Causal Universes
Followup to: Stuff that Makes Stuff Happen
Previous meditation: Does the idea that everything is made of causes and effects meaningfully constrain experience? Can you coherently say how reality might look, if our universe did not have the kind of structure that appears in a causal model?
I can describe to you at least one famous universe that didn't look like it had causal structure, namely the universe of J. K. Rowling's Harry Potter.
You might think that J. K. Rowling's universe doesn't have causal structure because it contains magic  that wizards wave their wands and cast spells, which doesn't make any sense and goes against all science, so J. K. Rowling's universe isn't 'causal'.
In this you would be completely mistaken. The domain of "causality" is just "stuff that makes stuff happen and happens because of other stuff". If Dumbledore waves his wand and therefore a rock floats into the air, that's causality. You don't even have to use words like 'therefore', let alone big fancy phrases like 'causal process', to put something into the loftysounding domain of causality. There's causality anywhere there's a noun, a verb, and a subject: 'Dumbledore's wand lifted the rock.' So far as I could tell, there wasn't anything in Lord of the Rings that violated causality.
You might worry that J. K. Rowling had made a continuity error, describing a spell working one way in one book, and a different way in a different book. But we could just suppose that the spell had changed over time. If we actually found ourselves in that apparent universe, and saw a spell have two different effects on two different occasions, we would not conclude that our universe was uncomputable, or that it couldn't be made of causes and effects.
No, the only part of J. K. Rowling's universe that violates 'cause and effect' is...
...the TimeTurners, of course.
A TimeTurner, in Rowling's universe, is a small hourglass necklace that sends you back in time 1 hour each time you spin it. In Rowling's universe, this timetravel doesn't allow for changing history; whatever you do after you go back, it's already happened. The universe containing the timetravel is a stable, selfconsistent object.
If a time machine does allow for changing history, it's easy to imagine how to compute it; you could easily write a computer program which would simulate that universe and its time travel, given sufficient computing power. You would store the state of the universe in RAM and simulate it under the programmed 'laws of physics'. Every nanosecond, say, you'd save a copy of the universe's state to disk. When the TimeChanger was activated at 9pm, you'd retrieve the saved state of the universe from one hour ago at 8pm, load it into RAM, and then insert the TimeChanger and its user in the appropriate place. This would, of course, dump the rest of the universe from 9pm into oblivion  no processing would continue onward from that point, which is the same as ending that world and killing everyone in it.[1]
Still, if we don't worry about the ethics or the disk space requirements, then a TimeChanger which can restore and then change the past is easy to compute. There's a perfectly clear order of causality in metatime, in the linear time of the simulating computer, even if there are apparent cycles as seen from within the universe. The person who suddenly appears with a TimeChanger is the causal descendant of the older universe that just got dumped from RAM.
But what if instead, reality is always  somehow  perfectly selfconsistent, so that there's apparently only one universe with a future and a past that never changes, so that the person who appears at 8PM has always seemingly descended from the very same universe that then develops by 9PM...?
How would you compute that in one sweepthrough, without any higherorder metatime?
What would a causal graph for that look like, when the past descends from its very own future?
And the answer is that there isn't any such causal graph. Causal models are sometimes referred to as DAGs, which stands for Directed Acyclic Graph. If instead there's a directed cycle, there's no obvious order in which to compute the joint probability table. Even if you somehow knew that at 8PM somebody was going to appear with a TimeTurner used at 9PM, you still couldn't compute the exact state of the timetraveller without already knowing the future at 9PM, and you couldn't compute the future without knowing the state at 8PM, and you couldn't compute the state at 8PM without knowing the state of the timetraveller who just arrived.
In a causal model, you can compute p(9pm8pm) and p(8pm7pm) and it all starts with your unconditional knowledge of p(7pm) or perhaps the Big Bang, but with a TimeTurner we have p(9pm8pm) and p(8pm9pm) and we can't untangle them  multiplying those two conditional matrices together would just yield nonsense.
Does this mean that the TimeTurner is beyond all logic and reason?
