It's independent of whether you describe it graviton based or geometry-based. Indeed, the very same apparent problem also occurs in electrodynamics:
Assume you've got a charged particle orbiting a much heavier particle of opposite charge, and let's assume we can neglect the back-action of the radiation that orbiting particle inevitably emits. The orbiting particle feels an electrostatic force towards the central particle it orbits (which, due to its much larger mass, essentially is at rest).
Now look at the very same system in a frame of reference where the whole thing is moving perpendicular to the orbital plane. Now you would naively say that the electron should orbit a point slightly behind the central charge (because — and that has been experimentally verified — the electromagnetic field also propagates just with the speed of light, and until the field has reached the orbiting particle, the central particle has already moved on). However if you actually calculate the electric field, you'll find it points exactly to the point where the charge actually is — or more exactly, at the place at which the charge would have been predicted to be at the time when the current position of the orbiting particle could be reached with light speed if one assumed that the central particle continued to go with its current speed unchanged. That is, if the speed of the central charge changed afterwards (that is, the central charge was accelerated in the mean time), the orbiting particle will still orbit the point where the central charge would have been until the information of the change (the radiation from the accelerated central charge) arrives.
One could argue that the propagation of gravity reveals information about the mass in question.
Yes. And gravity propagates with the speed of light. If some alien would manage to kick the sun out of the solar system, the earth would continue to follow its orbit for another 8 minutes. Only then would it feel the changed movement of the sun (at the same time you'd also see that the sun suddenly starts to move) and change its orbit accordingly.
Not quite. I think it is best seen by the Mermin paradox:
Three particles are brought into a special shared quantum state (termed GHZ state) and then distributed to three parties, who each can then make, on their own choice, one of two measurements on the particles, X or Y. Either measurement can result either in the value 1, or the value -1.
Now it turns out that while the individual results are completely random, whenever any two of them choose the measurement Y and the third one chooses X, the product of all three measures values are 1, every time.
Now, so far there's no problem: This could easily be explained by the original procedure producing not really the same state, but randomly different states which determine all measurement results, and which all fulfil the condition. This would be the analogue to your coin: Every actual state (heads up or tails up in the case of the coin, the set of six potential measurement results in the case of the Mermin paradox) fixes every measurement result, and all states fulfil a certain condition (the opposite sides of the coin having different symbols, the products of XYY-type measurements being 1 for the Mermin paradox), but the states are otherwise chosen by random. Due to the restriction on the states, you can predict one measurement result if you know the other(s) (for the coin, the down-facing symbol if you know the up-facing, for the Mermin paradox the third measured value of an XYY-type measurement if you know the other two).
Assuming this explanation, let's figure out what the product of measurement results should be if all three people measure X. To this end, let's label as x1 the measurement result the first person got from measuring X, y1 the result the first person would have gotten if measuring Y (which, in the above scenario, would be well-defined, just as in the case of the coin the symbol facing up is well defined even if you don't look at it), x2 the second person's result from measuring X, and so on.
Now we already know that y1*y2*x3=1, y1*x2*y3=1 and x1*y2*y3=1. If we multiply those three values together, we get x1*y1^2*x2*y2^2*x3*y3^2=1. But since the measurement results are all either 1 or -1, their squares are always 1, and thus we end up with x1*x2*x3=1. So according the above explanation, when all three people measure X, the product of their measurement results should be 1, every single time.
Now for the specific quantum state quantum mechanics predicts something different (and experiments confirm it, of course only within measurement error): When all three people measure X, the product of their measurement results is -1, every single time.
Even if the universe is infinite, the observable part of it is finite, and there's evidence (the homogeneity of the cosmic microwave background) that all of it was once causally connected. A quasar that is outside the observable part of the universe won't help you because you can't use anything it emits — it doesn't reach you.
What if they seed the PRNG with cosmic ray data? And/or XOR the PRNG with cosmic ray data? I think if that also shows Bell correlations, it would only leave two possibilities: * Either there's a god-like entity determining the results and actively misleading us. In which case, no amount of experimenting would help. * Or quantum mechanics is right.
OK, there's third one: * Actually the correlations don't really exist, but due to an extremely unlikely sequence of events the data still looks like we have one (similar to how a fair coin can land on the same side a million times in a row; it's just that it is so unlikely that we'd not believe that the coin is really unbiased if it happened; obligatory link).
Well, there's also a fourth one: * Quantum mechanics as such is wrong, but we have parallel universes with an analogue of quantum suicide, and some extraterrestrial race wants to prevent us from discovering the true laws (because those would lead us to powerful weapons and thus make us a threat to them), and immediately vaporizes the earth as soon as a measurement violates quantum mechanics. Therefore in all surviving copies of the earth, the laws of quantum mechanics seem to hold.
OK, I guess I should stop before my possibilities get even more silly.;-)
Unconstitutional? Only if, as they are designed to do, they capture American emails too.
If those nodes are in countries other than the US, the question whether they are unconstitutional is decided by the constitution of the country those nodes are in.
