find your question, don't have the latest version buried in a long thread).
Update: Eliezer's video answers to 30 questions from this thread can be found here.
ZFC's countable model isn't that weird.
Imagine a computer programmer, watching a mathematician working at a blackboard. Imagine asking the computer programmer how many bytes it would take to represent the entities that the mathematician is manipulating, in a form that can support those manipulations.
The computer programmer will do a back of the envelope calculation, something like: "The set of all natural numbers" is 30 characters, and essentially all of the special symbols are already in Unicode and/or TeX, so probably hundreds, maybe thousands of bytes per blackboard, depending. That is, the computer programmer will answer "syntactically".
Of course, the mathematician might claim that the "entities" that they're manipulating are more than just the syntax, and are actually much bigger. That is, they might answer "semantically". Mathematicians are trained to see past the syntax to various mental images. They are trained to answer questions like "how big is it?" in terms of those mental images. A math professor asking "How big is it?" might accept answers like "it's a subset of the integers" or "It's a superset of the power set of reals". The programmer's answer of "maybe 30 bytes" seems, from the mathematical perspective, about as ridiculous as "It's about three feet long right now, but I can write it longer if you want".
The weirdly small models are only weirdly small if what you thought were manipulating was something other than finite (and therefore Godel-numberable) syntax.
Models are semantics. The whole point of models is to give semantic meaning to syntactic strings.
I haven't studied the proof of the Löwenheim–Skolem theorem, but I would be surprised if it were as trivial as the observation that there are only countably many sentences in ZFC. It's not at all clear to me that you can convert the language in which... (read more)