Unless it's built by Dyson.

Really? You repeated the most frequently debunked and refuted out-of-context deliberately misleading piece of crap known to climate science, DELIBERATELY ELIDED THE MOST SIGNIFICANT PART OF THE ANSWER and actually acted like you were posting something worthwhile? You actually claimed that your link PROVES that climate science is a liberal plot, but somehow everybody but a select few brilliant conservatives have noticed this piece of evidence that the liberal conspirators have hidden in plain sight on one of the most-visited websites in the world?

Here's the actual answer, including the critical words that you DELIBERATELY OMITTED:

"Yes, but only just. I also calculated the trend for the period 1995 to 2009. This trend (0.12C per decade) is positive, but not significant at the 95% significance level. The positive trend is quite close to the significance level. Achieving statistical significance in scientific terms is much more likely for longer periods, and much less likely for shorter periods."

Hmmm, when you see it in full, it doesn't actually support your claim at all, does it? And the rest of the interview at that link also completely contradicts what you dishonestly claim it implies.

I can't decide from your one anonymous post whether you are willfully dishonest in your posting above, or merely so stupid that you failed to read or understand anything beyond the word "yes".

And then you have the effrontery to call other people "political hack" and "bigoted"?

Here's the actual answer, including the critical words that you DELIBERATELY OMITTED:

"Yes, but only just. I also calculated the trend for the period 1995 to 2009. This trend (0.12C per decade) is positive, but not significant at the 95% significance level. The positive trend is quite close to the significance level. Achieving statistical significance in scientific terms is much more likely for longer periods, and much less likely for shorter periods."

Hmmm, when you see it in full, it doesn't actually support your claim at all, does it? And the rest of the interview at that link also completely contradicts what you dishonestly claim it implies.

I can't decide from your one anonymous post whether you are willfully dishonest in your posting above, or merely so stupid that you failed to read or understand anything beyond the word "yes".

And then you have the effrontery to call other people "political hack" and "bigoted"?

I agree. I suspect that the next big breakthrough in foundational QM will come from experiments that probe what really happens during wavefunction collapse. And I also suspect that the reason most people find this so confusing is that they forget that the wavefunction evolves in configuration space, not physical spacetime. (Unfortunately, non-specialist presentations of QM often gloss over this distinction, and even compound the confusion by focusing on examples where the configuration space looks like a physical spacetime, e.g. the double slit experiment). As we understand decoherence better, I think it's going to turn out that wavefunction evolution (of which collapse is merely a special case) is in some sense "local" in configuration space. But understanding how this translates to the classical experience is going to require an understanding of how spacetime emerges from more fundamental concepts -- and that's way above my pay grade.

In my (decidely amateur) opinion, the Copenhagen Interpretation is a result of the fact that in the early days of quantum theory, physicists knew how to describe and calculate only with very simple systems. And they knew that by the time you got to very large systems, everything appeared to behave classically. They could say what happened either side of an "observation", but not in the middle. From there it is a huge and completely unjustified leap to the assertion that wave function collapse is "instantaneous". And unfortunately, the reputation and intellectual power of the Copenhagen school was such that any challenge to this assertion was effectively shouted down for many years -- look at the way De Broglie was treated.

These days experimentalists are working with increasingly large and increasingly widely separated entangled systems, and are able to ask what actually happens "during" wavefunction collapse (and I put that in quotes because the Copenhagen interpretation would deny that there is any such thing as "during"). I suspect what we're going to find is that there is no special, magical moment of observation associated with an instantaneous collapse, but rather a continuous process of decoherence whereby a system evolves from the spiky quantum state of superpositions into the muddy state we perceive as classical reality; and under all normal circumstances (i.e. anything other than carefully preserved laboratory experiments that isolate a system from environmental noise) this happens so quickly that we don't perceive it.

In other words: most interpretations of QM struggle with the question of "why doesn't quantum superposition propagate upwards into macro systems?"'; this is essentially what the Schrodinger's Cat thought experiment is trying to highlight. And I suspect that the answer will be something along the lines of "quantum superposition is a very special circumstance, and in normal circumstances, classical noise propagates downwards into micro systems."

In my (decidely amateur) opinion, the Copenhagen Interpretation is a result of the fact that in the early days of quantum theory, physicists knew how to describe and calculate only with very simple systems. And they knew that by the time you got to very large systems, everything appeared to behave classically. They could say what happened either side of an "observation", but not in the middle. From there it is a huge and completely unjustified leap to the assertion that wave function collapse is "instantaneous". And unfortunately, the reputation and intellectual power of the Copenhagen school was such that any challenge to this assertion was effectively shouted down for many years -- look at the way De Broglie was treated.

