Wow. I’ve never run into a text using “we have” as assuming something’s provability, rather than assuming its truth.
So the application of the deduction theorem is just plain wrong then? If what you actually get via Lob’s theorem is ◻((◻C)->C) ->◻C, then the deduction theorem does not give the claimed ((◻C)->C)->C, but instead gives ◻((◻C)->C)->C, from which the next inference does not follow.
The issue is not want of an explanation for the phenomenon, away or otherwise. We have an explanation of the phenomenon, in fact we have several. That’s not the issue. What I’m talking about here is the inherent, not-a-result-of-my-limited-knowledge probabilities that are a part of all explanations of the phenomenon.
Past me apparently insisted on trying to explain this in terminology that works well in collapse or pilot-wave models, but not in many-worlds models. Sorry about that. To try and clear this up, let me go through a “guess the beam-splitter result” game in many-worlds terminology and compare that to a “guess the trillionth digit of pi” game in the same terminology.
Aside: Technically it’s the amplitudes that split in many-worlds models, and somehow these amplitudes are multiplied by their complex conjugates to get you answers to questions about guessing games (no model has an explanation for that part). As is common around these parts, I’m going to ignore this and talk as if it’s the probabilities themselves that split. I guess nobody likes writing “square root” all the time.
Set up a 50⁄50 beam-splitter. Put a detector in one path and block the other. Write your choice of “Detected” or “Not Detected” on a piece of paper. Now fire a single photon. In Everett-speak, half of the yous end up in branches where the photon’s path matches your guess while half of the yous don’t. The 50⁄50 nature of this split remains even if you know the exact quantum state of the photon beforehand. Furthermore, the branching of yous that try to use all your physics knowledge to predict their observations have no larger a proportion of success than the branching of yous that make their predictions by just flipping a coin, always guessing Fire, or employing literally any other strategy that generates valid guesses. The 50⁄50 value of this branching process is completely decoupled from your predictions, no matter what information you use to make those predictions.
Compare this to the process of guessing the trillionth digit of pi. If you make your guess by rolling a quantum die, then 1 out of 10 yous will end up in a branch where your guess matches the actual trillionth digit of pi. If you instead use those algorithms you know to calculate a guess, and you code/run them correctly, then basically all of the yous end up in a branch where your guess is correct.
We now see the fundamental difference. Changing your guessing strategy results in different correct/incorrect branching ratios for the “guess the trillionth digit of pi” game but not for the “guess the beam-splitter result” game. This is the Everett-speak version of saying that the beam-splitter’s 50⁄50 odds is a property of the universe while the trillionth digit of pi’s 1⁄10 odds is a function of our (current) ignorance. You can opt to replace “odds” with “branching ratios” and declare that there is no probability of any kind, but that just seems like semantics to me. In particular the example of the ten trillionth digit of pi should not be what prompts this decision. Even in the many-worlds model there’s still a fundamental difference between that and the quantum processes that physicists cite as intrinsically random.
I two-box.
Three days later, “Omega” appears in the sky and makes an announcement. “Greeting earthlings. I am sorry to say that I have lied to you. I am actually Alpha, a galactic superintelligence who hates that Omega asshole. I came to predict your species’ reaction to my arch-nemesis Omega and I must say that I am disappointed. So many of you chose the obviously-irrational single-box strategy that I must decree your species unworthy of this universe. Goodbye.”
Giant laser beam then obliterates earth. I die wishing I’d done more to warn the world of this highly-improbable threat.
TLDR: I don’t buy this post’s argument that I should become the type of agent that sees one-boxing on Newcomb-like problems as rational. It is trivial to construct any number of no-less plausible scenarios where a superintelligence descends from the heavens and puts a few thousand people through Newcomb’s problem before suddenly annihilating those who one-box. The presented argument for becoming the type of agent that Omega predicts will one-box can be equally used to argue for becoming the type of agent that Alpha predicts will two-box. Why then should it sway me in either direction?
