uncool
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Sign rule for multiplication
uncool replied to neonwarrior's topic in Linear Algebra and Group Theory
Because the property (a + b)*c = a*c + b*c requires it. Or, to slightly modify what John Cuthber said: if you cancel someone else's debt, you are giving them money. 
So how is that n proven to exist in the Actor system? What you're saying reminds me of the fact that e.g. any strictly decreasing sequence of ordinals is, in fact, finite, even though (if the initial value is infinite) it can be arbitrarily long. However, I still don't see what it is about the Actor system that forces the "stop" message to be eventually acted on.

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?

The Greatest Laser Experiment In History  FECORE
uncool replied to Dr. Zack's topic in Speculations
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). 
The Greatest Laser Experiment In History  FECORE
uncool replied to Dr. Zack's topic in Speculations
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 "mult

plus or minus (sqrt(2)/2  i*sqrt(2)/2). Alternatively: if I've skimunderstood 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 sta

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 ontopic): 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 prot

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.

Where is the core principles that govern mathematics?
uncool replied to Alex Mercer's topic in Mathematics
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 ZermeloFraenkel 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 
I don't see how "base 10" makes x^2 = x/x.

I don't disagree.

Are there no good ways to solve polynomial equations?
uncool replied to Trurl's topic in Mathematics
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?"

Does Gödel's Incompleteness Theorems means 2+2=5?
uncool replied to francis20520's topic in Mathematics
You're thinking of completeness. Consistency means that no statement can be proven both true and false. 
Definitions, Identities, Equations, and Formulas
uncool replied to joigus's topic in Applied Mathematics
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 t

A gentle reminder: please DNFTT

A Critique and Revision of Roko's Basilisk
uncool replied to Jack Jectivus's topic in General Philosophy
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. 
A Critique and Revision of Roko's Basilisk
uncool replied to Jack Jectivus's topic in General Philosophy
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. 
A Critique and Revision of Roko's Basilisk
uncool replied to Jack Jectivus's topic in General Philosophy
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". 
A Critique and Revision of Roko's Basilisk
uncool replied to Jack Jectivus's topic in General Philosophy
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 mak 
A Critique and Revision of Roko's Basilisk
uncool replied to Jack Jectivus's topic in General Philosophy
Not if committing to the punishment is how it acausally promotes its creation. Which is part of the point of "updateless decision theory".