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homunq comments on Pascal's Muggle: Infinitesimal Priors and Strong Evidence - Less Wrong
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Why was this downvoted? Because everyone knows that Matrix Lord simulations don't actually follow MWI, they just seem to for the poor deluded scientists trapped inside? Sure, I know that. But I was just saying, what if they did. Riddle me that, downvoter person!
Seriously: I've now posted variants of this idea (that MWI means we are all legion, which makes threats/promises involving simulations significantly less scary/enticing) at least 5 or 6 times, between here and Quora. And it's downvoted to oblivion every time. Now, obviously, this makes me question whether there's something stupid about the idea. But though I'm generally acknowledged to be not a stupid guy, I can't see the fatal flaw. It's very tempting to think that you cats are all just too mainstream to see the light, man. That kind of thinking has to overcome a large self-servingness penalty, which is why I state it in ridiculous terms, but unless someone can talk me down here, I'm close to embracing it.
So: what is so very wrong about this thought? Aside from the fact that it embraces two premises which are too unconventional for non-LW'ers, but reaches a conclusion that's too mainstream for LW'ers?
And please, don't downvote this comment without responding. I'm happy to take the karma penalty if I learn something, but if all you get for being wrong is downvoted, that's just a dead end. So, to sweeten the pot: I will upvote any even-minimally-thoughtful response to this comment or to the one above.
I didn't downvote, but I couldn't see what MWI actually changed about the problem. The simulations are also subject to MWI, so you're multiplying both sides of the comparison by the same large number. Hmm. Unless the simulations are implemented on quantum computers, which would minimize the branching. It's not clear to me that you can mimic the algorithm without having the same degree of total decoherence.
No, the simulations are not subject to MWI. I mean, we don't know what "matrix lord physics" is, but we have his word that there are 3^^^^3 individuals inside those simulations, and presumably that's after any MWI effects are factored in.
If instead of Matrix Lord, we were just facing Galaxy Of Computronium Woman, we'd be even better off. She can presumably shift any given bit of her galaxy between quantum and normal computation mode, but it doesn't help her. If GOCW is in normal computation mode, her computations are deterministic and thus not multiplied by MWI. And if she's in quantum mode, she only gets a multiplier proportional to an exponential of the number of qubits she's using. In order to get the full multiplier that ordinary made-of-matter you are getting naturally, she has to simulate everything about the quantum wave function of every particle in you and your environment. We don't know how efficient her algorithms are for doing so, but presumably it takes her more than a gram of computronium to simulate a gram of normal matter at that level of detail, and arguably much more. Obviously she can do hybrid quantum/conventional tricks, but there's nothing about the hybridization itself that increases her multiplier.
So you're saying, what if MWI is just a local phenomenon to our world, and doesn't apply to these 3^^^^3 other simulations that the matrix lords are working with, because they aren't quantum in the first place?
I agree that in the case of a mere galaxy of computronium, it's much less credible that one can simulate an extremely high number of people complex enough that we wouldn't be able to prove that we aren't them. In the former case, we've got much less information.
Unlike Eliezer, I very publicly do not privilege MWI on this site, but let's assume that it's "true" for the sake of argument. How many (subtly different) copies of you got offered the same deal? No way to tell. How many accept or reject it? Who knows. If there are 3^...^^3 copies of you who accepted, then the matrix lord has a lot of money (assuming they care for money) to do what it promised. But what if there are only 3^^^3 (or some other conveniently "small" number) of you who accept? Then you are back to the original problem. Until you have a believable model of this "magical reality fluid", adding MWI into the mix gives you nothing.
(Note: this comment now moved to respond to nshepperd above)
Isn't the thought that even if only one Homunq is offered the deal and accepts, the next few seconds will generate [insert some large number] of worlds in which Homunq copies have $5 less because of that one original Homunq's decision? I don't think Homunq means to refer to preexisting other worlds (which couldn't be affected by his actions), but to the worlds that will be generated just after his decision.
They aren't generated. The one world would be split up among the resulting worlds. The magical reality fluid (a.k.a. square amplitude) is conserved.
I strongly disagree that you can make that assumption; see my comment on your larger explanation for why.
Okay, thanks. But I don't know what magical reality fluid is, so I don't really understand you.
Before I answer, I'd like to know how much you do understand, so I can answer at an appropriate level. Is this a 'I don't know what's going on here' question, or is it a statement that you understand the system well enough that the basics no longer are convincingly basic?
The former, mostly. I've read the sequences on this point and done a little side reading on my own, but I don't understand the math and I have no real education in quantum physics. In other words, I would really appreciate an explanation, but I will also entirely understand if this is more work than you're prepared to put in.
To condense to a near-absurd degree:
QM indicates that if you take any old state of the universe, you can split it up any way you feel like. Take any state, and you can split it up as a sum of 2 or more other states (A = B + C + D+ E, say). If you then 'run' each of the parts separately (i.e. calculate what the future state would be, yielding B', C', D', E') and then combine the results by adding, it's the same as if you ran the original (A' = B' + C' + D' + E').
This is because QM is a linear theory. You can add and subtract and rescale entire states and those operations pass right through into the outcomes.
This doesn't mean that you won't get any surprises if you make predictions based on just B, C, D, and E individually, then add those together. In general, with arbitrary B, C, D, and E, combining them can yield things that just don't happen when you'd expect that they would based on the parts individually (and other things that happen more than you'd expect, to compensate).