Complete philosophical panic is basically never justified. We should even be reluctant to say anything like, "The socalled TimeTurner is beyond coherent description; we only think we can imagine it, but really we're just talking nonsense; so we can conclude a priori that no such TimeTurner that can exist; in fact, there isn't even a meaningful thing that we've just proven can't exist." This is also panic  it's just been made to sound more dignified. The first rule of science is to accept your experimental results, and generalize based on what you see. What if we actually did find a TimeTurner that seemed to work like that? We'd just have to accept that Causality As We Previously Knew It had gone out the window, and try to make the best of that.
In fact, despite the somewhatjustified conceptual panic which the protagonist of Harry Potter and the Methods of Rationality undergoes upon seeing a TimeTurner, a universe like that can have a straightforward logical description even if it has no causal description.
Conway's Game of Life is a very simple specification of a causal universe; what we would today call a cellular automaton. The Game of Life takes place on a twodimensional square grid, so that each cell is surrounded by eight others, and the Laws of Physics are as follows:
 A cell with 2 living neighbors during the last tick, retains its state from the last tick.
 A cell with 3 living neighbors during the last tick, will be alive during the next tick.
 A cell with fewer than 2 or more than 3 living neighbors during the last tick, will be dead during the next tick.
It is my considered opinion that everyone should play around with Conway's Game of Life at some point in their lives, in order to comprehend the notion of 'laws of physics'. Playing around with Life as a kid (on a Mac Plus) helped me gutlevelunderstand the concept of a 'lawful universe' developing under exceptionless rules.
Now suppose we modify the Game of Life universe by adding some prespecified cases of time travel  places where a cell will descend from neighbors in the future, instead of the past.
In particular we shall take a 4x4 Life grid, and arbitrarily hack Conway's rules to say:

On the 2nd tick, the cell at (2,2) will have its state determined by that cell's state on the 3rd tick, instead of its neighbors on the 1st tick.
It's no longer possible to compute the state of each cell at each time in a causal order where we start from known cells and compute their notyetknown causal descendants. The state of the cells on the 3rd tick, depend on the state of the cells on the 2nd tick, which depends on the state on the 3rd tick.
In fact, the timetravel rule, on the same initial conditions, also permits a live cell to travel back in time, not just a dead cell  this just gives us the "normal" grid! Since you can't compute things in order of cause and effect, even though each local rule is deterministic, the global outcome is not determined.
However, you could simulate Life with time travel merely by bruteforce searching through all possible Lifehistories, discarding all histories which disobeyed the laws of Life + time travel. If the entire universe were a 4by4 grid, it would take 16 bits to specify a single slice through Time  the universe's state during a single clock tick. If the whole of Time was only 3 ticks long, there would be only 48 bits making up a candidate 'history of the universe'  it would only take 48 bits to completely specify a History of Time. 2^48 is just 281,474,976,710,656, so with a cluster of 2GHz CPUs it would be quite practical to find, for this rather tiny universe, the set of all possible histories that obey the logical relations of time travel.
It would no longer be possible to point to a particular cell in a particular history and say, "This is why it has the 'alive' state on tick 3". There's no "reason"  in the framework of causal reasons  why the timetraveling cell is 'dead' rather than 'alive', in the history we showed. (Well, except that Alex, in the real universe, happened to pick it out when I asked him to generate an example.) But you could, in principle, find out what the set of permitted histories for a large digital universe, given lots and lots of computing power.
Here's an interesting question I do not know how to answer: Suppose we had a more complicated set of cellular automaton rules, on a vastly larger grid, such that the cellular automaton was large enough, and supported enough complexity, to permit people to exist inside it and be computed. Presumably, if we computed out cell states in the ordinary way, each future following from its immediate past, the people inside it would be as real as we humans computed under our own universe's causal physics.
Now suppose that instead of computing the cellular automaton causally, we hack the rules of the automaton to add large timetravel loops  change their physics to allow TimeTurners  and with an unreasonably large computer, the size of two to the power of the number of bits comprising an entire history of the cellular automaton, we enumerate all possible candidates for a universehistory.
