Physicist and dabbler in writing fantasy/science fiction.
Ben
I remember reading something about the Great Leap Forward in China (it may have been the Cultural Revolution, but I think it was the Great Leap Forward) where some communist party official recognised that the policy had killed a lot of people and ruined the lives of nearly an entire generation, but they argued it was still a net good because it would enrich future generations of people in China.
For individuals you weigh up the risk/rewards of differing your resource for the future. But, as a society asking individuals to give up a lot of potential utility for unborn future generations is a harder sell. It requires coercion.
I think we might be talking past each other. I will try and clarify what I meant.
Firstly, I fully agree with you that standard game theory should give you access to randomization mechanisms. I was just saying that I think that hypotheticals where you are judged on the process you use to decide, and not on your final decision are a bad way of working out which processes are good, because the hypothetical can just declare any process to be the one it rewards by fiat.
Related to the randomization mechanisms, in the kinds of problems people worry about with predictors guessing your actions in advance its very important to distinguish between [1] (pseudo-)randomization processes that the predictor can predict, and [2] ones that it cannot.
[1] Randomisation that can be predicted by the predictor is (I think) a completely uncontroversial resource to give agents in these problems. In this case we don’t need to make predictions like “the agent will randomise”, because we can instead make the stronger prediction “the agent will randomize, and the seed of their RNG is this, so they will take one box” which is just a longer way of saying “they will one box”. We don’t need the predictor to show its working by mentioning the RNG intermediate step.
[2] Randomisation that is beyond the predictor’s power is (I think) not the kind of thing that can sensibly be included in these thought experiments. We cannot simultaneously assume that the predictor is pretty good at predicting our actions and useless at predicting a random number generator we might use to choose our actions. The premises: “Alice has a perfect quantum random number generator that is completely beyond the power of Omega to predict. Alice uses this machine to make decisions. Omega can predict Alice’s decisions with 99% accuracy” are incoherent.
So I don’t see how randomization helps. The first kind, [1] doesn’t change anything, and the second kind [2], seems like it cannot be consistently combined with the premise of the question. Perfect predictors and perfect random number generators cannot exist in the same universe.
Their might be interesting nearby problems where you imagine the predictor is 100% effective at determining the agents algorithm, but because the agent has access to a perfect random number generator that it cannot predict their actions. Maybe this is what you meant? In this kind of situation I am still much happier with rules like “It will fill the box with gold if it knows their is a <50% chance of you picking it”, [the closest we can get to “outcomes not processes” in probabilistic land], (or perhaps the alternative “the probability that it fills the box with gold is one-minus the probability with which it predicts the agent will pick the box”.). But rules like “It will fill the box with gold if the agents process uses either randomisation or causal decision theory” seem unhelpful to me.
I see where you are coming from. But, I think the reason we are interested in CDT (for any DT) in the first place is because we want to know which one works best. However, if we allow the outcomes to be judged not just on the decision we make, but also on the process used to reach that decision then I don’t think we can learn anything useful.
Or, to put it from a different angle, IF the process P is used to reach decision X, but my “score” depends not just on X but also P then that can be mapped to a different problem where my decision is “P and X”, and I use some other process (P’) to decide which P to use.
For example, if a student on a maths paper is told they will be marked not just on the answer they give, but the working out they write on the paper—with points deducted for crossings outs or mistakes—we could easily imagine the student using other sheets of paper (or the inside of their head) to first work out the working they are going to show and the answer that goes with it. Here the decision problem “output” is the entire exame paper, not just the answer.
I like this framing.
An alternative framing, which I think is also part of the answer is that some art is supposed to hit a very large audience and give each a small amount of utility, and other art is supposed to hit a smaller, more specialized, audience very hard. This framing explains things like traditional daytime TV, stuff that no one really loves but a large number of bored people find kind of unobjectionable. And how that is different from the more specialist TV you might actually look forward to an episode off but might hit a smaller audience.
(Obviously some things can hit a big audience and be good, and others can be bad on both counts. But the interesting quadrants two compare are the other two).