> This comes as Merkel's government faces criminal complaints for assisting aspects of the NSA's programs." > twitter facebook linkedin Share on Google+
My favorite part of the whole thing is that they are facing criminal complaints for assisting the NSA, all while having also been spied on by the very people they assisted. Hmm a happy satisfied feeling from seeing others get what has been coming to them? I believe the Germans just might have a word for that.
You can easily counteract this by assigning the same part to several humans and comparing the results.
Anyway, with shorter proofs, you generally have to trust other humans as well. Nobody has the time to check every proof himself. And how can you be sure that you can trust yourself? You might have learned something wrong, and thus unknowingly applying erroneous rules.
Also, even if you manage to get the proof down to the set axioms, and check every single step yourself, there's still the possibility that the set axioms are contradictory.
But if there turns out to be an error in the simplified proof, how do you know whether it's an error in the original proof, or an error of the simplification?
Who says it must be checked by a single human? In the extreme, each single step could be verified by a different human. And that even in parallel.
And even if it takes a century for humans to check that proof, it doesn't mean it's impossible. Unless we have a conclusive proof that humanity will not last that long.
Of course you can learn coding in a year. You'll not become a stellar coder. You might not even get recursion or pointers in that time frame. But you'll learn the fundamentals, and find out if you like it (in which case you'll continue to learn and get better by your own motivation) or don't (in which case you'll probably never achieve anything non-trivial in that field anyway and can safely omit learning more about it).
You clearly don't know Usenet rules. A more specific group for comp.misc would be comp.slashdot. Which could then be split up into comp.slashdot.developers, comp.slashdot.ask, etc. with comp.slashdot.misc for the stuff that doesn't go into one of the more specific groups.
However given the group creation rules (assuming they are still enforced), it would be easier to create alt.slashdot instead of comp.slashdot (alt.ALL is a hierarchy with much more relaxed group creation rules).
Slashdot Mirror
No, you misunderstood. After not finding the solution themselves, Toyota asked on Stack Overflow, and they could explain the problem to Toyota.
It's independent of whether you describe it graviton based or geometry-based. Indeed, the very same apparent problem also occurs in electrodynamics:
Assume you've got a charged particle orbiting a much heavier particle of opposite charge, and let's assume we can neglect the back-action of the radiation that orbiting particle inevitably emits. The orbiting particle feels an electrostatic force towards the central particle it orbits (which, due to its much larger mass, essentially is at rest).
Now look at the very same system in a frame of reference where the whole thing is moving perpendicular to the orbital plane. Now you would naively say that the electron should orbit a point slightly behind the central charge (because — and that has been experimentally verified — the electromagnetic field also propagates just with the speed of light, and until the field has reached the orbiting particle, the central particle has already moved on). However if you actually calculate the electric field, you'll find it points exactly to the point where the charge actually is — or more exactly, at the place at which the charge would have been predicted to be at the time when the current position of the orbiting particle could be reached with light speed if one assumed that the central particle continued to go with its current speed unchanged. That is, if the speed of the central charge changed afterwards (that is, the central charge was accelerated in the mean time), the orbiting particle will still orbit the point where the central charge would have been until the information of the change (the radiation from the accelerated central charge) arrives.
Yes. And gravity propagates with the speed of light. If some alien would manage to kick the sun out of the solar system, the earth would continue to follow its orbit for another 8 minutes. Only then would it feel the changed movement of the sun (at the same time you'd also see that the sun suddenly starts to move) and change its orbit accordingly.
Not quite. I think it is best seen by the Mermin paradox:
Three particles are brought into a special shared quantum state (termed GHZ state) and then distributed to three parties, who each can then make, on their own choice, one of two measurements on the particles, X or Y. Either measurement can result either in the value 1, or the value -1.
Now it turns out that while the individual results are completely random, whenever any two of them choose the measurement Y and the third one chooses X, the product of all three measures values are 1, every time.
Now, so far there's no problem: This could easily be explained by the original procedure producing not really the same state, but randomly different states which determine all measurement results, and which all fulfil the condition. This would be the analogue to your coin: Every actual state (heads up or tails up in the case of the coin, the set of six potential measurement results in the case of the Mermin paradox) fixes every measurement result, and all states fulfil a certain condition (the opposite sides of the coin having different symbols, the products of XYY-type measurements being 1 for the Mermin paradox), but the states are otherwise chosen by random. Due to the restriction on the states, you can predict one measurement result if you know the other(s) (for the coin, the down-facing symbol if you know the up-facing, for the Mermin paradox the third measured value of an XYY-type measurement if you know the other two).
Assuming this explanation, let's figure out what the product of measurement results should be if all three people measure X. To this end, let's label as x1 the measurement result the first person got from measuring X, y1 the result the first person would have gotten if measuring Y (which, in the above scenario, would be well-defined, just as in the case of the coin the symbol facing up is well defined even if you don't look at it), x2 the second person's result from measuring X, and so on.