So far, we've just generated all 2^N possible bitstrings of size N, for some large N; nothing more. You wouldn't expect this procedure to generate any people or make any experiences real, unless enumerating all finite strings of size N causes all lawless universes encoded in them to be real. There's no causality there, no computation, no law relating one timeslice of a universe to the next...
Now we set the computer to look over this entire set of candidates, and mark with a 1 those that obey the modified relations of the timetraveling cellular automaton, and mark with a 0 those that don't.
If N is large enough  if the size of the possible universe and its duration is large enough  there would be descriptions of universes which experienced natural selection, evolution, perhaps the evolution of intelligence, and of course, time travel with selfconsistent TimeTurners, obeying the modified relations of the cellular automaton. And the checker would mark those descriptions with a 1, and all others with a 0.
Suppose we pick out one of the histories marked with a 1 and look at it. It seems to contain a description of people who remember experiencing time travel.
Now, were their experiences real? Did we make them real by marking them with a 1  by applying the logical filter using a causal computer? Even though there was no way of computing future events from past events; even though their universe isn't a causal universe; even though they will have had experiences that literally were not 'caused', that did not have any causal graph behind them, within the framework of their own universe and its rules?
I don't know. But...
Our own universe does not appear to have TimeTurners, and does appear to have strictly local causality in which each variable can be computed strictly forwardintime.
And I don't know why that's the case; but it's a likelylooking hint for anyone wondering what sort of universes can be real in the first place.
The collection of hypothetical mathematical thingies that can be described logically (in terms of relational rules with consistent solutions) looks vastly larger than the collection of causal universes with locally determined, acyclically ordered events. Most mathematical objects aren't like that. When you say, "We live in a causal universe", a universe that can be computed inorder using local and directional rules of determination, you're vastly narrowing down the possibilities relative to all of Mathspace.
So it's rather suggestive that we find ourselves in a causal universe rather than a logical universe  it suggests that not all mathematical objects can be real, and the sort of thingies that can be real and have people in them are constrained to somewhere in the vicinity of 'causal universes'. That you can't have consciousness without computing an agent made of causes and effects, or maybe something can't be real at all unless it's a fabric of cause and effect. It suggests that if there is a Tegmark Level IV multiverse, it isn't "all logical universes" but "all causal universes".
Of course you also have to be a bit careful when you start assuming things like "Only causal things can be real" because it's so easy for Reality to come back at you and shout "WRONG!" Suppose you thought reality had to be a discrete causal graph, with a finite number of nodes and discrete descendants, exactly like Pearlstandard causal models. There would be no hypothesis in your hypothesisspace to describe the standard model of physics, where space is continuous, indefinitely divisible, and has complex amplitude assignments over uncountable cardinalities of points.
Reality is primary, saith the wise old masters of science. The first rule of science is just to go with what you see, and try to understand it; rather than standing on your assumptions, and trying to argue with reality.
But even so, it's interesting that the pure, ideal structure of causal models, invented by statisticians to reify the idea of 'causality' as simply as possible, looks much more like the modern view of physics than does the old Newtonian ideal.
If you believed in Newtonian billiard balls bouncing around, and somebody asked you what sort of things can be real, you'd probably start talking about 'objects', like the billiard balls, and 'properties' of the objects, like their location and velocity, and how the location 'changes' between one 'time' and another, and so on.
But suppose you'd never heard of atoms or velocities or this 'time' stuff  just the causal diagrams and causal models invented by statisticians to represent the simplest possible cases of cause and effect. Like this:
And then someone says to you, "Invent a continuous analogue of this."
You wouldn't invent billiard balls. There's no billiard balls in a causal diagram.
You wouldn't invent a single time sweeping through the universe. There's no sweeping time in a causal diagram.
You'd stare a bit at B, C, and D which are the sole nodes determining A, screening off the rest of the graph, and say to yourself:
"Okay, how can I invent a continuous analogue of there being three nodes that screen off the rest of the graph? How do I do that with a continuous neighborhood of points, instead of three nodes?"
You'd stare at E determining D determining A, and ask yourself:
"How can I invent a continuous analogue of 'determination', so that instead of E determining D determinining A, there's a continuum of determined points between E and A?"
