Physicist and dabbler in writing fantasy/science fiction.
Ben
Karma: 1,502
Imagine you have a machine that flicks a classical coin and then makes either one wavefunction or another based on the coin toss. Your ordinary ignorance of the coin toss, and the quantum stuff with the wavefunction can be rolled together into an object called a density matrix.
There is a one-to-one mapping between density matrices and Wigner functions. So, in fact there are zero redundant parameters when using Wigner functions. In this sense they do one-better than wavefunctions, where the global phase of the universe is a redundant variable. (Density matrices also don’t have global phase.)
That is not to say there are no issues at all with assuming that Wigner functions are ontologically fundamental. For one, while Wigner functions work great for continuous variables (eg. position, momentum), Wigner functions for discrete variables (eg. Qubits, or spin) are a mess. The normal approach can only deal with discrete systems in a prime number of dimensions (IE a particle with 3 possible spin states is fine, but 6 is not.). If the number of dimensions is not prime weird extra tricks are needed.
A second issue is that the Wigner function, being equivalent to a density matrix, combines both quantum stuff and the ignorance of the observer into one object. But the ignorance of the observer should be left behind if we were trying to raise it to being ontologically fundamental, which would require some change.
Another issue with “ontologising” the Wigner function is that you need some kind of idea of what those negatives “really mean”. I spent some time thinking about “If the many worlds interpretation comes from ontologising the wavefunction, what comes from doing that to the Wigner function?” a few years ago. I never got anywhere.
Something you and the OP might find interesting is one of those things that is basically equivalent to a wavefunction, but represented in different mathematics is a Wigner function. It behaves almost exactly like a classical probability distribution, for example it integrates up to 1. Bayes rule updates it when you measure stuff. However, in order for it to “do quantum physics” it needs the ability to have small negative patches. So quantum physics can be modelled as a random stochastic process, if negative probabilities are allowed. (Incidentally, this is often used as a test of “quantumness”: do I need negative probabilities to model it with local stochastic stuff? If yes, then it is quantum).
If you are interested in a sketch of the maths. Take W to be a completely normal probability distribution, describing what you know about some isolated, classical ,1d system. And take H to be the classical Hamiltonian (IE just a function for the system’s energy). Then, the correct way of evolving your probability distribution (for an isolated classical, 1D system) is:
Where the arrows on the derivatives have the obvious effect of firing them either at H or W. The first pair of derivatives in the bracket is Newton’s Second law (rate of change of Energy (H) with respect to X is going to turn potential’s into Forces, and the rate of change with momentum on W then changes the momentum in proportion to the force), the second term is the definition of momentum (position changes are proportional to momentum).Instead of going to operators and wavefunctions in Hilbert space, it is possible to do quantum physics by replacing the previous equation with:
Where sin is understood from Taylor series, so the first term (after the hbars/2 cancel) is the same as the first term for classical physics. The higher order terms (where the hbars do not fully cancel) can result in W becoming negative in places even if it was initially all-positive. Which means that W is no longer exactly like a probability distribution, but is some similar but different animal. Just to mess with us the negative patches never get big enough or deep enough for any measurement we can make (limited by uncertainty principle) to have a negative probability of any observable outcome. H is still just a normal function of energy here.
(Wikipedia is terrible for this topic. Way too much maths stuff for my taste: https://en.wikipedia.org/wiki/Moyal_bracket)
Also, the OP is largely correct when they say “destructive interference is the only issue”. However, in the language of probability distributions dealing with that involves the negative probabilities above. And once they go negative they are not proper probabilities any more, but some new creature. This, for example, stops us from thinking of them as just our ignorance. (Although they certainly include our ignorance).
That is really interesting, thanks for sharing it. Japan has such a reputation for this that it is fascinating to see that eg. Italians and Spaniards work more hours despite the European working time directive.
Question 2: Why do Japanese automakers operate some factories in America instead of importing everything from Japan?
