Even though it's been quite a few years since I attended any quantum mechanics courses, I did do a talk as an undergraduate on this very experiment, so I'm hoping that what I write below will not be complete rubbish. I'll quickly go through the double slit experiment, and then try to explain what's happening in the delayed choice quantum eraser and why it happens. Disclaimer: I know (or knew) the maths, but our professors did not go to great lengths explaining what 'really' happens, let alone what happens according to the MWI, so my explanation comes from my understanding of the maths and my admittedly more shoddy understanding of the MWI. So take the following with a grain of salt, and I would welcome comments and corrections from better informed people! (Also, the names for the different detectors in the delayed choice explanation are taken from the wikipedia article)
In the normal double slit experiment, letting through one photon at a time, the slit through which the photon went cannot be determined, as the world-state when the photon has landed could have come from either trajectory (so it's still within the same Everett branch), and so both paths of the photon were able to interfere, affecting where it landed. As more photons are sent through, we see evidence of this through the interference pattern created. However, if we measure which slit the photon goes through, the world states when the photon lands are different for each slit the photon went through (in one branch, a measurement exists which says it went through slit A, and in the other, through slit B). Because the end world states are different, the two branch-versions of the photon did not interfere with each other. I think of it like this: starting at a world state at point A, and ending at a world state at point B, if multiple paths of a photon could have led from A to B, then the different paths could interfere with each other. In the case where the slit the photon went through is known, the different paths could not both lead to the same world state (B), and so existed in separate Everett branches, unable to interfere with each other.
Now, with the delayed choice: the key is to resist the temptation to take the state "signal photon has landed, but idler photon has yet to land" as point B in my above analogy. If you did, you'd see that the world state can be reached by the photon going through either slit, and so interference inside this single branch must have occurred. But time doesn't work that way, it turns out: the true final world states are those that take into account where the idler photon went. And so we see that in the world state where the idler photon landed in D1 or D2, this could have occurred whether the photon went through either slit, and so both on D0 (for those photons) and D1/D2, we end up seeing interference patterns, as we're still within a single branch, so to speak (when it comes to this limited interaction, that is). Whereas in the case where the idler photon reaches D3, that world state could not have been reached by the photon going through either slit, and so the trajectory of the photon did not interfere with any other trajectory (since the other trajectory led to a world state where the idler photon was detected at D4, so a separate branch).
So going back to my point A/B analogy, imagine three world states A, B and C as points on a page, and STRAIGHT lines represent different hypothetical paths a photon could take, you can see that if two paths lead from point A to point B, the lines would be on top of each other, meaning a single branch, and the paths would interfere. But if one of the paths led to point A and the other to point B, they would not be on top of each other, they go into different branches, and so the paths would not interfere.
I wonder what probability epiphenomenalists assign to the theory that they are themselves conscious, if they admit that belief in consciousness isn't caused by the experiences that consciousness brings.
The more I think about it, the more absurdly self-defeating it sounds, and I have trouble believing that ANYONE could hold such views after having thought about it for a few minutes. The only reason I continue to think about it is because it's very easy to believe that some people, no matter how an AI acted and for how long, would never believe the AI to be conscious. And that bothers me a lot, if it affects their moral stance on that AI.
I really enjoyed this, it was very well written! Lots of fun new concepts, and plenty of fun old ones being used well.
Looking forward to reading more! Even if there aren't too many new weird things in whatever follows, I really want to see where the story goes.
I very much like bringing these concepts of unambiguous past and ambiguous future to this problem.
As a pattern theorist, I agree that only memory (and the other parts of my brain's patterns which establish my values, personality, etc) matter when it comes to who I am. If I were to wake up tomorrow with Britney Spear's memories, values, and personality, 'I' will have ceased to exist in any important sense, even if that brain still had the same 'consciousness' that Usul describes at the bottom of his post.
Once one links personal identity to one's memories, values and personality, the same kind of thinking about uploading/copying can be applied to future Everett branches of one's current self, and the unambigous past/ambiguous future concepts are even more obviously important.
In a similar way to Usul not caring about his copy, one might 'not care' about a version of oneself in a different Everett branch, but it would still make sense to care about both future instances of yourself BEFORE the split happens, due to the fact that you are uncertain which future you will be 'you' (and of course, in the Everett branch case, you will experience being both, so I guess both will be 'you'). And to bring home the main point regarding uploading/copying, I would much prefer that an entity with my memories/values/personality continue to exist in at least one Everett branch, even if such entities will cease existing in other branches.
Even though I don't have a strong belief in quantum multiverse theory, thinking about Everett branches helped me resolve the is-the-copy-really-me? dilemma for myself, at least. Of course, the main difference (for me) is that with Everett branches, the different versions of me will never interact. With copies of me existing in the same world, I would consider my copy as a maximally close kin and my most trusted ally (as you explain elsewhere in this thread).
Surely there is a difference in kind here. Deleting a copy of a person because it is no longer useful is very different from deleting the LAST existing copy of a person for any reason.
Does the fact that naive neural nets almost always fail when applied to out of sample data constitute a strong general argument against the anti-universalizing approach?
I think this demonstrates the problem rather well. In the end, the phenomenon you are trying to model has a level of complexity N. You want your model (neural network or theory or whatever) to have the same level of complexity - no more, no less. So the fact that naive neural nets fail on out of sample data for a given problem shows that the neural network did not reach sufficient complexity. That most naive neural networks fail shows that most problems have at least a bit more complexity than that embodied in the simplest neural networks.