If you generalized in a certain simple and obvious fashion...
The continuum of relatedness from B to C to D would be what we call space.
The continuum of determination from E to D to A would be what we call time.
There would be a rule stating that for epsilon time before A, there's a neighborhood of spatial points delta which screens off the rest of the universe from being relevant to A (so long as no descendants of A are observed); and that epsilon and delta can both get arbitrarily close to zero.
There might be  if you were just picking the simplest rules you could manage  a physical constant which related the metric of relatedness (space) to the metric of determination (time) and so enforced a simple continuous analogue of local causality...
...in our universe, we call it c, the speed of light.
And it's worth remembering that Isaac Newton did not expect that rule to be there.
If we just stuck with Special Relativity, and didn't get any more modern than that, there would still be little billiard balls like electrons, occupying some particular point in that neighborhood of space.
But if your little neighborhoods of space have billiard balls with velocities, many of which are slower than lightspeed... well, that doesn't look like the simplest continuous analogues of a causal diagram, does it?
When we make the first quantum leap and describe particles as waves, we find that the billiard balls have been eliminated. There's no 'particles' with a single point position and a velocity slower than light. There's an electron field, and waves propagate through the electron field through points interacting only with locally neighboring points. If a particular electron seems to be moving slower than light, that's just because  even though causality always propagates at exactly c between points within the electron field  the crest of the electron wave can appear to move slower than that. A billiard ball moving through space over time, has been replaced by a set of points with values determined by their immediate historical neighborhood.
vs.
And when we make the second quantum leap into configuration space, we find a timeless universal wavefunction with complex amplitudes assigned over the points in that configuration space, and the amplitude of every point causally determined by its immediate neighborhood in the configuration space.[2]
So, yes, Reality can poke you in the nose if you decide that only discrete causal graphs can be real, or something silly like that.
But on the other hand, taking advice from the math of causality wouldn't always lead you astray. Modern physics looks a heck of a lot more similar to "Let's build a continuous analogue of the simplest diagrams statisticians invented to describe theoretical causality", than like anything Newton or Aristotle imagined by looking at the apparent world of boulders and planets.
I don't know what it means... but perhaps we shouldn't ignore the hint we received by virtue of finding ourselves inside the narrow space of "causal universes"  rather than the much wider space "all logical universes"  when it comes to guessing what sort of thingies can be real. To the extent we allow noncausal universes in our hypothesis space, there's a strong chance that we are broadening our imagination beyond what can really be real under the Actual Rules  whatever they are! (It is possible to broaden your metaphysics too much, as well as too little. For example, you could allow logical contradictions into your hypothesis space  collections of axioms with no models  and ask whether we lived in one of those.)
If we trusted absolutely that only causal universes could be real, then it would be safe to allow only causal universes into our hypothesis space, and assign probability literally zero to everything else.
But if you were scared of being wrong, then assigning probability literally zero means you can't change your mind, ever, even if Professor McGonagall shows up with a TimeTurner tomorrow.
Meditation: Suppose you needed to assign nonzero probability to any way things could conceivably turn out to be, given humanity's rather young and confused state  enumerate all the hypotheses a superintelligent AI should ever be able to arrive at, based on any sort of strange world it might find by observation of TimeTurners or stranger things. How would you enumerate the hypothesis space of all the worlds we could remotely maybe possibly be living in, including worlds with hypercomputers and Stable Time Loops and even stranger features?
[1] Sometimes I still marvel about how in most timetravel stories nobody thinks of this. I guess it really is true that only people who are sensitized to 'thinking about existential risk' even notice when a world ends, or when billions of people are extinguished and replaced by slightly different versions of themselves. But then almost nobody will notice that sort of thing inside their fiction if the characters all act like it's okay.)
[2] Unless you believe in 'collapse' interpretations of quantum mechanics where Bell's Theorem mathematically requires that either your causal models don't obey the Markov condition or they have fasterthanlight nonlocal influences. (Despite a large literature of obscurantist verbal words intended to obscure this fact, as generated and consumed by physicists who don't know about formal definitions of causality or the Markov condition.) If you believe in a collapse postulate, this whole post goes out the window. But frankly, if you believe that, you are bad and you should feel bad.
