PedroCarvalho

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The Cartoon Guide to Löb's Theorem

Yrg'f frr, V xabj sbe n snpg gung ¬(CN ⊢ (◻P → P) → P), gung vf, gung guvf fhccbfrq "nccyvpngvba" bs gur Qrqhpgvba Gurberz qb Yöo'f Gurberz vf abg n gurberz bs CN.

Yöo'f Gurberz vgfrys vf whfg gung -

Buuuu tbg vg.

Yöo'f Gurberz fnlf gung vs CN ⊢ ◻P → P, gura CN ⊢ P; be, fvzcyl, gung CN ⊢ ◻(◻P → P) → ◻P. Gur Qrqhpgvba Gurberz fnlf gung sbe "ernfbanoyr" (va n pregnva frafr) qrqhpgvir flfgrzf va svefg-beqre ybtvp naq nal frg bs nkvbzf Δ, vs vg'f gur pnfr gung, sbe fbzr N naq O, Δ ∪ {N} ⊢ O, gura Δ ⊢ N → O. Ubjrire, vg vf abg gur pnfr gung CN ∪ {◻P → P} ⊢ P, fvapr CN ∪ {◻P → P, ¬P} vf cresrpgyl pbafvfgrag (vss CN vf nyfb pbafvfgrag) naq vzcyvrf ¬◻P.

Be, va bgure jbeqf, nqqvat gur nkvbz ◻P → P gb CN sbe nal P bayl znxrf P n gurberz bs CN vs ◻P vf nyernql gurberz bs CN; ubjrire, ernfbavat "bhgfvqr" bs CN, jr xabj nyernql gung vs CN ⊢ ◻P gura CN ⊢ P (juvpu pna nyfb or sbeznyvfrq nf CN ⊢ ◻◻P → ◻P, juvpu vf n gurberz bs CN), fb nqqvat ◻P → P gb CN qbrf abg va snpg znxr CN "fgebatre" guna vg jnf orsber va nal zrnavatshy frafr, naq whfg znxrf CN gehfg vgf cebbs bs P, vs vg rire svaqf nal.

Gur pbeerpg nccyvpngvba bs gur Qrqhpgvba Gurberz gb Yöo'f Gurberz fnlf gung CN ∪ {◻(◻P → P)} ⊢ ◻P, juvpu jr nyernql xabj gb or gehr (orpnhfr... gung'f Yöo'f Gurberz), ohg fvapr ◻P → P vf abg va trareny n gurberz bs CN, guvf qbrf abg thnenagrr gung P jvyy or gehr. Naq phevbhfyl, guvf vzcyvrf gung nqqvat rvgure ◻(◻P → P) sbe nyy P be ◻P → P sbe nyy P gb CN qbrfa'g znxr CN nal fgebatre - qbvat gur sbezre npghnyyl eraqref ◻ rssrpgviryl zrnavatyrff, fvapr gura ◻P jvyy or gehr sbe nyy P, naq vg jvyy ab ybatre ercerfrag svaqvat n Töqry Ahzore bs n cebbs bs P, fb bar pbhyq fnl gung vg znxrf CN "jrnxre" va fbzr ybbfr frafr -, ohg nqqvat obgu sbe nyy P znxrf vg vapbafvfgrag.

Open thread, July 23-29, 2013

Well, I'm in France (Palaiseau, near Paris) right now, and I'm going to spend two years here. Then I'm returning to Brazil, which makes my prospects even worse? x.x'' From what I've read of CI it's pretty much the same, spending money on having a coroner put you in a bag of ice and ship you to the US... --- Yes I expect I'll do that. --- The US government would have to be a lot more receptive of Brazilians for a terminally ill one to simply be able to move and die there (I'm not sure how much their foreign policies have been changing these past few years, though...) --- I'm pretty sure if anyone could actually predict and prevent that most people wouldn't sign up with any cryonics institute until right before they got terminally ill or very old and cryonics wouldn't be there.

Open thread, July 23-29, 2013

So, I just moved to Europe for two years and finally got finantial independence from my (somewhat) Catholic parents and I want to sign up for cryonics. Is there international coverage? Is there anything I should be aware of? Are there any steps I should be taking?

Open Thread, June 16-30, 2013

So, I just moved to Europe for two years and finally got finantial independence from my (somewhat) Catholic parents and I want to sign up for cryonics. Is there international coverage? Is there anything I should be aware of? Are there any steps I should be taking?

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Open Thread, June 16-30, 2013

I have started writing a Death Note fanfiction where the characters aren't all as dumb as a bag of bricks (or one could say a rationalist fic) and... I need betas. The first chapter is available on http://www.fanfiction.net/s/9380249/1/Rationalising-Death and the second is pretty much written, but the first is confirmedly "funky" in writing and since I'm not a native English speaker I'm not sure I can actually pinpoint what exactly is wrong with it. Also I'd love the extra help.

