Surely, as rationalists, we should do a controlled test to determine if these are scams? This will require some blindly chosen users to respond in a variety of different ways, some of whom should go through with the possible scam, and report the results.
EDIT: I think it's time to come clean. No, I am not the scammer, but this post wasn't serious. I'm rather surprised anyone thought it could be, to be honest!
(comment written after only reading the introduction and the "Napoleonic exemplar" section)
In contrast the fourth process is literally insane. It's mental process correspond to nothing in reality (or at least, nothing in its reality). It emerges by coincidence, its predictions are wrong or meaningless, and it will almost certainly be immediately destroyed by processes it has completely failed to model. The symbols exist only within its own head.
I'm not so sure about this. You say that it's "literally insane" and that its thought processes happen to exactly mimic Napoleon's "by sheer coincidence". But I don't see a way for its thought processes to exactly mimic Napoleon's unless it started in the same state as Napoleon's brain and then proceeded to carry out the same calculations, while (by sheer coincidence) happening to receive the exact same sensory data throughout the 24-hour period as Napoleon did.
Yes, the Boltmann brain's reasoning doesn't actually model anything in its immediate (objective) surroundings, but it does process the data it's given correctly, and make the correct predictions from it - at least to the same extent that we presume Napoleon to have been processing his sense data correctly and making correct predictions from it.
It's true that it will soon be destroyed by processes it has completely failed to model. But anybody might be destroyed by processes they have completely failed to model - that just means they haven't been subjected to the right information sources.
I think an analogy to math might be useful here. In one sense, you could say that mathematicians are reasoning about things that are totally divorced from the world - there's no such thing as a perfect circle or an infinitely thin line in real life. Yet once you have assumed those things as axioms, you can still do completely sane and lawful reasoning on what would follow from those axioms. Similarly, the Boltzmann brain accepts the sensory data it gets as axiomatic (as do most of us), and then proceeds to carry out lawful reasoning based on that.
I'm not sure if you can argue that the Boltzmann brain is insane without also arguing that mathematicians are insane. Though, to be fair, I have noticed that the professors in the math department tend to be more colorful than the ones in other departments... :-)
Even if the Boltzmann brain is completely chaotic, internally it contains the same structures/processes as whatever we find meaningful about Napoleon's brain. It is only by external context that we can claim that those things are now meaningful.
For us, that may be a valid distinction -- how can we talk to or interact with the brain? It's essentially in it's own world.
For the Boltzmann!Napoleon, the distinction isn't remotely meaningful. It's in it's own world, and it can't talk to us, interact with us, or know we are here.
Even if the internal processes of the brain are nothing more than randomised chance, it maps to 'real', causal processes in brains in 'valid' ontological contexts.
The question is -- do those contexts/brains exists, and is there any real distinction between the minds produced by Boltmann!Napoleon, Virtual!Napoleon, etc.? I would say yes, and no. Those contexts exist, and we are really discussing one mind that corresponds to all those processes .
As to why I would say that, it's essentially Greg Egan's Dust hypothesis/Max Tegmark's Mathematical Universe thing.
So... what we have here is a kind of minimum and maximum entitlement: x/2 and x, with incentives to work more to get more back. Interesting
Scott, I am sure that would be a deeply satisfying explanation, and moreover, I would be able to find a nice concrete example by which I could explain it to all my readers, if only I knew what the hell a density matrix means, physically. Not how to define it, what it means. This information seems to have been left out of physics textbooks and Wikipedia.
I have never really had time to sit down and just study QM properly. I'm sure that the meaning of a density matrix will be completely obvious in retrospect. I'm sure that I will slap myself on the forehead for not getting earlier. And I'm sure that, once I finally get it, I will be filled with the same feeling of absolute indignation that overtook me when I realized why the area under a curve is the anti-derivative, realized how truly beautiful it was, and realized that this information had not been mentioned anywhere in my goddamned calculus textbook. Why?
Another late response from me as I read through this series again:
"I realized why the area under a curve is the anti-derivative, realized how truly beautiful it was"
Would this be that the curve is the rate-of-change of the area (as the curve goes up, so does the area beneath it)?
And when you add up all the ways the photon can go from S to P, you find that most of the amplitude comes from the middle part of the mirror - the contributions from other parts of the mirror tend to mostly cancel each other out, as shown at the bottom of Feynman's figure.
Eliezer, one thing that is confusing me is that you are trying to show that the billiard ball and the "particles have identities" analogy is wrong. At the same time you keep speaking from "the photon". In the quotation the impression I get is that "the photon" splits up into the different paths it travels. Why does it split up in the first place? Again the "splitting up" assumes that there is a particle(alias small billiard ball) but your writing seems to imply this.
Btw, I have posted a question to your last entry "The quantum arena" which unfortunately wasn't answered and has to do with this confusion.
Thanks, Roland
PS: I'm no physicist and from reading the other comments I have the impression that most who are following this are physicists or at least have quite an advanced knowledge of QM. Please don't subestimate the inferential distance for those of us who don't have all that knowledge.
Very late response:
I think that the splitting of the photon's path is pretty much entirely a human construction - the smaller the components it is split into, the more accurate the calculation, and each partition is itself an approximation that can be refined by splitting it up further in exactly the same manner. Essentially, it's a shortcut to doing a path integral over the entire range down to the planck level. Maybe... I'm not sure!
Another comment to add a few years later than the original post and hence be pretty useless:
My thoughts are that consciousness (as in the experience of it) is a kind of epiphenomenon:
The sensation is derived from cognitive processes that map isomorphically to an abstract model of consciousness in mindspace (and I do not make any distinction or heirarchy between realspace and mindspace in terms of privileged levels of existence).
It does this because the brain is doing exactly what it feels like consciousness does - integrating various inputs into a representation of self and environment, making plans and telling a consistent story about it all. And the mapping, by being possible, is also real.
Are humans capable of, collectively, keeping real and humorous/ironic racism separate? No, they are not. What South Park "kicked" off as an ironic commentary on racism is becoming actual racism.
See also Truffaut's famous dictum that there's no such thing as a true anti-war film (obligatory TVtropes warning).
And then there is Kurt Vonnegut's warning from Mother Night: "We are what we pretend to be, so we must be careful about what we pretend to be."
I'm also an atheist because I see theism as an extra-ordinarily arbitrary and restrictive constraint on what should or must be true in order for us to exist.
The way I've been envisioning theism is as a pretty broad class of hypotheses that is basically described as 'this patch of the universe we find ourselves in is being computed by something agenty'. What is your conception of theism that makes it more arbitrary and restrictive than this?
Since my metaphysical position is (and I'm going to have to come up with a better term for it) pan-existence, having gods that create and influence things requires that those possibilities where they don't (or where other, similar-but-different gods do) are somehow rendered impossible or unlikely.
Gods being statistically significant requires some metaphysical reason for them to be so simply in order to stop the secular realities dominating, and the arbitrary focus of theistic gods on humanity and our loose morals only serves to make them ever more over-specified and unlikely.
I'm in the 'everything that can exist does so; we're a fixed point in a cloud of possibilities' camp. I'm also an atheist because I see theism as an extra-ordinarily arbitrary and restrictive constraint on what should or must be true in order for us to exist.
It's simply too narrow and unjustified for me to take seriously, and the fact that its trappings are naive and full of wishful thinking and ulterior motives means I certainly don't.
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Why? Why do you believe that spending resources to run a controlled test is worth the effort?
I'm not sure whether people thinking I was being serious means I was being too dry, or exactly dry enough :D