Subsidies and tariffs are the reason for this. Importing a finished car into the USA from Japan will face tariffs (taxes) imposed by the US government. A car built in the USA by a Japanese company will benefit from subsidies given out by the US government. The entire point of these policies is so that the factories are moved from eg. Japan to the USA. This makes the cars more expensive overall (if it was cheaper to make them in America the companies would have already done this without the government intervention), but has the effect of moving employment from Japan to the USA.
Overall it makes the whole world a tiny bit poorer than it could have been, and moves a small amount of employment from one place to another. (IE it may be net-good for the USA, assuming that you think workers are more important than consumers, but it is pure-bad for Japan and net-bad for the world. Its kind of like Defecting in a two-country prisoner’s dilemma, with the added twist that the prize you get for defecting is only beneficial to some of your citizens and is harmful to others.)
Question 1: Why would an hour of labor from an American be worth 2x as much as an hour from a Japanese employee?
An hour spent working in Japan produces half the value of an hour spent working in the USA. This does not mean that an American can do the same job twice as fast as a Japanese person. For one thing, American’s have different jobs than Japanese people. For another: Japanese people have office culture rules that nobody goes home before the boss. This means that at 8pm on a weekday, if the boss hasn’t gone home yet, nobody else has either (a common occurrence). But they all got brain-fried from overwork at 6pm and have been twiddling their thumbs for two hours. The statistics will then show is the total number of hours (including those two hours wasted) and the output, and they will come out on-average less productive than Americans. That is just one example of the kind of thing that can move the dial on that. As another example, one hour of labour from a man with a combine harvester really is worth dozens or hundreds times as much as one hour of labour from a man with a scythe. Japan’s use of technology may be behind the US’s. Not with literal scythes. Maybe faxes instead of emails. Things like that.
That fight (when I scanned over it briefly yesterday) seemed to be you and one other user (Shankar Sivarajan), having a sort of comment tennis game where you were pinging back an fourth, and (when I saw it) you both had downvotes that looked like you were both downvoting the other, and no one else was participating. I imagine that neither of was learning or having fun from that conversation. Ending that kind of chain might be the place the rate-limit has a use case. Whether it is the right solution I don’t know.
I certainly understand this feeling.
My (optimistic?) expectation is that it ends up (long run) a bit like baking. You can go into a supermarket and buy bread or cakes, but many people enjoy baking at home and there is a wonderful social sharing aspect to all tucking into a cake that someone at the table baked. In this context a human using an AI tool but applying some prompt changes or edits is maybe (depending on the level of AI use and human intervention) somewhere like using packet-mix, or premade pastry, or even just one of those already-made cakes that is intended for you to decorate with icing.
As a consumer, if I am listening to the Beatles say, I don’t think the fact that they were human is relevant to the enjoyment I derive from it. I never expect to meet any of them, some of them died before I was born. The same notes composed and synthesised from a computer would be the same notes and affect me the same way. But, when my wife plays me a song she wrote on the piano then that is something special that I would certainly not automate.
Many musicians on radio interviews or similar try and show more of who they are out to the audience (or at least a persona), presumably to try and make it feel more like the “song by someone I know” thing. At that scale its more “celebrity-following”, but that is also something the AI would not have—I don’t know how big a deal that is.
Also, thank you for mentioning Worth the Candle. I had not heard of it before but am now enjoying it quite a lot.
I not getting the “he should never have published his last name” thing. If Scot didn’t want his surname to be published then it would be a kindness to respect his wishes. But can you imagine writing a newspaper article where you are reporting on the actions of an anonymous person? Its borderline nonsense. Especially if it is true that 5 minutes is all that it takes to find out who they are. If I read a newspaper article about the antics of a secret person, then I worked out who they were in 5 mins, my estimate of the journalist writing it would drop through the floor. Imagine you read about the mysterious father of bitcoin, or an unknown major donor to a political party, all dressed in secrecy, and then two googles later you know who it is. It would reflect so badly on the paper you were reading.