Anyone interested? My email for contact is pedromvilar@gmail.com (and I also have a tumblr account, http://scientiststhesis.tumblr.com )

Mixed Reference: The Great Reductionist Project

MW is obviously much better in this regard than theism, but one of the problems with theism (it promises a simple reduction, but leaves the 'simple' undemonstrated) is interestingly analogous to the problem with MW (it promises a simple reduction, but leaves the 'reduction' undemonstrated). I don't take this to be a distinct argument against MW; I just wanted to call it to attention.

I guess we'll have to wait until we have interstellar travels to observe completely superposed civilisations so that we can actually see MW? That was a joke, by the way.

If your commitment to locality is strong enough, then you can recover locality by positing that you've imperceptibly fallen into another world in interacting with one of the particles, dragging everything around you into a somehow-distinct component of a larger, quasi-dialetheist (really, complex) reality. I don't begrudge those who pursue this path; I only encourage careful scrutiny of exactly which priors we're appealing to in taking that first step away from the naive, superficial interpretation of the experimental result that caused this aspect of the problem.

It's not really "fallen into another world" as much as "being in a superposed state." If you assume that superposition is a real effect of wavefunctions (particles), then you have to assume that you also belong in states. The only way of escaping that is not believing superposition is an actual, real effect, which to me looks like exactly what Bohm says. Now I'm not saying that I give a > .9 probability to MW. It's > .5, but I do not trust my own ability to gauge my probability estimates the way you did.

I don't find the idea of clearly distinct universes mystical or strange or scary. I do find it strange and very-nearly-incoherent to think of worlds 'bleeding together' at the edges; and I very much wonder what it would be like to fully inhabit that intersection between worlds.

Point. I think mr. Yudkowsky mentioned something about a non-existence of worlds at that intersection? As in, the leakage from the "larger" worlds is so big that the intersection ceases existing, and then you have clearly distinct universes. Or at least that's what I understood. I don't think I like or even agree with the idea; it, too, sounds to me like trying to fit physics into intuition. But anyway, I agree with you that one of the main points in my head against MW is that intersection. That, and what I mentioned above, of completely impossible situations (like zombie Kennedy) never having happened in recorded history.

BM requires some really unpleasant initial commitments, but there don't seem to be any special interpretive problems, paradoxes, or unsolved problems in BM, aside from the 'ordinary' legwork required in any general microphysical theory (e.g., we need a Bohmian QFT). BM has solved the Measurement Problem; MW merely has some really suggestive hints that it might someday offer a more elegant solution of its own.

Point. Which is why I agree with you that BM is the only other serious candidate. [whine]But those initial commitments are really unpleasant.[/whine]

The sole difficulty BM faces, in contrast, is that it's just kind of... ugly. Overtly, avowedly, unabashedly ugly. (That's really what I respect most about the theory. It doesn't hide its flaws; it defines itself in terms of them.) But until these same problems have been solved in at least one of BM's competitors, we have no way of knowing that some analogous ugliness (like 'magical reality fluid') won't be demanded in the end in any empirically adequate interpretation! Scary thought, eh?

Scary indeed. Magical reality fluid actually terrifies me, and if it turns out that MW requires it... well, I think I prefer non-locality to that.

Mixed Reference: The Great Reductionist Project

Yes, I'm sorry, by "lawful" I'd meant exactly that, universes that obey our particular set of physics.

Mixed Reference: The Great Reductionist Project

Sure, but the theory with the simplest sound-bite axiomatization may not be the most parsimonious theory at the end of the day. And your confidence in that starting point will depend heavily on how confident you are in the prospects for extracting the Born probabilities from the Schrödinger equation on its lonesome. A theist will claim that his starting point is maximally simple relative to its explanatory power -- heck, one of his axioms is that his starting point is maximally simple! that's how simplicity works, right? -- but the difficulty of actually extracting normality from theism without recourse to 'deep mysteries' undermines the project in spite of its promising convergences with the data.

I meant not simplest as in simplest sound bite, I meant in the way mr. Yudkowsky has painfully explained elsewhere when he treated Occam's Razor. One single equation is always a simpler proposition than two; and a whole intelligent being that sparked Existence itself and is not made of parts is so far off the map it's not even worth considering as a preliminary hypothesis.

The wave occurs at both positions (or with both spin components); the particle does not. Being made of particles, I have a determinate brain-state, not a superposed one; and I observe a determinate particle position, though the dynaymics of that particle (and of my brain-state) are guided by the wave function. Many Worlds seems to predict that I will both see a spin-up measurement result and a spin-down measurement result, when I observe the superposed state. But in fact I seem to either see spin-up or spin-down, not both. So at this simple stage, Bohm correctly predicts our observation, and Many Worlds does not. That's why the challenge for Many Worlds is to make sense of the probabilistic element of QM. The Schrödinger dynamics leave no room for probability; they are, as you note, deterministic.

