personal opinion of the status of the various ideas labelled "multiverse", inappropriately presented as fact. There is certainly not a consensus view that these opinions are correct, as you might mistakenly infer.
In fact, "..., with different Big Bangs but very likely with the same fundamental laws and constants" -- it seems to me the weight of professional opinion is actually more on the other side here.
His views on Everett's many-worlds interpretation are also counter to those of most people who accept it as valid in the first place.
Perhaps most egregiously, if he is going to borrow (linking to) Tegmark's categorization of the different levels of multiverse, he should at least get them right. But he refers to Tegmark's level 1 as level 0, level 2 as level 1, and is a little confused about the distinction between 1 and 2.
If you want a much more thorough, and objective, discussion of the various multiverse ideas, you want to read Brian Greene's The Hidden Reality. And of course Tegmark's Our Mathematical Universe is the latest entry into this field, a manifesto of sorts.
Generalized (NxN) sudoku is NP-complete. That's the only sense in which any puzzle is computationally intractable.
This is very fascinating work, but I am skeptical. I design puzzles like this, with computer assistance, and automatically gauging how difficult a puzzle is seems to be basically impossible. The fundamental problem is that the logical structure of a puzzle is not in itself sufficient to gauge difficulty. A huge amount of it is in the presentation, and how the player conceptualizes the puzzle, and how much of the problem can be handled automatically by visual processes. There are puzzles with trivial game trees that I have watched players get totally lost in, because the game tree is not apparent in the puzzle manifestation.
If this research addresses this problem, I will be very impressed.
Not going to get into all the arguments here. Yes, it is more complicated in detail than the simple model Walker lays out. But in practice, *if* you count calories as prescribed, *then* the model is good enough.
I'd like to provide an update here. I read about the Hacker's Diet first on Slashdot, in fall 1999. I followed it, and during 2000 I lost 50 pounds. I've kept it off for 13 years now. A few years later I started running. I've now run 96 marathons and ultramarathons, heading towards my 10th consecutive Boston Marathon, I've broken 3 hours four times, and I've run three 100 milers, including Western States. Couldn't be happier with that part of my life.
The running has been a bigger life change than losing weight. But I couldn't have done it, no way, without losing the weight first. And I have the Hacker's Diet to thank for that.
And yes, running 60-70 miles / week, I *still* have to count calories.
I would guess that you've never entered one of these competitions. To do well, it is not sufficient to come up with quick and dirty solutions; these will generally fail. You have to be able to find a good algorithm, quickly, and implement it, catching all the edge cases. These are certainly valuable real-world skills.
Disclaimer -- I was on the Rice team that took 3rd in 1986 (before there were any international teams at all).
But this mechanism relies on general relativistic effects, and only works in curved spacetime. Momentum conservation is not violated, because while the location of the object changes, its momentum (thus velocity) does not -- it simply cyclicly translates itself through space.
My first thought reading about the EmDrive was that Shaywer had found a way to reproduce this effect using a microwave cavity. But unless I'm mistaken, this does not appear to be the case, and I don't follow the arguments that Shaywer's drive should work.
Left out of that history is the branch that almost happened: for quite a while the smart money was that Apple would buy Be, Inc. and use BeOS as the basis for their future OSes. More than a few developers (myself included) based their business models on this happening.
"This fits me perfectly as a Java programmer,"
on
Programming Clojure
·
· Score: 3, Interesting
Exactly. That was the big problem I had with the book: it's written for Java programmers. I am intrigued by the language, but I would much prefer a book that treats the language on its own terms.
The reason that fun games tend to be NP-hard (or harder) is that if a game's "physics" supports interesting constructions requiring complex reasoning to solve, then probably that same physics can be used to build computational gadgets, which is how you show hardness of the generalized version. This quality expresses itself even on small, fixed-size board.
Chess and Go are actually EXPTIME-complete, even harder than NP-complete problems and PSPACE-complete problems.
In general, one-player games of bounded length (like Flood-It, or Sudoku) tend to be NP-complete; one-player unbounded games (like sliding-block puzzles, or Sokoban) tend to be PSPACE-complete; two-player bounded-length games (like Hex, or Amazons) also tend to be PSPACE-complete, and two-player unbounded games (like Chess, Checkers, and Go) tend to be EXPTIME-complete.