“Why did the universe seem to start from a condition of low entropy?”
I’m confused here. If we don’t go with a big universe and instead just say that our observable universe is the whole thing, then tracing back time we find that it began with a very small volume. While it’s true that such a system wold necessarily have low entropy, that’s largely because small volume = not many different places to put things.
Alternative hypothesis: The universe began in a state of maximal entropy. This maximum value was “low” compared to present day because the early universe was small. As the universe expands, its maximum entropy grows. Its realized entropy also grows, just not as fast as its maximal entropy.
“Specifically, going between two universal machines cannot increase the hypothesis length any more than the length of the compiler from one machine to the other. This length is fixed, independent of the hypothesis, so the more data you use, the less this difference matters.”
This doesn’t completely resolve my concern here, as there are infinitely many possible Turing machines. If you pick one and I’m free to pick any other, is there a bound on the length of the compiler? If not, then I don’t see how the compiler length placing a bound on any specific change in Turing machine makes the problem of which machine to use irrelevant.
To be clear: I am aware that starting with different machines, the process of updating on shared observations will eventually lead us to similar distributions even if we started with wildly different priors. My concern is that if “wildly different” is unbounded then “eventually” might also be unbounded even for a fixed value of “similar.” If this does indeed happen, then it’s not clear to me how S I does anything more useful than “Pick your favorite normalized distribution without any 0s or 1s and then update via Bayes.”
Edit: Also thanks for the intro. It’s a lot more accessible than anything else I’ve encountered on the topic.
You’ve only moved the problem down one step.
Five years ago I sat in a lab with a beam-spitter and a single-photon multiplier tube. I watched as the SPMT clicked half the time and didn’t click half the time, with no way to predict which I would observe. You’re claiming that the tube clicked every time, and the the part of me that noticed one half is very disconnected from the part of me that noticed the other half. The problem is that this still doesn’t allow me to postdict which of the two halves the part of me that is typing this should have in his memory right now.
Take the me sitting here right now, with the memory of the specific half of the clicks he has right now. As far as we understand physics, he can’t postdict which memory that should have been. Even in your model, he can postdict that there will be many branches of him with each possible memory, but he can’t postdict which of those branches he’ll be—only the probability of him being any one of the branches.
Did the survey, except digit ratio due to lack of precision measuring devices.
As for feedback, I had some trouble interpreting a few of the questions. There were some times when you defined terms like human biodiversity, and I agreed with some of the claims in the definition but not others, but since I had no real way to weight the claims by importance it was difficult for me to turn my conclusions into a single confidence measurement. I also had no idea weather the best-selling computer game question was supposed to account for inflation or general growth of the videogame market, nor whether we were measuring in terms of copies sold or revenue earned or something else entirely, nor whether console games or games that “sell” for 0$ counted. I ended up copping out by listing a game that is technically included in a bit of software I knew sold very well for its time (and not for free), but the software was not sold as a computer game.
Also, a weird thing happened with the calibration questions When I was very unsure which of a large number of possible answers was correct, and especially if I wasn’t even sure how many possible answers there were, I found myself wanting to write an answer that was obviously impossible (like writing “Mars” for Obama’s birth state) and putting a 0 for the calibration. I didn’t actually do this, but it sure was tempting.
The Many Physicists description never talked about the electron only going one way. It talked about detecting the electron. There’s no metaphysics there, only experiment. Set up a two-slit configuration and put a detector at one slit, and you see it firing half the time. You may say that the electron goes both ways every time, but we still only have the detector firing half the time. We also cannot predict which half of the trials will have the detector firing and which won’t. And everything we understand about particle physics indicates that both the 1⁄2 and the trial-by-trial unpredictability is NOT coming from ignorance of hidden properties or variables but from the fundamental way the universe works.
I don’t think this is what’s actually going on in the brains of most humans.
Suppose there were ten random people who each told you that gravity would be suddenly reversing soon, but each one predicted a different month. For simplicity, person 1 predicts the gravity reversal will come in 1 month, person 2 predicts it will come in 2 months, etc.