These days experimentalists are working with increasingly large and increasingly widely separated entangled systems, and are able to ask what actually happens "during" wavefunction collapse (and I put that in quotes because the Copenhagen interpretation would deny that there is any such thing as "during"). I suspect what we're going to find is that there is no special, magical moment of observation associated with an instantaneous collapse, but rather a continuous process of decoherence whereby a system evolves from the spiky quantum state of superpositions into the muddy state we perceive as classical reality; and under all normal circumstances (i.e. anything other than carefully preserved laboratory experiments that isolate a system from environmental noise) this happens so quickly that we don't perceive it.

In other words: most interpretations of QM struggle with the question of "why doesn't quantum superposition propagate upwards into macro systems?"'; this is essentially what the Schrodinger's Cat thought experiment is trying to highlight. And I suspect that the answer will be something along the lines of "quantum superposition is a very special circumstance, and in normal circumstances, classical noise propagates downwards into micro systems."

And yet, Many Worlds *does* require a special interaction that that distinguishes an observer who becomes entangled with a system in a special way as distinct from a superposition of states (e.g. two entangled photons) in a laboratory. The distinction is that with two entangled photons, an observer can observe the superposition; but as far as we know an observer cannot observe his own superposition: he always finds himself in one state (or one World, if you prefer) or another. Observers are special. So again, Many Worlds fails to explain what this observation is or when it takes place; nor what an observer's perception is; nor even what an observer is.

In fact, Many Worlds suffers from much the same Measurement Problem as the Copenhagen Interpretation: there is no rigorous definition of when an observation (or the perception of an observation, whatever that means -- I can't find "perception" in the wave equation anywhere?) takes place. And this is what has led some theorists to propose variations on Many Worlds that assign a special status to consciousness... which brings us full circle.

I also don't know what this "outside view" you refer to is. By definition, the Many Worlds are all that there is. So where would an outside viewer sit in order to get this outside view from which nothing special happened?

Incidentally, Everett's original thesis addresses none of this. Ever since it was published, in fact, other physicists have been trying to figure out what exactly he meant.

In fact, Many Worlds suffers from much the same Measurement Problem as the Copenhagen Interpretation: there is no rigorous definition of when an observation (or the perception of an observation, whatever that means -- I can't find "perception" in the wave equation anywhere?) takes place. And this is what has led some theorists to propose variations on Many Worlds that assign a special status to consciousness... which brings us full circle.

I also don't know what this "outside view" you refer to is. By definition, the Many Worlds are all that there is. So where would an outside viewer sit in order to get this outside view from which nothing special happened?

Incidentally, Everett's original thesis addresses none of this. Ever since it was published, in fact, other physicists have been trying to figure out what exactly he meant.

Damn, I wrote a long and careful reply to this and then hit the wrong button.

Brief recapitulation: No, physicists have largely (there's still a little wiggle room) ruled out*local* hidden variable theories. See Bell's Theorem. But if you give up locality you can keep "reality" which is what hidden variable theories give you. As Bell himself pointed out, DeBroglie-Bohm theory survives his test just fine, and he actually advocated that it deserved more attention.

And since QM increasingly seems to be non-local for other reasons anyway, hidden variable theories are still ruled in. Plus, they don't require the "and then some magic happens" invocation of mechanisms that have no basis in the physical theory of the two most popular interpretations that are required to explain what actually happens when a measurement is made. In the case of the Copenhagen interpretation, "And then the wave function instantaneously collapses everywhere"; in the case of Many Worlds, "And then the entire universe instantaneously splits into two and you find yourself in one of the copies", both of which sound pretty damn non-local to me.

Brief recapitulation: No, physicists have largely (there's still a little wiggle room) ruled out

And since QM increasingly seems to be non-local for other reasons anyway, hidden variable theories are still ruled in. Plus, they don't require the "and then some magic happens" invocation of mechanisms that have no basis in the physical theory of the two most popular interpretations that are required to explain what actually happens when a measurement is made. In the case of the Copenhagen interpretation, "And then the wave function instantaneously collapses everywhere"; in the case of Many Worlds, "And then the entire universe instantaneously splits into two and you find yourself in one of the copies", both of which sound pretty damn non-local to me.

Def. 14 precisely defines a solid body as the volume swept out by the area of the semicircle.