I think our journalist is correct when he says that the choice was not to write about him at all, or to give his full name, by the standards of every newspaper I have ever read (only UK papers, maybe there are differences in the US). In print journalism it is the standard to refer to people by Title Firstname Surname, the/a REASON WE CARE. (EG. “Mr Ed Miliband, the Shadow Secretary for the Environment”, “Dr Slate Star a prominent blogger”).
Maybe there is an angle on this I am missing? (His name is a BIG DEAL for some reason? But that just makes publishing it more essential not less.)
A couple of years ago a company I had never heard of sent me a questionaire, in which they said they were responsible for the pipes that took gas to my home. One question was “Do you have a positive opinion of whoever we are?” to which I answered “Neither positive nor negative opinion.”
In the “any other comments” section I told them they were really great. Because the fact that I had never heard of them before was a product of never having a gas problem. For them “no one has heard of us” is a sign of wining.
I think the veto thing you suggest is an ad-hoc patch that might be able to hold things together if they have already gone very wrong.
If you have one monolithic group of 51% who share a particular culture, religion, ethnicity, industry and class vs 49% who are different on every metric then I don’t think any system (baring splitting the country in two) is going to deal with it well. But, if religion cuts the population in pieces. And so does ethnicity. And so does conservatism, and so does class and so does culture, but they are all uncorrelated, then there is little room for a tyranny of the majority. Nobody can build an election platform on any specific one of those splits, because there is someone else muddying the waters by trying to drive a wedge through a different one.
As a voter you set out into the demagogue market, the first person tries to sell you on the idea of the Christian majority bashing up the rest. The second in your ethnicity sticking it to the others. The third says “Eat the rich, and take their money”. You leave disappointed, as what you wanted was someone who would advance the interests of farmers, who after all, are 51% of the population. Each of these groups trips over the others.
The American civil war is a good example. The North and South were divided by the issue of slavery, but the North was also richer, more industrialised, more cosmopolitan and more urban. I imagine the troubles in Northern Ireland would have been much less violent if the Protestant—Catholic divide had been uncorrelated with the Unionist—Republican one.
Very interesting.
I am wondering, do you think your clients are lying to you because they don’t trust you specifically (which would be understandable to some extent)? Or do you think its more that they don’t trust themselves to act out two different narratives? [IE in the case where they tell you its all true, but still want to keep open the option of denying it to the court]. That somehow by committing completely to the “wasn’t me” narrative in every action (and, as much as possible, every thought) they have a chance of dragging the timeline into a parallel universe where it really wasn’t, or by some other mechanism improve there chances.
Whether Beauty should bet each time she wakes up depends very critically on the rules of the wager. Some examples:
Rule 1: Independent awakening bets: Each awakening beauty can bet $1 on the outcome of the coin. The bets at each awakening all stand independently. -In this case she should bet as if it was a 2/3rd chance of tails. After 100 coin tosses she has awoken 150 times, and for 100 of them it was tails.
Rule 2: Last bet stands: Each awakening beauty can bet $1 on the outcome of the coin. Only beauty’s final decision for each toss is taken into account, for example any bet she makes Tuesday replaces anything decided on Monday. -She treats it as 50⁄50.
Rule 2: Guess Right You Live (GRYL): On each awakening beauty must guess the coins outcome. If she has made no correct guess by the end of the run, she is killed. -For fair coin pick randomly between heads and tails, but for an unfair coin its a bit weird: https://www.lesswrong.com/posts/HQFpRWGbJxjHvTjnw/?commentId=BrvGnFvpK3fpndXGB
Rule 3: Guess Wrong you Die (GRYD): On each awakening beauty must guess the coins outcome. If she has made any incorrect guesses by the end of the run, she is killed. -She should pick either heads or tails beforehand and always pick that. Picking heads is just as good as picking tails.