Decoherence tells you how and when you can pick these B, C, D, and E so that you in fact won't get any such surprises. That this is possible is how we can perceive a classical world made of the quantum world.
One tiny and in no way sufficient part of the technique of decoherence to require that B, C, D and E are all perpendicular to each other. What does that do? You can apply the Pythagorean theorem. When working with vectors In general, with A being the hypotenuse and B, C, D, and E the perpendicular vector components, we get AA = BB + CC + DD + EE (try doing this with three vectors near the corner of a room. Have a point suspended in air. Drop a line to the floor. Construct a right triangle from that point to one of the walls. You'll get AA = WW + ZZ, then split W into X and Y, for AA = XX + YY + ZZ)
Anyway, what the Pythagorean theorem says is that if you take a vector and split it up into perpendicular components, one thing that stays the same is the sum of the squared magnitudes.
And it turns out that if you do the math, the mathematical structure that works like probability in QM-with-decoherence is proportional to this squared magnitude. This is the basis of calling this square magnitude 'reality fluid'. It seems to be the measure of how much something actually happens - how real it is.
Thanks, that's really quite helpful. I take it then that the problem with Homunq's objection is that all the subsequent 'worlds' would have the same total reality fluid as the one in which he made the distinction, and so the 'splitting' wouldn't have any real effect on the total utility: $5 less for one person with reality R is the same disutility as $5 less for a [large number of] people with reality R/[large number]?
But maybe that's not right. At the end, you talked about 'how much reality fluid something has' as being a matter of how much something happens. This makes sense as a way of talking about events, but what about substances? I gather that substances like people don't see much play in the math of QM (and have no role in physics at all really), but in this case the questions seems relevant.
Your first paragraph is correct.
As for the second, well, substances are kind of made of colossal numbers of events in a convenient pattern such that it's useful to talk about the pattern. Like, I'm not falling through my chair over and over and over again, and I anticipate this continuing to be the case... that and a bunch of other things lead me to think of the chair as substantial.
Good explanation. But you're assuming a theory in which "reality fluid" is conserved. To me, that seems obviously wrong (and thus even more obviously unproven). I mean, if that were true, my experiences would be getting rapidly and exponentially less real as time progresses and I decohere with more and more parts of the wave function.
I acknowledge that it is difficult to make probability work right in MWI. I have an intuitive understanding which feels as if it works to me, that does not conserve "reality fluid"; but I'm not so unwise as to imagine that a solid intuition is worth a hill of beans in these domains. But again, your theory where "reality fluid" is equal to squared amplitude seems to me probably provably wrong, and definitely not proven right. And it was not the assumption I was working under.
Well, yes, I'm assuming that QM is correct. That's kind of the point: we're talking about predictions of QM.
No... why do you think that you would be able to feel it? It seems to me rather like the argument that the Earth can't be moving since we don't feel a strong wind.
An important part of QM being a linear theory is that it is 100% independent of overall amplitude. Scale everything up or down by an arbitrary (finite nonzero) factor and all the bits on the inside work exactly the same.
So, whether something likely happens or something unlikely happens, the only difference between those two outcomes is a matter of scale and whatever it was that happened differently.
Right, I should have been clearer. What I meant is that s/he is privileging one aspect of MWI from unimaginably many, and I simply pointed out another one just as valid, but one that s/he overlooked. Once you start speculating about the structure of Many Worlds, you can come up with as many points and counterpoints as you like, all on the same footing (of the same complexity).
I don't think I had overlooked the point you brought up: I said "...naively speaking it seems that [MWI] should be something more akin to 3^^^3 (or googolplex) than to 3^^^^3. So the problem may still exist..."
As to the idea that everything is just a hopeless mess once you bring MWI into it: that may indeed be a reason that this entire discussion is irresolvable and pointless, or it may be that the "MWI" factors precisely balance out on either side of the argument; but there's no reason to assume that either of those is true until you've explored the issue carefully.
As I said, I don't think MWI leads to really large numbers of copies; back-of-the-envelope calculations suggest it should be "closer to" 3^^^3 or googlplex than to 3^^^^3. So yes: I tried to indicate that this idea does NOT solve the dilemma on its own. However, even if 3^^^^3 is so big as to make 3^^^3 look tiny, the latter is still not negligible, and deserves at least a mention. If Eleizer had mentioned it and dismissed it, I would have no objection. But I think it is notable that he did not.
For instance: Say that there earthwormchuck163 is right and there are fewer than 3^^^^3 intelligent beings possible before you start to duplicate. For instance say it's (x^^^x)^y, and that due to MWI there are (x^^^x) copies of a regular human spawned per fortnight. So MWI is reducing Matrix Lord's threat from (x^^^x)^y to (x^^^x)^(y-1). Doesn't seem like a big change; but if you suppose that only one of them is decisive for this particular Matrix Lord threat, you've just changed the cost/benefit ratio from order-of-1 to order-of-1/(x^^^x), which is a big shift.
I know that there are a number of possible objections to that specific argument. For instance, it's relying on the symmetry of intelligence; if Matrix Lord were offering 3^^^^3 paperclips to clippy, it wouldn't help figure out the clipperific thing to do. The intent is not to make a convincing argument, but simply to demonstrate that a factor on the order of x^^^x can in principle be significant, even when the threat is on the order of 3^^^^3.