Now you wait a month, and there’s no gravity reversal, so clearly person 1 is wrong. You wait another month, and clearly person 2 is wrong. Then person 3 is proved wrong, as is person 4 and then 5 and then 6 and 7 and 8 and 9. And so when you approach the 10-month mark, you probably aren’t going to be expecting a gravity-reversal.
Now, do you not suspect the gravity-reversal at month ten simply because it’s not as simple as saying “there will never a be a gravity reversal,” or is your dismissal substantially motivated by the fact that the claim type-matches nine other claims that have already been disproven? I think that in practice most people end up adopting the latter approach.
Suppose my decision algorithm for the “both boxes are transparent” case is to take only box B if and only if it is empty, and to take both boxes if and only if box B has a million dollars in it. How does Omega respond? No matter how it handles box B, it’s implied prediction will be wrong.
Perhaps just as slippery, what if my algorithm is to take only box B if and only if it contains a million dollars, and to take both boxes if and only if box B is empty? In this case, anything Omega predicts will be accurate, so what prediction does it make?
Come to think of it, I could implement the second algorithm (and maybe the first) if a million dollars weighs enough compared to the boxes. Suppose my decision algorithm outputs: “Grab box B and test it’s weight, and maybe shake it a bit. If it clearly has a million dollars in it, take only box B. Otherwise, take both boxes.” If that’s my algorithm, then I don’t think the problem actually tells us what Omega predicts, and thus what outcome I’m getting.
The problem isn’t objectification of women, it’s a lack of non-objectified female characters.
Men are objectified a lot in media. As a simple example, the overwhelming majority of mooks are male, and these characters exist solely to be mowed down so the audience can see how awesome the hero(ine) is (or sometimes how dangerous the villain is). They are hapless, often unthinking and with basically no backstory to speak of. Most of the time they aren’t even given names. So why doesn’t this common male objectification bring outrage?
I think the reason is that there are also plenty of male characters who aren’t objectified. Male characters with clear agency abound in fiction, far more so than female characters. And this way, male viewers can identify with the agency-bearing male characters, and the objectified mooks become far less problematic.
The issue isn’t with there merely being a bunch of objectified female characters. The issue is that until very recently, objectified characters were pretty much all that women got. If we get a healthy number of non-objectified female characters with clear agency, who obtain value in a myriad of ways (and not just by being sexy), then the objectified ones won’t be nearly as problematic.
Took the survey. I definitely did have an IQ test when I was a kid, but I don’t think anyone ever told me the results and if they did I sure don’t remember it.
Also, as a scientist I counted my various research techniques as new methods that help make my beliefs more accurate, which means I put something like 2/day for trying them and 1/week for them working. In hindsight I’m guessing this interpretation is not what you meant, and that science in general might count as ONE method altogether.
But there’s also the observed matter-antimatter asymmetry. Observations strongly indicate that right now we have a lot more electrons than positrons. If it was just one electron going back and forth in time (and occasionally being a photon), we’d expect at most one extra electron.
Not to mention the fact that positrons = electrons going backwards in time only works if you ignore gravity.
There’s also the observed matter-antimatter asymmetry. Even if you want to argue that virtual electrons aren’t real and thus don’t count, it still seems to be the case that there are a lot more electrons than positrons. If it was just one electron going back and forth in time, we’d expect at most one extra electron.
Not to mention the fact that positrons = electrons going backwards in time only works if you ignore gravity.
Eliezer, why no mention of the no-cloning theorem?
Also, some thoughts this has triggered:
Distinguishability can be shown to exist for some types of objects in just the same way that it can be shown to not exist for electrons. Flip two coins. If the coins are indistinguishable, then the HT state is the same as the TH state, and you only have three possible states. But if the coins are distinguishable, then HT is not TH, and there are four possible states. You can experimentally verify that the probability obeys the latter situation, and not the former. And of course, you can experimentally verify that electron pairs obeys the former situation, and not the latter. This is probably just because the coins are qualitatively distinct, while the electrons are not.