Part of the sequence Highly Advanced Epistemology 101 for Beginners
Next post: "Mixed Reference: The Great Reductionist Project"
Previous post: "Logical Pinpointing"
Comments (383)
This happens in the ordinary passage of time anyway. (Stephen King's story "The Langoliers" plays this for horror  the reason the past no longer exists is because monsters are eating it.)
If your theory of time is 4dimensionalist, then you might think the past people are 'still there,' in some timeless sense, rather than wholly annihilated. Interestingly, you might (especially if you reject determinism) think that moving through time involves killing (possible) futures, rather than (or in addition to) killing the past.
Hard to see why you can't make a version of this same argument, at an additional remove, in the time travel case. For example, if you are a "determinist" and / or "ndimensionalist" about the "metatime" concept in Eliezer's story, the future people who are lopped off the timeline still exist in the metatimeless eternity of the "metatimeline," just as in your comment the dead still exist in the eternity of the past.
In the (seemingly degenerate) hypothetical where you go back in time and change the future, I'm not sure why we should prefer to say that we "destroy" the "old" future, rather than simply that we disconnect it from our local universe. That might be a horrible thing to do, but then again it might not be. There's lots of atleastconceivable stuff that is disconnected from our local universe.
Yes, that seems more consistent with the rest of the sequences (and indeed advocacy of cryonics/timeless identity). "You" are a pattern, not a specific collection of atoms. So if the pattern persists (as per successive moments of time, or destroying and recreating the pattern), so do "you".
"Death" is the absence of a future self that is continuous with your present self. I don't know exactly what constitutes "continuous" but it clearly is not the identity of individual particles. It may require continuity of causal derivation, for example.
Why?
Upload yourself to a computer. You've got a copy on the computer, you've got a physical body. Kill the physical body a few milliseconds after upload.
Repeat, except now kill the physical body a few milliseconds before the upload.
Do you mean to define the former situation as involving a "Death" because a few milliseconds worth of computations were lost, but the latter situation as simple a transfer?
I don't think the word "death" really applies anymore when we are talking at the level of physical systems, any more than "table" or "chair" would. Those constructs don't cross over well into (real or imaginary) physics.
(Even the billiard ball model of "classical" chemistry is enough to eliminate "individual particles" as the source of personal identity; you aren't made of the same atoms you were a year ago, because of eating, respiration, and other biological processes.)
There could be special "mind particles" in you brain and I can't believe I just said that.
1) If we ask whether the entities embedded in strings watched over by the selfconsistent universe detector really have experiences, aren't we violating the antizombie principle?
2) If Tegmark possible worlds have measure inverse their algorithmic complexity, and causal universes are much more easily computable than logical ones, should we not then find it not surprising that we are in an (apparently) causal universe even if the UE includes logical ones?
This.
I think that a correct metaphor for computersimulating other universe is not that we create it, but that we look at it. It already exists somewhere in the multiverse, but previously it was separated from our universe.
If simulating things doesn't add measure to them, why do you believe you're not a Boltzmann brain just because lawful versions of you are much more commonly simulated by your universe's physics?
This is not a full answer (I don't have one), just a sidenote: Believing to most likely not be a Boltzmann brain does not necessarily mean that Boltzmann brains are less likely. It could also be some kind of a survivor bias.
Imagine that every night when you sleep, someone makes hundred copies of you. One copy, randomly selected, remains in your bed. Other 99 copies are taken away and killed horribly. This was happening all your life, you just didn't know it. What do you expect about tomorrow?
From the outside view, tomorrow the 99 copies of you will be killed, and 1 copy will continue to live. Therefore you should expect to be killed.
But from inside, today's you is the lucky copy of the lucky copy, because all the unlucky copies are dead. Your whole experience is about surviving, because the unlucky ones don't have experiences now. So based on your past, you expect to survive the next day. And the next day, 99 copies of you will die, but the remaining 1 will say: "I told you so!".
