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Everything posted by uncool

  1. 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?"
  2. You're thinking of completeness. Consistency means that no statement can be proven both true and false.
  3. From my area of math, the "definitional equality" is usually written as "x := ". For example: "Let f(x) := (x - 1)/(x + 1)".
  4. 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.
  5. 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.
  6. 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.
  7. 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".
  8. 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.
  9. Not if committing to the punishment is how it acausally promotes its creation. Which is part of the point of "updateless decision theory".
  10. 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.
  11. 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.
  12. The point of the problem is to use induction and the properties of determinants to find the answer, not to find each determinant separately.
  13. Depends on what you mean. For any angle A, sin(A) = (e^(i*A) - e^(-i*A))/2i, which is an expression of the sine using exponents, but I'm guessing that's not what you're going for (in part, because you seem to have an objection to numerically finding the value). It sounds like you are trying to define sines in terms of radicals of rational numbers. There are uncountably many angles, and only countably many expressions using radicals. So we'd have to restrict ourselves to some countable subset of angles. You chose to look at pi/4; that suggests using only rational multiples of pi. And with that restriction, the answer is yes - sin(pi*(a/b)) can always be expressed in terms of radicals. In fact, the expression I gave above can count: sin(pi*(a/b)) = (1^(a/2b) - 1^(-a/2b))/(2*(-1^(1/2))). That expression...isn't really helpful in finding the value of sin, but I'm pretty sure it can be converted to an expression that is.
  14. No matter the other 394 digits, nor the other 600 digits of the larger number, no, it can't be the smallest (non-trivial)-factor. Because the quotient would be around 10^207.
  15. I think you are thinking of "normal vectors", which are not cotangent vectors, no. For one thing, normal vectors depend on how you have embedded your manifold into a larger Euclidean space, whereas tangent and cotangent vectors do not.
  16. Yes (even better: that the map is a local diffeomorphism; the difference being whether there is *some* map or whether it is *this* map), but that is a very weak statement; any two smooth manifolds of the same dimension are locally diffeomorphic - because locally, the differential topology is that of Euclidean n-dimensional space. The term I think you want is that they are locally isometric (or more specifically, that the "wrapping map" is a local isometry), that is, that the metric, or the geometry, matches.
  17. Because the map is not invertible - only locally invertible. When you wrap the sheet around the cylinder, it will cover itself (infinitely many times, even). Also, "diffeomorphism" is a term properly from differential topology - the metric plays no role in it (e.g. a "smoothed" coffee cup is diffeomorphic to a donut). The term "isometry" is much stronger - literally "same metric".
  18. I think you mean the opposite: the spaces are not diffeomorphic, but they are locally isometric.
  19. You are missing the logic behind the idea of taking limits, which is to avoid actually dividing by zero. The fact that you seem to think that the process is "magical" is a strong indicator of why.
  20. you're missing the point taeto is making. Let me put it quite simply: no, the process of taking the derivative never involves a division by 0. Period.
  21. ...y = 1 is a horizontal line, not a vertical one; f(x) = 1 is a function.
  22. ...yes, it does. The definition of the limit of a function specifically excludes the value of the function of the limiting value from being relevant. "For all epsilon greater than 0, there exists a delta greater than 0 such that for any 0 < |x - a| < delta, |f(x) - L| < epsilon"
  23. Please point out where you explained any actual division by 0, which is the specific distinction taeto is making. ...no, it isn't.
  24. Except in neither case is there any actual division by 0.
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