The above set gives 1 “thirder’s game”, two “halfer’s games” and one that I can’t classify (GRYL). She will certainly find herself betting in twice as many tails situations as heads ones (hence the Rule 1 solution), but whether that should determine her betting strategy depends on the rules of the bet. As Ape in Coat has said Rule 1 can be interpreted as “50/50 coin, but your deposit and winnings are both doubled on tails” (because on tails Beauty makes two wagers).
This is a very nice post, that has clarified my understanding a lot.
Previously I thought that it was just “per experiment” vs “per awakening” being underspecified in the problem. But you are completely correct that when we consider “per awakening” then its not really acceptable to treat it as random when consecutive awakenings are correlated.
I assume that the obvious extension to some of the anthropic thought experiments where I am copied also holds? For example: a coin is flicked, on heads I wake up in a room, on tails 1E6 identical copies of me wake up in separate rooms. I don’t reason “its almost certainly tails because I am in a room.”, I instead reason “the two options were heads&awake, and heads(&awake)^E6, two options: so its 50⁄50. [I can still legitimately decide that I care more about worlds where more of me exist, and act accordingly, but that is a values argument, not a probability one.]
I think there is some context missing. When I see “taking nicotine” I think “smoking a cigarette, but expressed using more science-y language to make it sound like a less awful idea”. Whereas you seem to be taking nicotine gum or something, which is a different proposition. (I think smoking is a very bad idea, with very high confidence. I think nicotine by other sources is also a very bad idea, but my confidence is lower).
“No no no. Bob, a crackpot is someone who proposes new theories without being a professor.”—Fantastic line.
Most (all?) predictions are actually conditional. A prediction about the next election is understood to be conditional on “assuming the sun doesn’t go supernova and kill us all first”, the same supernova-exception applied to the pendulum, along with a host of others.
The professor, doing Newtonian mechanics, didn’t just make a prediction. They presented a derivation, where they made many assumptions, some explicit (ignoring air resistance) others implicit (the hook holding the pendulum was assumed stationary in the diagrams/explanation, no supernova was represented in the diagram). The pendulum falling over violated the assumptions that were made clear (beforehand) in the explanation/derivation. So the Bayesian has data something like “Newtonian says P(period =~ 3.6| these assumptions) is high”. “these assumptions” was not true, so we can say nothing about the conditional.
The explanation is where the professor committed to which things would be allowed to count against the theory. A prediction based on this model of what happened is that pseudo-scientific theories will very often engage in explanations that lack clarity and precision, in order to sweep more genuine failures into the “assumptions didn’t apply” bucket.
It is very interesting how weak the correlation is.
I like the use of the median, I can’t remember what I put on the survey but it could easily have been 1%, 0.1% or 0.01% depending on what I was thinking at that moment (this I consider a big downside of asking for a numerical probability instead of forcing a choice of terms like “unlikely” etc). Median should avoid that issue.
I am very impressed with the art, interrace and most especially the way they synergise. I didn’t realise until I came to writing this that, as I am on dark mode, the fact that it looks good and is easy to use from my perspective is doubly impressive.
As a side-note to the existing great answers. If a deontological constraint simply prevents you from taking an action under any circumstances, then it might as well be a physical constraint (eg. you cannot fly).
Operating with more constraints (physical or otherwise) gives you less power, so typically results in you getting less of what you want. But if all agents with limits could be money-pumped, then all agents could be.
I think it depends on the meaning attached to the word “love”. There are two possibilities:
I “love” this, because it brings me benefits. (it is instrumental in increasing my utility function, like chocolate ice cream)
I “love” this, in that I want it to benefit. (Its happiness appears as a parameter in my utility function)
You can have a partner or family member who means one the other or both to you. The striking dementia example from Odd Anon is a case where the dementia makes it so the person’s company no longer makes you happy, but you may still be invested in them being happy.
The first one is obviously never going to be unconditional. The second one seems like it could be unconditional in some cases. In that a parent or spouse really wants their child or partner to be happy even if that child or partner is a complete villain. Its not even necessary that they value the child/partner over everything else, only that they maintain a strong-ish preference for the them being happy over not being happy, all else being equal.