I can't resist here a plug for my book (with Erik Demaine), Games, Puzzles, and Computation, which discusses all these issues in detail. A theme running throughout the book is the same as the view expressed in this paper: most interesting games and puzzles seem to be as hard as their "natural" complexity class, outlined above.
by John Gribbin, (Analog Science Fiction/Science Fact, 105(2):120?125, Feb 1985). In that story a powerful particle accelerator seemingly fails to operate, for no good reason. Then a physicist realizes that if it were to work, it would effectively destroy the entire universe, by initiating a transition from a cosmological false vacuum state to a lower-energy vacuum state. In this story, the explanation of the failures assumes a many-worlds interpretation of quantum mechanics. So instead of explicit backward causality, there is effective backward causality: only the branches of reality with equipment failures contain observers; therefore, observers can only experience histories with equipment failures. The effect is the same.
I also discussed this idea in the context of novel models of computation in my MIT Ph.D. thesis, Games, Puzzles, and Computation (section 8.2; also published as a book by A.K. Peters). The idea was a bit similar to Nielsen and Ninomiya's proposed experiment. It turns out that by connecting an accelerator capable of destroying the universe to a computation depending on random numbers, one could in principle solve problems that are otherwise intractable. I termed this "doomsday computation", as a variation on the similar concept of "anthropic computation" proposed earlier by Scott Aaronson.
What the hell are Romulans doing in this movie anyway? The first time anyone in the Federation ever saw a Romulan was after this movie is set (Balance of Terror).
The point is that if you're an iPhone developer, you're stuck with sucky camera APIs. There are better, private APIs, which header files are available for. But if you use them, your app will not be approved.
Slashdot Mirror
personal opinion of the status of the various ideas labelled "multiverse", inappropriately presented as fact. There is certainly not a consensus view that these opinions are correct, as you might mistakenly infer. In fact, "..., with different Big Bangs but very likely with the same fundamental laws and constants" -- it seems to me the weight of professional opinion is actually more on the other side here. His views on Everett's many-worlds interpretation are also counter to those of most people who accept it as valid in the first place. Perhaps most egregiously, if he is going to borrow (linking to) Tegmark's categorization of the different levels of multiverse, he should at least get them right. But he refers to Tegmark's level 1 as level 0, level 2 as level 1, and is a little confused about the distinction between 1 and 2. If you want a much more thorough, and objective, discussion of the various multiverse ideas, you want to read Brian Greene's The Hidden Reality. And of course Tegmark's Our Mathematical Universe is the latest entry into this field, a manifesto of sorts.
Generalized (NxN) sudoku is NP-complete. That's the only sense in which any puzzle is computationally intractable.
This is very fascinating work, but I am skeptical. I design puzzles like this, with computer assistance, and automatically gauging how difficult a puzzle is seems to be basically impossible. The fundamental problem is that the logical structure of a puzzle is not in itself sufficient to gauge difficulty. A huge amount of it is in the presentation, and how the player conceptualizes the puzzle, and how much of the problem can be handled automatically by visual processes. There are puzzles with trivial game trees that I have watched players get totally lost in, because the game tree is not apparent in the puzzle manifestation.
If this research addresses this problem, I will be very impressed.
I probably wouldn't renew at $119. And without free shipping, I would order less stuff from Amazon. That doesn't sound too good for the shareholders.
Not going to get into all the arguments here. Yes, it is more complicated in detail than the simple model Walker lays out. But in practice, *if* you count calories as prescribed, *then* the model is good enough.
I'd like to provide an update here. I read about the Hacker's Diet first on Slashdot, in fall 1999. I followed it, and during 2000 I lost 50 pounds. I've kept it off for 13 years now. A few years later I started running. I've now run 96 marathons and ultramarathons, heading towards my 10th consecutive Boston Marathon, I've broken 3 hours four times, and I've run three 100 milers, including Western States. Couldn't be happier with that part of my life.
The running has been a bigger life change than losing weight. But I couldn't have done it, no way, without losing the weight first. And I have the Hacker's Diet to thank for that.
And yes, running 60-70 miles / week, I *still* have to count calories.
I would guess that you've never entered one of these competitions. To do well, it is not sufficient to come up with quick and dirty solutions; these will generally fail. You have to be able to find a good algorithm, quickly, and implement it, catching all the edge cases. These are certainly valuable real-world skills.
Disclaimer -- I was on the Rice team that took 3rd in 1986 (before there were any international teams at all).
... sort of. And it is established physics. See Swimming in Spacetime: Motion by Cyclic Changes in Body Shape, Science, 2/27/2003, by Jack Wisdom.
