uncool

I guess my question is, if the "stop" message can be postponed for an unbounded time, why it couldn't be postponed forever, analogous to the Turing machine algorithm.

Why is one of the computations guaranteed to stop while the other isn't?

That said, curvature of a (near-)circle is supposed to be 1/radius, which in the case of the Earth is (if I haven't made a mistake) 16 in/mi^2. I'm guessing that the source thinks that the deviation from flat is supposed to be curvature*distance^2, rather than half that (similar to how the displacement after constant acceleration from a standstill is not a*t^2, but (1/2) a*t^2).

Um. What? Don't get me wrong, I think the OP is wrong, but this almost sounds like the objection to acceleration in the form of meters per seconds squared because there's no such thing as a square second. "8 inches per miles squared" just means that each mile, the rate at which the Earth "drops away" changes by 8 inches per mile (using an approximation where the surface looks like a parabola). The units of curvature are inverse distance, and 8 inches/miles^2 is inverse distance.

Sorry, I didn't quite read closely enough; replace j in the above with k. When you have an answer for that: I think that you have not understood what is so essential about the complex numbers. They are algebraically closed, that is, any nonconstant polynomial with complex coefficients will have a complex root. For example, the complex polynomial x^2 - i will have a complex root. As such, any "addition" of the type you have constructed will, inevitably, result in some kind of redundancy. In most cases, all that happens is that you essentially come up with something equivalent to "multiple copies of the complex numbers". In this case: any "recomplex" number can be expressed as: a + b*(1/2 + j*sqrt(2)/4 - k*sqrt(2)/4) for some complex numbers a and b. I'll call the constant in the above C. Then (a1 + b1*C) + (a2 + b2*C) = (a1 + a2) + (b1 + b2)*C, and (a1 + b1*C)*(a2 + b2*C) = (a1*a2) + (b1*b2*C), if I haven't made any arithmetic errors. You can see some effects of this, e.g. if you try to find (sqrt(2)*j - i + 1)/(sqrt(2)*j + i - 1). Depending how close you approximate sqrt(2), you will get absurdly large values, which are an artifact of the fact that you are, in essence, dividing by 0.

plus or minus (sqrt(2)/2 - i*sqrt(2)/2). Alternatively: if I've skim-understood correctly, you've defined j such that j^2 = -i. In that case, what do you get when you multiply (sqrt(2)*j - i + 1) and (sqrt(2)*j + i - 1)?

I accept that this is an impression, and that I probably overstated with "blatantly". My point isn't simply that Maxine Waters called for violence; my point is that the method in which Pelosi analyzed Waters's statement is very different from the method in which she analyzed Trump's statements. And yes, there are reasons to do so - Trump has been and was blatantly dishonest, and blatantly pandered to white supremacists and conspiracy theorists. But I don't think that someone who can analyze Trump's statements and see beyond the perfunctory "Peacefully protest!" can think that Waters's statement was only about "confrontation in the manner of the civil rights movement".

Before I do, I want to make clear: I do not think of any of this as disqualifying, or even that important. I think of Nancy Pelosi as, for the most part, a pretty typical politician; I think that nearly every politician at her level has similar hypocrisies. For a recent example (that is on-topic): Pelosi's response to Maxine Waters's statement that protesters should get "more confrontational". Maxine Waters said "[...] and we've got to get more active, we've got to get more confrontational, we've got to make sure that they know that we mean business" in response to a question of what protesters should do if the Chauvin verdict wasn't 3 guilties (manslaughter, murder 3, murder 2 - though she may have only heard "what should protesters do?" without the specific circumstances). The phrase "more confrontational" got pushback, which led Pelosi to say "No, Maxine talked about confrontation in the manner of the civil rights movement." I don't think that she can believe this is as simple as that, given her support for the impeachment of Trump for the riot at the capitol. She appropriately noted there that even if Trump said to protest peacefully, that the context easily allowed people to interpret it as support for intimidation. The same is true, if on a much smaller scale (and with less direct import), for Waters's comment. Now, I agree that this is arguable, and not only that, but that there are many, many worse cases. But there is reason to dislike her beyond "liberal".

Mehh. I'm pretty strongly against Republicans, but there is valid reason to dislike her. She's a blatantly pandering politician who is willing to say things, not because they are true, not even because she believes them, but because they are convenient to the current narrative she wants. In other words, a typical politician. And, in my opinion, not as bad as many Republicans (see: Ted Cruz, Lindsey Graham), but one of the more blatant on the Democratic side of the aisle, if only because of her prominence.