As for how to approach the problem in view of all this... Consider this: for any particular problem of complexity N, there are N - 1 levels of complexity below it, which may fail to make accurate predictions due to oversimplification. And then there's an infinity of complexity levels above N, which may fail to make accurate predictions due to overfitting. So it makes sense to start with simple theories, and keep adding complexity as new observations arrive, and gradually improve the predictions we make, until we have the simplest theory we can which still produces low errors when predicting new observations.
I say low errors because to truly match all observations would certainly be overfitting! So there at the end we have the same problem again, where we trade off accuracy on current data against overfitting errors on future data... Simple (higher errors) versus complex (higher overfitting)... At the end of the process, only empiricism can help us find the theory that produces the lowest error on future data!
The first paper he mentions in the machine learning section can be found here, if you'd like to take a look: Murphy and Pazzani 1994 I had more trouble finding the others which he briefly mentions, and so relied on his summary for those.
As for the 'complexity of phenomena rather than theories' bit I was talking about, your reminder of Solomonoff induction has made me change my mind, and perhaps we can talk about 'complexity' when it comes to the phenomena themselves after all.
My initial mindset (reworded with Solomonoff induction in mind) was this: Given an algorithm (phenomenon) and the data it generates (observations), we are trying to come up with algorithms (theories) that create the same set of data. In that situation, Occam's Razor is saying "the shorter the algorithm you create which generates the data, the more likely it is to be the same as the original data-generating algorithm". So, as I said before, the theories are judged on their complexity. But the essay is saying, "Given a set of observations, there are many algorithms that could have originally generated it. Some algorithms are simpler than others, but nature does not necessarily choose the simplest algorithm that could generate those observations."
So then it would follow that when searching for a theory, the simplest ones will not always be the correct ones, since the observation-generating phenomenon was not chosen by nature to necessarily be the simplest phenomenon that could generate those observations. I think that may be what the essay is really getting at.
Someone please correct me if I'm wrong, but isn't the above only kinda valid when our observations are incomplete? Intuitively, it would seem to me that given the FULL set of possible observations from a phenomenon, if you believe any theory but the simplest one that generates all of them, surely you're making irrefutably unnecessary assumptions? The only reason you'd ever doubt the simplest theory is if you think there are extra observations you could make which would warrant extra assumptions and a more complex theory...
Looking at the machine learning section of the essay, and the paper it mentions, I believe the author to be making a bit too strong a claim based on the data. When he says:
"In some cases the simpler hypotheses were not the best predictors of the out-of-sample data. This is evidence that on real world data series and formal models simplicity is not necessarily truth-indicative."
... he fails to take into account that many more of the complex hypotheses get high error rates than the simpler hypotheses (despite a few of the more complex hypotheses getting the smallest error rates in some cases), which still says that when you have a whole range of hypotheses, you're more likely to get higher error rates when choosing a single complex one than a single simple one. It sounds like he says Occam's Razor is not useful just because the simplest hypothesis isn't ALWAYS the most likely to be true.
Similarly, when he says:
"In a following study on artificial data generated by an ideal fixed 'answer', (Murphy 1995), it was found that a simplicity bias was useful, but only when the 'answer' was also simple. If the answer was complex a bias towards complexity aided the search."
This is not actually relevant to the discussion of whether simple answers are more likely to be fact than complex answers, for a given phenomenon. If you say "It turns out that you're more likely to be wrong with a simple hypothesis when the true answer is complex", this does not affect one way or the other the claim that simple answers may be more common than complex answers, and thus that simple hypotheses may be, all else being equal, more likely to be true than complex hypotheses when both match the observations.
That being said, I am sympathetic to the author's general argument. While complexity (elaboration), when humans are devising theories, tends to just mean more things which can be wrong when further observations are made, this does not necessarily point to whether natural phenomena is generally 'simple' or not. If you observe only a small (not perfectly representative) fraction of the phenomenon, then a simple hypothesis produced at this time is likely to be proven wrong in the end. I'm not sure if this is really an interesting thing to say, however - when talking about the actual phenomena, they are neither really simple nor complex. They have a single true explanation. It's only when humans are trying to establish the explanation based on limited observation that simplicity and complexity come into it.
If the many-worlds interpretation is truly how the world is, and if having multiple copies of myself as an upload is more valuable than just having one copy on more powerful (or distributed) hardware, then...
I could bid for a job asking for a price which could be adequate if I were working by myself. I could create N copies of myself to help complete the job. Then, assuming there's no easy way to meld my copies back into one, I could create a simple quantum lottery that deletes all but one copy.
Each copy is guaranteed to live on in its own Everett branch, able to enjoy the full reward from completing the job.
Interesting questions to think about. Seeing if everyone independently describes the clothes the same way (as suggested by others) might work, unless the information is leaked. Personally, my mind went straight to the physics of the thing, 'going all science on it' as you say - as emperor, I'd claim that the clothes should have some minimum strength, lest I rip them the moment I put them on. If a piece of the fabric, stretched by the two tailors, can at least support the weight of my hand (or some other light object if you're not too paranoid about the tailor's abilities as illusionists), then it should be suitable.
Then, when your hand (or whatever) goes straight through, either they'll admit that the clothes aren't real, or they'll come up with some excuse about the cloth being so fine that it ripped or things go straight through, at which point you can say that these clothes are useless to you if they'll rip at the slightest movement or somehow phase through flesh, etc.
Incidentally, that's one of my approaches to other things invisible to me that others believe in. Does it have practical uses or create a physical effect in the world? If not, then even if it's really there, there's not much point in acknowledging it...