But this mechanism relies on general relativistic effects, and only works in curved spacetime. Momentum conservation is not violated, because while the location of the object changes, its momentum (thus velocity) does not -- it simply cyclicly translates itself through space.
My first thought reading about the EmDrive was that Shaywer had found a way to reproduce this effect using a microwave cavity. But unless I'm mistaken, this does not appear to be the case, and I don't follow the arguments that Shaywer's drive should work.
I managed to get bib # tau for a marathon last year. Gave the timekeeper fits.
Then, when somebody wants to argue that twice e is actually a better constant, we can say "2e or not 2e, that is the question."
This was being done at MIT 10 years ago.
http://people.csail.mit.edu/rweiss/
Left out of that history is the branch that almost happened: for quite a while the smart money was that Apple would buy Be, Inc. and use BeOS as the basis for their future OSes. More than a few developers (myself included) based their business models on this happening.
Grover's search algorithm gives only a quadratic speedup.
Exactly. That was the big problem I had with the book: it's written for Java programmers. I am intrigued by the language, but I would much prefer a book that treats the language on its own terms.
It's on my list...
I'll mention it to my publisher, but honestly it would lose a lot without all the color figures.
The book is based on my Ph.D. thesis, which you can download for free:
http://www.swiss.ai.mit.edu/~bob/hearn-thesis-final.pdf
The reason that fun games tend to be NP-hard (or harder) is that if a game's "physics" supports interesting constructions requiring complex reasoning to solve, then probably that same physics can be used to build computational gadgets, which is how you show hardness of the generalized version. This quality expresses itself even on small, fixed-size board.
Ah, it doesn't mean that either. :-)
If a problem is NP-hard, it means it is at least as hard as any other problem that can be solved in polynomial time on a nondeterministic computer.
It is an open question (P=NP) whether this is equivalent to saying that there is no deterministic polynomial-time algorithm.
Chess and Go are actually EXPTIME-complete, even harder than NP-complete problems and PSPACE-complete problems.
In general, one-player games of bounded length (like Flood-It, or Sudoku) tend to be NP-complete; one-player unbounded games (like sliding-block puzzles, or Sokoban) tend to be PSPACE-complete; two-player bounded-length games (like Hex, or Amazons) also tend to be PSPACE-complete, and two-player unbounded games (like Chess, Checkers, and Go) tend to be EXPTIME-complete.
I can't resist here a plug for my book (with Erik Demaine), Games, Puzzles, and Computation, which discusses all these issues in detail. A theme running throughout the book is the same as the view expressed in this paper: most interesting games and puzzles seem to be as hard as their "natural" complexity class, outlined above.
"George Takei as Chief Physicist"
Helmsman, swordsman, physicist... the guy can do everything!
Yes! Thanks; I hadn't seen that.
Yes, see NP-complete Problems and Physical Reality, by Scott Aaronson.
But the great thing is, they propose an experiment to *test* whether this is happening.
by John Gribbin, (Analog Science Fiction/Science Fact, 105(2):120?125, Feb 1985). In that story a powerful particle accelerator seemingly fails to operate, for no good reason. Then a physicist realizes that if it were to work, it would effectively destroy the entire universe, by initiating a transition from a cosmological false vacuum state to a lower-energy vacuum state. In this story, the explanation of the failures assumes a many-worlds interpretation of quantum mechanics. So instead of explicit backward causality, there is effective backward causality: only the branches of reality with equipment failures contain observers; therefore, observers can only experience histories with equipment failures. The effect is the same.
I also discussed this idea in the context of novel models of computation in my MIT Ph.D. thesis, Games, Puzzles, and Computation (section 8.2; also published as a book by A.K. Peters). The idea was a bit similar to Nielsen and Ninomiya's proposed experiment. It turns out that by connecting an accelerator capable of destroying the universe to a computation depending on random numbers, one could in principle solve problems that are otherwise intractable. I termed this "doomsday computation", as a variation on the similar concept of "anthropic computation" proposed earlier by Scott Aaronson.
Surely, you mean how many cubic beard seconds is that?
What the hell are Romulans doing in this movie anyway? The first time anyone in the Federation ever saw a Romulan was after this movie is set (Balance of Terror).
The point is that if you're an iPhone developer, you're stuck with sucky camera APIs. There are better, private APIs, which header files are available for. But if you use them, your app will not be approved.