Again: In higher mathematical usage, yes. In standard geometrical usage, no.
At the risk of repeating myself, in topics such as Euclidean solid geometry, "sphere" means the same thing it means in common usage, i.e. a solid. Thus we talk about the volume "of" a sphere, not the volume "inside" a sphere.
If you're going to use "sphere" in the higher mathematical sense as in topics that require you to distinguish carefully between the surface ("sphere") and the space bounded by the surface ("ball"), you are better off avoiding the term entirely and using something more specific such as 2-sphere.
If there's one thing worse in a Slashdot thread than people who don't know what they're talking about, it's people who think they know what they're talking about (or equally, people quoting Wikipedia out of context)

Since qualia are nonsensical inventions of the over-imaginative egos of philosophers whose feet are not planted on scientific ground, the relationship between normal humans and philosophical zombies is one of idempotency.

And yet, it still moves me.

I don't pretend to understand the proof, but physicists are adamant that hidden variables have been ruled out.

That's a popular misconception, but almost completely untrue. J.S. Bell (of Bell's Theorem fame) himself was a proponent of DeBroglie-Bohm wave mechanics, a hidden variable theory, stating explicitly that it was consistent with his theorem and lamenting that it was given so little attention.

Bell's Theorem shows this: no local, hidden variable theory can reproduce the predictions of QM.

Now let's unpack this. First of all, it doesn't *disprove* local, hidden variable theories; it does provide a way to distinguish experimentally between those theories and standard QM, i.e. because they make different predictions in a specific experiment. So far, experiments (starting with Alain Aspect) are on the side of standard QM, BUT conscientious experimentalists point out that no experiment so far has precisely and pedantically fulfilled the requirements of Bell's Theorem, so there is still some wiggle room.

But let's grant for a moment that tests of Bell's Theorem are one day confirmed on the side of standard QM. All that rules out is *local* hidden variable theories. As Bell himself pointed out, non-local hidden variable theories, such as DeBroglie-Bohm, survive just fine (as do local, non-hidden variable theories). Basically, you have to give up either locality or "reality" [a term of art in QM]. And the more we understand about entanglement, quantum information, and related topics, the less tenable locality becomes anyway. So at this point, both flavors of non-local theory -- those with and those without hidden variables are equally supportable.

The big advantage of hidden variable theories is that they do away with the need for the "and then some magic happens" special pleading required in the other two main interpretations, where they introduce a mechanism to resolve the outcome of experiments that has no basis or description in the physical theory. (In the case of the Copenhagen interpretation, "and then the wave function instantaneously collapses everywhere at once"; in the case of Many Worlds, "and then the entire universe instantaneously splits, and you find yourself in one of the copies". And if both of those sound pretty damn non-local to you, well done.)

Well, kinda. In common geometrical usage, a sphere is a three dimensional SOLID whose surface is as you described. That's how Euclid used the term, and it's how anybody who studied math to less than college level would use the term.
In higher mathematical usage, an n-sphere is an n-dimensional object embedded in an (n+1) dimensional Euclidean space that satisfies the corresponding equation of constant distance from a point in that space. So a circle is a 1-sphere (a one dimensional line embedded in the two dimensional plane); the surface of a ball is a 2-sphere (a two dimensional surface embedded in three dimensional space); and 3-sphere is something you cannot picture because it's a three dimensional "surface" embedded in four dimensional space (and not, as some people mistakenly think, a ball).
So if we're going to be strictly pedantic, you could say that the solid body is a sphere [common geometrical usage] or the surface is a 2-sphere [strict mathematical usage], but it's nothing but confusing to define "sphere" the way you did.
Normally I'd just shrug and let this go, but since you used the phrase "rather than use math terms that you don't really understand"...
In other news, The Pedantic Spheres will be the name of my next band.

You forgot to say: The party of the first part shall be known in this contract as the party of the first part.

Information doesn't "want" anything. Information doesn't have needs, goals, purposes or desires. People do.
Using the expression "information wants to be free" merely clouds a complicated issue by loading one side of the argument with emotive, unarguable assertions. Who could possibly be against freedom? End slavery! Emancipate information! It's empty rhetoric of the worst kind.
If you mean something substantive about the nature of information, please state it in terms that are actually amenable to rational debate.

...seem to involve somebody else with valuable skills working for free?

Unfortunately parents EGO gets in the way (of having a looser kid)

If I were funnier I would have some joke about the looseness of the kid. Instead I will just pause to wonder who is the greater loser, the one who complains about other people's academic achievements, or the one who can't manage the difference between "loser" and "looser"?

That should read

5. Divide by zero

6. Profit!

We warn the reader in advance that the proof presented here depends on a clever but highly unmotivated trick. -- Howard Anton, "Elementary Linear Algebra"