Keep in mind that in one sense, most mathematicians don't ascribe an enormous amount of importance to mathematical foundations, but in another they very much do: The standard place where most mathematicians place the foundations of mathematics is set theory, most commonly in the form of Zermelo-Fraenkel with the axiom of Choice (or ZFC). I say standard because there is quite a bit of work on nonstandard foundations - simply removing the axiom of choice is common; some replace ZFC with Homotopy Type Theory (which is beyond me entirely). I say most because there are some mathematicians that don't work in ZFC at all - some even reject the consistency of ZFC (some even reject the consistency of ZF, though that's rare). The sense in which it's not important is that for the most part, mathematicians don't need to know exactly how every symbol works; as long as certain things can be done, most mathematicians don't need to care what underlies it. The sense in which it is very important is that it's still necessary to know (or at least, strongly believe) that it can be done consistently; a failure in the foundation would be a failure of mathematics as a whole. So imagine it like the foundation of a building: it's not important that you know the details of the foundation, but it's important that you know the foundation is there doing its job.

I don't see how "base 10" makes x^2 = x/x.

I don't disagree.

1) That is not a polynomial equation; note the division. 2) Basic manipulation can turn it into the equation x^4 = 0, which means that it has no solutions (since when x = 0, the RHS involves division by 0). 3) What, precisely, do you mean by "solve"? Numerically? Using radicals? Finding a minimal polynomial?

It's worth noting that the Schrodinger equation isn't really a single system. It's a family of systems. Some simple examples have been solved (as noted); some more complex ones have been numerically approximated by perturbation theory. So the question doesn't quite make sense; it's kind of like asking "Has A + B = C been solved?"

You're thinking of completeness. Consistency means that no statement can be proven both true and false.

From my area of math, the "definitional equality" is usually written as "x := ". For example: "Let f(x) := (x - 1)/(x + 1)".

Generally speaking, I am on your side. In this specific case, they made a comment where it is difficult to interpret it in any way that isn't racist: The first part of this comment implies that the people that Hitler deliberately committed genocide against don't get to count as "people". The second part is so facially false in its misrepresentation of basic history that it indicates the writer is either a troll or such a committed racist that they don't even care about the genocide itself. Either way, a forum setting is not going to convince them to change their ways. Part of the difference is that they did more than express distaste. They used that distaste to make derogatory claims about black culture as a whole, and to dismiss the protests without even engaging with the basic claims of the protests, with a strong implication that black people don't deserve to protest. On a side note: I strongly disagree with the implication that "disrespect for authority" is necessarily a problem. To a large extent, the protests are about the claim that that authority is being abused - and authority being abused should not be respected.

A gentle reminder: please DNFTT

True - or if it could credibly threaten to punish. And in this "theory", the way to credibly threaten is to always follow through on threats. To not have to update - even when that update is being created. Basically, you seem to be trying to analyze from the moment of the AI's creation, as if that is set in stone. In this "theory", that is an error. Instead, analyze which class of AI gets to optimization sooner - one that credibly makes the threat by committing to following through, and therefore may convince people to contribute to creating it earlier, or one that doesn't.

Again: if people of the past can't guess whether punishment would be carried out, then the threat fails to motivate them. Which means that an AI that wants to be created (and which also subscribes to updateless decision theory) would prefer to be in the class of AI that made and carried out that threat, according to this theory.

That's part of the argument, yes. Part of the idea of "acausal trade" is that all parties should be able to predict the strategy the other will use. A common example given is where both sides have the other's "source code".

Sorry if I'm insisting a bit much, but you have missed the point of updateless decision theory. If the AI doesn't plan to carry out its threat, then it fails as a threat. Have you read Yudkowsky's answer to Newcomb's paradox? Because your critique is a lot like the answer of "Why don't I plan to take one box, then change my mind and take both?" If you don't accept his argument there, then you are undermining one of the foundational assumptions behind the basilisk. Note: I am not saying that you are necessarily wrong to reject the argument; however, if you do so, it doesn't really make sense to talk about something that depends so heavily on that argument.

Not if committing to the punishment is how it acausally promotes its creation. Which is part of the point of "updateless decision theory".

Not especially famous, no. It's a niche thought experiment from LessWrong. And your post takes it out of its specific context, namely, as a thought experiment about the effects of Eliezer Yudkowsky's "updateless decision theory" and "acausal trade". Note: I'm not saying that any of the above named things are correct or make sense, but your post ignores the foundation on which the thought experiment is based.

Because big things are made of small things. Alternatively: because large spaces can be broken down to small spaces, in a way that respects the laws of physics. A little more technically, because the laws of physics are local. They are differential equations where all derivatives of things at a point are determined by values of those things at the same point. "Why" for that can be explained by relativity: things can only be affected by what has happened within the past light-cone, which is necessarily small when time is short.