Now we already know that y1*y2*x3=1, y1*x2*y3=1 and x1*y2*y3=1. If we multiply those three values together, we get x1*y1^2*x2*y2^2*x3*y3^2=1. But since the measurement results are all either 1 or -1, their squares are always 1, and thus we end up with x1*x2*x3=1. So according the above explanation, when all three people measure X, the product of their measurement results should be 1, every single time.
Now for the specific quantum state quantum mechanics predicts something different (and experiments confirm it, of course only within measurement error): When all three people measure X, the product of their measurement results is -1, every single time.
Whether all light cones lead to the big bang is independent of whether you believe it.
Even if the universe is infinite, the observable part of it is finite, and there's evidence (the homogeneity of the cosmic microwave background) that all of it was once causally connected. A quasar that is outside the observable part of the universe won't help you because you can't use anything it emits — it doesn't reach you.
What if they seed the PRNG with cosmic ray data? And/or XOR the PRNG with cosmic ray data?
I think if that also shows Bell correlations, it would only leave two possibilities:
* Either there's a god-like entity determining the results and actively misleading us. In which case, no amount of experimenting would help.
* Or quantum mechanics is right.
OK, there's third one:
* Actually the correlations don't really exist, but due to an extremely unlikely sequence of events the data still looks like we have one (similar to how a fair coin can land on the same side a million times in a row; it's just that it is so unlikely that we'd not believe that the coin is really unbiased if it happened; obligatory link).
Well, there's also a fourth one:
* Quantum mechanics as such is wrong, but we have parallel universes with an analogue of quantum suicide, and some extraterrestrial race wants to prevent us from discovering the true laws (because those would lead us to powerful weapons and thus make us a threat to them), and immediately vaporizes the earth as soon as a measurement violates quantum mechanics. Therefore in all surviving copies of the earth, the laws of quantum mechanics seem to hold.
OK, I guess I should stop before my possibilities get even more silly. ;-)
If those nodes are in countries other than the US, the question whether they are unconstitutional is decided by the constitution of the country those nodes are in.
> This comes as Merkel's government faces criminal complaints for assisting aspects of the NSA's programs."
> twitter facebook linkedin Share on Google+
My favorite part of the whole thing is that they are facing criminal complaints for assisting the NSA, all while having also been spied on by the very people they assisted. Hmm a happy satisfied feeling from seeing others get what has been coming to them? I believe the Germans just might have a word for that.
Negativhandlungsreziprozitätsbeobachtungsfröhlichkeitszufriedenheitsgefühl? ;-)
You can easily counteract this by assigning the same part to several humans and comparing the results.
Anyway, with shorter proofs, you generally have to trust other humans as well. Nobody has the time to check every proof himself. And how can you be sure that you can trust yourself? You might have learned something wrong, and thus unknowingly applying erroneous rules.
Also, even if you manage to get the proof down to the set axioms, and check every single step yourself, there's still the possibility that the set axioms are contradictory.
That way I also can easily write a very powerful build environment:
I leave obvious improvements to the reader. ;-)
Th ultimate programming model: Inactive programming. You do nothing, but still get a working program.
But if there turns out to be an error in the simplified proof, how do you know whether it's an error in the original proof, or an error of the simplification?
So how long will it take to check if you give it to 1000 people and let each one check 6500 pages?
Actually it contains the step "then a miracle occurs."
I'd hesitate to call one big for loop "AI."
So you would more readily accept a big while loop as AI? ;-)
I thought it was Volkswagens for a while. All these changes in measurement make me wish for the good old days when we used cubits.
Don't worry, when we have quantum computers on our desks, we will use qubits. Almost the same as cubits, isn't it? ;-)
So you say the real reason why they cannot check the proof is that they would violate the DMCA by doing so?
Who says it must be checked by a single human? In the extreme, each single step could be verified by a different human. And that even in parallel.
And even if it takes a century for humans to check that proof, it doesn't mean it's impossible. Unless we have a conclusive proof that humanity will not last that long.
Opps, "too long, didn't check." I guess I should have checked.
ITYM: Oops ...
SCNR
Division by zero is mathematically undefineable.
No, it isn't.
Of course you can learn coding in a year. You'll not become a stellar coder. You might not even get recursion or pointers in that time frame. But you'll learn the fundamentals, and find out if you like it (in which case you'll continue to learn and get better by your own motivation) or don't (in which case you'll probably never achieve anything non-trivial in that field anyway and can safely omit learning more about it).
Those people want both Windows and Open Source. Maybe ReactOS would be a better match.
If their bulbs emit beta radiation, they indeed should replace them immediately. ;-)
Why not something more specific.
comp.misc.slashdot perhaps?
You clearly don't know Usenet rules. A more specific group for comp.misc would be comp.slashdot. Which could then be split up into comp.slashdot.developers, comp.slashdot.ask, etc. with comp.slashdot.misc for the stuff that doesn't go into one of the more specific groups.
However given the group creation rules (assuming they are still enforced), it would be easier to create alt.slashdot instead of comp.slashdot (alt.ALL is a hierarchy with much more relaxed group creation rules).