If you have any system that is in a given state A and that system interacts with another one that is in a superposition of states X and Y, it no longer makes sense to talk about the first and second system: the whole system is now in a superposition of states. Same thing with observing the measurement: what you actually observe is a computer telling you "spin-up" or "spin-down". So that's a gazillion atoms and molecules and particles and whatnot that's different depending simply on the state of the electron. Now suppose you somehow isolated that computer completely from the outside, so that not a single photon left it, then you could say that the computer is in a superposition. And as soon as you looked, so would you. The fact that you don't actually see the computer accusing both "spin-up" and "spin-down" or some combination is just a consequence of the fact that, while the whole system, including you, your brain, the computer, the room you're in, the air you're breathing, etc., is in a superposition, the amplitude for the two states to interact is infinitesimal. For all intents and purposes, these two states have decohered. That's not to say superposition is gone; it's just to say that the amplitude for those two states to interact is nearly zero.

A multiverser may respond: 'But we've come so far! We've made such progress! Surely we deserve to be treated as the standard view by this point. All that's left is the small problem of explaining the emergence of the real.'

Eh... I don't know about that. I mean... well, I'll come to that in a bit.

This is not to say that the quantum world is obliged to match our intuitions. It is only to say that for an interpretation to even qualify as an interpretation, it will have to give some content to its formalism. As content goes, 'world-splitting' and 'Magical Reality Fluid' is not much of an improvement, if improvement it is, over 'particle' and 'wave.'

I'll comment on it in a bit, too.

But I think most physicists who have a view on the issue assign a greater-than-.9 probability to their preferred variants of MW; and I haven't seen evidence that they've grappled with the foundational questions enough to warrant that much confidence.

I think that is the same problem I had with any other theories. The very idea of non-locality triggers alarm bells all over my brain. That > .9 probability to MW, I believe, stems, at least partially, from an implicit < .01 probability to non-locality. So that really leaves very little room for other interpretations, and those, from what I've read, sound more bogus than Bohm.

[...] and in particular in challenging MW to become more rigorous and explicit in what it means with all this world-talk. Bohm may sound unfashionably 19th-century at times, but at least it never sounds mystical.

I, personally, don't think MW sounds all that "mystical." I guess that comes from having lived half my life in the 21st century, so even in fiction the notion of multiple universes has never been a scary, strange one. The existence of a multiverse has always been a... persistent idea in my mind, and once I started reading up on Q.M. and studying the subject I just gave form to that intuition. That being said, I do agree with you that, at least from Wikipedia's list of interpretations, Bohm's does look like the most solid alternative to MW.

And coming to my final point... the Born probabilities. I honestly, truly have not a clue where they come from. I am hoping that any final unified theory might be able to solve that little problem (HA, little, right), but it wouldn't be bad if someone solved it from within Q.M. itself. Some have tried, and I haven't yet gotten to the point where I believe I am ready to read their attempts and truly grok what they mean so I can myself judge my probability estimates.

Mixed Reference: The Great Reductionist Project

Does adding Magical Reality Fluid and an infinity of invisible Worlds sound simple, at the outset?

That's not at all what Relative State states... it just states that the Schrödinger Equation is all there is, full stop. The existence of a number of worlds is a consequence, not an assumption.

Bell's way of framing BM is very intuitive, I think:

"Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored."

Please forgive me if I misunderstand, but that sounds, to me, just a way of making wavefunctions fit into the intuitive "particle" and "wave" molds. And it also looks like it ignores the fact that people are made of particles (wavefunctions), so whatever effects of any given particle (wavefunction) are detected by us would cause us to be superposed. I don't... really see a way out of being superposed at macroscopic level.

"Prefer" as in it sounds more elegant, or as in it seems more likely to be true? Untangling those two is the real problem. We also need to keep in mind that the MW style of locality is a rather strange one. (Consider MW theories on which worlds 'split;' does this conservation-of-energy-violating split propagate outward at the speed of light? What basis does it occur in?)

"Prefer" as in both sounds more elegant and seems, to me, more likely to be true. Also, the conservation of energy is never violated, I don't think, since we already had to multiply the total energy by the normalised amplitude squared of the different states anyway.

Bayesian reasoning isn't bivalent; our goal is not simply to pick the Best Option, but to try to roughly estimate how uncertain we should be. For instance, at this point should we assign a .4 probability to BM? .1? .005?

I'm sorry, you're right. What I meant by "failed to convince me" and "wins my favour" is that I still assign a > .5 probability to MW, or any interpretation that doesn't try to sneak away from macroscopic superposition, or tries to tell me physics is non-local. As I said, I have done my share of research on alternative interpretations of Q.M. after I started studying it (I'm not nearly done studying it, though) before, and the one that sounded to me the simplest was MW.

I'm not convinced of BM either, but I take it seriously as the main rival to the entire MW family of interpretations. I take Collapse interpretations far less seriously, not just because of their strange dualism but because they have more promise of being empirically verified (hence their lack of verification counts against them), whereas BM and MW don't seem to be distinguishable. (Also, BM-style views predate Everett by decades, so one can't make the case that BM is an ad-hoc distortion of MW.)

I guess I don't take it seriously because, to my untrained eyes, it looks like a theory that's trying to escape quantum effects affecting the macroscopic world by sticking macroscopic intuitions into the quantum world.

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