But it seems that if you did make a quantum copy (no-cloning theorem be damned!) then after a bit of interaction with the different environments, the two would become distinguishable (on the basis of developing different qualitative identities) and start behaving more like the coins than the electrons. In fact, if you’re actually using the lightspeed limit then the reconstructed you would be several years younger, and immediately distinguishable from what the scanned you has since evolved into. At the time of reconstruction, the two are already acting like coins and not electrons. Does this break the argument? I’m not really sure, because the reconstructed you at the time of reconstruction would still be indistinguishable from the you at the time of scanning, if you could somehow get them both around at the same time.
Bonus! The reconstructed you could be seen to have a very qualitatively different time-evolution. The scanned you evolves throughout its entire history via a Hamiltonian which itself changes continuously as scanned-you moves continuously through your environment. Reconstructed you, however, has a clear discontinuity in its Hamiltonian at the time of reconstruction (the state is effectively instantly moved from one environment into a completely different environment). The state of the reconstructed you would still evolve continuously, it would just have a discontinuous derivative. So I’m not really sure if reconstructed you would fail to pass the bar of having a “continuity of identity” that a lot of people talk about when dealing with the concept of self. My gut says no, but I’m not sure why.
Okay, we need to be really careful about this.
If you sign up for cryonics at time T1, then the not-signed-up branch has lower amplitude after T1 than it had before T1. But this is very different from saying that the not-signed up branch has lower amplitude after T1 than it would have had after T1 if you had not signed up for cryonics at T1. In fact, the latter statement is necessarily false if physics really is timeless.
I think this latter point is what the other posters are driving at. It is true that if there is a branch at T1 where some yous go down a path where they sign up and others don’t, then the amplitude for not-signed-up is lower after T1. But this happens even if this particular you doesn’t go down the signed-up branch. What matters is that the branch point occurs, not which one any specific you takes.
In other words, amplitude is always being seeped from the not-signed-up branch, even if some particular you keeps not leaving that branch.
Edit: Looks like I was assuming probability distributions for which Lim (Y → infinity) of Y*P(Y) is well defined. This turns out to be monotonic series or some similar class (thanks shinoteki).
I think it’s still the case that a probability distribution that would lead to TraderJoe’s claim of P(Y)*Y tending to infinity as Y grows would be un-normalizable. You can of course have a distribution for which this limit is undefined, but that’s a different story.
You can have a credence of 1⁄2 for heads in the absence of which-day knowledge, but for consistency you will also need P(Heads | Monday) = 2⁄3 and P(Monday) = 3⁄4. Neither of these match frequentist notions unless you count each awakening after a Tails result as half a result (in which case they both match frequentist notions).
With individual differences, people are being judged as individuals, and on the basis of their individual capabilities.
With racial differences, people are being judged as members of a race, and not on the basis of their individual capabilities.
At least, that’s the fear.
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I see three distinct issues with the argument you present.
First is line 1 of your reasoning. A finite universe does not entail a finite configuration space. I think the cleanest way to see this is through superposition. If |A> and |B> are two orthogonal states in the configuration space, then so are all states of the form a|A> + b|B>, where a and b are complex numbers with |a|^2 + |b|^2 = 1. There are infinitely many such numbers we can use, so even from just two orthogonal states we can build an infinite configuration space. That said, there’s something called Poincare recurrence which is sort of what you want here, except...
Line 4 is in error. Even if you did have a finite configuration space, a non-static point could just evolve in a loop, which need not cover every element of the configuration space. Two distinct points could evolve in loops that never go anywhere near each other.
Finally, even if you could guarantee that two distinct points would each eventually evolve through some common point A, line 6 does not necessarily follow because it is technically possible to have a situation where both evolutions do in fact reach A infinitely many times, but never simultaneously. Admittedly though, it would require fine-tuning to ensure that two initially-distinct states never hit “nearly A” at the same time, which might be enough.