Random thoughts. You can relatively simply get a global phase factor at each timestep if you want. I don;t think a global phase factor at each step really counts as meaningfully different though. Anyway, as an example of this:
So that, at each (classical) timestep every single element of the CA tape just moves one step to the right. (So any patterns of 1′s and 0′s just orbit the tape in circles forever, unchanging.). Its quite a boring CA, but a simple example.
We can take the quantum CA that is exactly the same, but with some complex phase factor:
Where the delta function is saying “1 iff , else 0.”
This is exactly the same as the old classical one (everything moves on step to the right), but this time we also have a global phase factor applied to the total system. The total phase factor is , where N is the total number of cells on the tape.
Tiny bit more interesting:
Now we only gain phase factors on values of 1, so the global phase depends on the total number of 1′s on the tape, rather than its length.
To get proper quantum stuff we need phase factors that are not global. (IE some relative phases). I feel like this equation below is a reasonable kind of place to start, but I have run out of time for now so might return to this later.
After finding a Unitary that comes from one of your classical Cellular Automata then any power of that unitary will also be a valid unitary. So for example in classical logic their is a the “swap” gate for binary inputs, but in quantum computing the “square-root swap” gate also exists.
So you can get one of your existing unitary matrices, and (for example) take its square root. That would kind of be like a quantum system doing the classical Cellular Automata, that is interrupted halfway through the first step. (Because applying the root matrix twice is the same as applying the matrix). Similarly you can look at the 1/3rd step by applying the cube root of the matrix.
So would you consider the square root matrix a quantum elementary CA? Its not exactly equivalent to anything classical, because classically you can’t look “between the steps”.
[This is a long winded way of me saying that I don’t “get” the question. You want a unitary, U, of the form given in that equation for <y|U|x>, but you also don’t want U to be “basically equivalent” to a classical CA. How are you defining “basically equivalent”, is anything satisfying your equation automatically “basically equivalent”?]
I think the limitations to radius set by material strength only apply directly to a cylinder spinning by itself without an outer support structure. For example, I think a rotating cylinder habitat surrounded by giant ball bearings connecting it to a non-rotating outer shell can use that outer shell as a foundation, so each part of the cylinder that is “suspended” between two adjacent ball bearings is like a suspension bridge of that length, rather than the whole thing being like a suspension bridge of length equal to the total cylinder diameter. Obviously you would need really smooth, low-friction bearings for this to be a plan to consider, although they would also help with wobble. One way of reducing the friction would be a Russian doll configuration of nested cylinders where each one out was rotating less fast than the previous, which (along with bearings etc) could maybe work.
On a similar vein, you could replace the mechanical bearings with a gas or fluid, in which the cylinder is immersed. Similar advantages in damping the wobble modes and (for fluids or very high pressure gases) helping support the cylinder against its own centrifugal weight. The big downside again would be friction.
If this was the setup I would bet on “hard man” fitness people swearing that running with the spin to run in a little more than earth normal gravity was great for building strength and endurance and some doctor somewhere would be warning people that the fad may not be good for your long term health.
Yes, its a bit weird. I was replying because I thought (perhaps getting the wrong end of the stick) that you were confused about what the question was, not (as it seems now) pointing out that the question (in your view) is open to being confused.
In probability theory the phrase “given that” is a very important, and it is (as far as I know) always used in the way used here. [“given that X happens” means “X may or may not happen, but we are thinking about the cases where it does”, which is very different from meaning “X always happens”]
A more common use would be “What is the probability that a person is sick, given that they are visiting a doctor right now?”. This doesn’t mean “everyone in the world is visiting a doctor right now”, it means that the people who are not visiting a doctor right now exist, but we are not talking about them. Similarly, the original post’s imagined world involves cases where odd numbers are rolled, but we are talking about the set without odds. It is weird to think about how proposing a whole set of imaginary situations (odd and even rolls) then talking only about a subset of them (only evens) is NOT the same as initially proposing the smaller set of imaginary events in the first place (your D3 labelled 2,4,6).
But yes, I can definitely see how the phrase “given that”, could be interpreted the other way.
That Iran thing is weird.
If I were guessing I might say that maybe this is happening:
Right now the more trade China has with Iran the more America might make a fuss. Either complaining politically, putting tariffs, or calling on general favours and good will for it to stop. But if America starts making a fuss anyway, or burns all its good will, then their is suddenly no downside to trading with Iran. Now substitute “China” for any and all countries (for example the UK, France and Germany, who all stayed in the Iran Nuclear Deal even after the USA pulled out).
“given that all rolls were even” here means “roll a normal 6 sided dice, but throw out all of the sequences that included odd numbers.” The two are not the same, because in the case where odd numbers can be rolled, but they “kill” the sequence it makes situations involving long sequences of rolls much less likely to be included in the dataset at all.As other comments explain, this is why the paradox emerges. By stealth, the question is actually “A: How long do I have to wait for two 6s in a row, vs B: getting two 6′s, not necessarily in a row, given that I am post selecting in a way that very strongly favors short sequences of rolls”.
I suppose its the difference between the LW team taking responsibility for any text the feature shows people (which you are), and the LW team endorsing any text the feature shows (which you are not). I think this is Richard’s issue, although the importance is not obvious to me.
Could be an interesting poll question in the next LW poll.
Something like:
How often do you use LLMs?
Never used them
Messed about with one once or twice
Monthly
Weekly
Every Day
I think a reasonable-seeming metric on which humans are doubtless the winners is “energy controlled”.
Total up all the human metabolic energy, plus the output of the world’s power grids, the energy of all that petrol/gas burning in cars/boilers. If you are feeling generous you could give humans a percentage of all the metabolic energy going through farm animals.
Its a bit weird, because on the one hand its obvious that collectively humans control the planet in a way no other organism does. But, you are looking for a metric where plants and single-celled organisms are allowed to participate, and they can’t properly be said to control anything, even themselves.
I think this question is maybe logically flawed.
Say I have a shuffled deck of cards. You say the probability that the top card is the Ace of Spades is 1⁄52. I show you the top card, it is the 5 of diamonds. I then ask, knowing what you know now, what probability you should have given.
I picked a card analogy, and you picked a dice one. I think the card one is better in this case, for weird idiosyncratic reasons I give below that might just be irrelevant to the train of thought you are on.
Cards vs Dice: If we could reset the whole planet to its exact state 1 week before the election then we would I think get the same result (I don’t think quantum will mess with us in one week). What if we do a coarser grained reset? So if there was a kettle of water at 90 degrees a week before the election that kettle is reset to contain the same volume of water in the same part of my kitchen, and the water is still 90 degrees, but the individual water molecules have different momenta. For some value of “macro” the world is reset to the same macrostate but not the same microstate, it had 1 week before election day. If we imagine this experiment I still think Trump wins every (or almost every) time, given what we know now. For me to think this kind of thermal-level randomness made a difference in one week it would have to have been much closer.
In my head things that change on the coarse-grained reset feel more like unrolled dice, and things that don’t more like facedown cards. Although in detail the distinction is fuzzy: it is based on an arbitrary line between micro an macro, and it is time sensitive, because cards that are going to be shuffled in the future are in the same category as dice.
EDIT: I did as asked, and replied without reading your comments on the EA forum. Reading that I think we are actually in complete agreement, although you actually know the proper terms for the things I gestured at.
This idea (without the name) is very relevant in First Aid training.
For example, if you learn CPR from some organisations they will teach you compressions-only CPR, while others will also teach you to do the breaths. I have heard it claimed by first aid teachers that the reason for this is because doing the best possible CPR requires the breaths, but that someone who learned CPR one afternoon over a year ago and hasn’t practiced since is unlikely to do effective breaths, and that person would be better of keeping to compressions only.
In First Aid books a common attempt to solve this problem is to give sweeping commands at the beginning (often with the word “never” somewhat abused), and then give specific exceptions later. The aim is that if you will remember one thing it will hopefully be the blanket rule, not the specific exception. I think that method probably has something to recommend for it, its hard to imagine how you could remember the exception without remembering the rule it is an exception too.
[For example the Life Support book, tells you ‘never’ to give anyone medicine or drugs, as you are a First Aider, not a Doctor. It also tells you to give aspirin to someone having a heart attack if they have not taken any other drugs. I think it also recommends antihistamines for swelling insect stings.]
I find that surprising, given that so much of your writing feels kind of crisp and minimalist. Short punchy sentences. If that is how you think your mind is very unlike mine.
Much as I liked the book I think its not a good recomendation for an 11 year old. There are definitely maths-y 11 year olds who would really enjoy the subject matter once they get into it. (Stuff about formal systems and so on). But if we gave GEB to such an 11 year old I think the dozens of pages at the beginning on the history of music and Bach running around getting donations would repel most of them. (Urgh, mum tricked me into reading about classical music).
I am all for giving young people a challenge, but I think GEB is challenging on too many different fronts all at once. Its loooong. Its written somewhat in academic-ese. And the subject matter is advanced. So any 11 year old who could deal with one of that trinity also has to face the other two.
Yes, you could fix it by making the portal pay for lifting. An alternative fix would be to let gravity go through portals, so the ball feels the Earth’s gravity by the direct route and also through the portal. Which I think makes the column between the two portals zero G, with gravity returning towards normal as you move radially. This solution only deals with the steady-state though, at the moment portals appear or disappear the gravitational potential energy of objects (especially those near the portal) would step abruptly.
Its quite a fun situation to think about.
At least in my view, all the questions like the “Doomsday argument” and “why am I early in cosmological” history are putting far, far too much weight on the anthropic component.
If I don’t know how many X’s their are, and I learn that one of them is numbered 20 billion then sure, my best guess is that there are 40 billion total. But its a very hazy guess.
If I don’t know how many X’s will be produced next year, but I know 150 million were produced this year, my best guess is 150 million next year. But is a very hazy guess.
If I know that the population of X’s has been exponentially growing with some coefficient then my best guess for the future is to infer that out to future times.
If I think I know a bunch of stuff about the amount of food the Earth can produce, the chances of asteroid impacts, nuclear wars, dangerous AIs or the end of the Mayan calendar then I can presumably update on those to make better predictions of the number of people in the future.
My take is that the Doomsday argument would be the best guess you could make if you knew literally nothing else about human beings apart from the number that came before you. If you happen to know anything else at all about the world (eg. that humans reproduce, or that the population is growing) then you are perfectly at liberty to make use of that richer information and put forward a better guess. Someone who traces out the exponential of human population growth out to the heat death of the universe is being a bit silly (lets call this the Exponentiator Argument), but on pure reasoning grounds they are miles ahead of the Doomsday argument, because both of them applied a natural, but naïve, interpolation to a dataset, but the exponentiator interpolated from a much richer and more detailed dataset.
Similarly to answer “why are you early” you should use all the data at your disposal. Given who your parents are, what your job is, your lack of cybernetic or genetic enhancements, how could you not be early? Sure, you might be a simulation of someone who only thinks they are in the 21st centaury, but you already know from what you can see and remember that you aren’t a cyborg in the year 10,000, so you can’t include that possibility in your imaginary dataset that you are using to reason about how early you are.
As a child, I used to worry a lot about what a weird coincidence it was that I was born a human being, and not an ant, given that ants are so much more numerous. But now, when I try and imagine a world where “I” was instead born as the ant, and the ant born as me, I can’t point to in what physical sense that world is different from our own. I can’t even coherently point to in what metaphysical sense it is different. Before we can talk about probabilities as an average over possibilities we need to know if the different possibilities are even different, or just different labelling on the same outcome. To me, there is a pleasing comparison to be made with how bosons work. If you think about a situation where two identical bosons have their positions swapped, it “counts as” the same situation as before the swap, and you DON’T count it again when doing statistics. Similarly, I think if two identical minds are swapped you shouldn’t treat it as a new situation to average over, its indistinguishable. This is why the cyborgs are irrelevant, you don’t have an identical set of memories.