So even if the Boltzmann brains are more simulated, and 99.99% of my copies are dying horribly in vacuum within the next seconds, they don't have a story. The remaining copy does. And the story says: "I am not a Boltzman brain".
By the way, how precise must be a simulation to add measure? Did I commit genocide by watching Star Wars, or is particlelevel simulation necessary?
A possible answer could be that an imprecise simulation adds way less, but still nonzero measure, so my pleasure from watching Star Wars exceeds the suffering of all the people dying in the movie, multiplied by the epsilon increase of their measure. (A variant of a torture vs dust specks argument.) Running a particlelevel Star Wars simulation would be a real crime.
This would mean there is no clear boundary between simulating and not simulating, so the ethical concerns about simulation must be solved by weighting how detailed is the simulation versus what benefits do we get by running it.
If you can't tell the difference, what's the use of considering that you might be a Boltzmann brain, regardless of how likely it is?
First, knowing you're a Boltzmann brain doesn't give you anything useful. Even if I believed that 90% of my measure were Boltzmann brains, that wouldn't let me make any useful predictions about the future (because Boltzmann brains have no future). Our past narrative is the only thing we can even try and extract any useful predictions from.
Second, it might be possible to recover "traditional" predictability from vanity. If some observer looks at a creature that implements my behavior, I want that someone to find that creature to make correct predictions about the future. Assuming any finite distribution of probabilities over observers, I expect observers finding me via a causal, coherent, simple simulation to vastly outweigh observers finding me as a Boltzmann brain (since Boltzmann brains are scattered [because there's no prior reason to anticipate any brain over another] but causal simulations recur in any form of "iterate all possible universes" search, and in a causal simulation, I am much more likely to implement this reasoning). Call it vanity logic  I want to be found to have been correct. I think (intuitively), but am not sure, that given any finite distribution of expectation over observers, I should expect to be observed via a simple simulation with nearcertainty. I mean  how would you find a Boltzmann brain? I'm fairly sure any universe that can find me in simulation space is either looking for me specifically  in which case, they're effectively hostile and should not be surprised at finding that my reasoning failed  or are iterating universes looking for brains, in which case they'll find vastly more thisreasoningimplementers through causal processes than random ones.
This is a side point, but I'm curious if there is a strong argument for claiming lawful brains are more common (had an argument with some theists on this issue, they used BB to argue against multiverse theories)
"Correct" is too strong. It might be a useful metaphor in showing which way the information is flowing, but it doesn't address the question about the moral worth of the action of running a simulation. Certain computations must have moral worth, for example consider running an uploaded person in a similar setup (so that they can't observe the outside world, and only use whatever was prepackaged with them, but can be observed by the simulators). The fact of running this computation appears to be morally relevant, and it's either better to run the computation or to avoid running it. So similarly with simulating a world, it's either better to run it or not.
Whether it's better to simulate a world appears to be dependent on what's going on inside of it. Any decision that takes place within a world has an impact on the value of each particular simulation of the world, and if there are more simulations, the decision has a greater impact, because it influences the moral value of more simulations. Thus, by deciding to run a simulation, you are amplifying the moral value of the world that you are simulating and of decisions that take place in it, which can be interpreted as being equivalent to increasing its probability mass.
Just how much additional probability mass a simulation provides is unclear, for example a second simulation probably adds less than the first, and the first might matter very little already. It probably depends on how a world is defined in some way.
It's starting to seem like the concept of "probability mass" is violating the "antizombie principle".
Edit: this is why I don't believe in the "antizombie principle".
Why? Seems like the simulated universe gets at least as much additional reality juice as the simulating universe has.
We're not asking if they have experiences; obviously if they exist, they have experiences. Rather we're asking if their entire universe gains any magical realityfluid from our universe simulating it (e.g., that mysterious stuff which, in our universe, manifests in proportion to the integrated squared modulus in the Born probabilities) which will then flow into any conscious agents embedded within.
Sadly, my usual toolbox for dissolving questions about consciousness does not seem to yield results on realityfluid as yet  all thought experiments about "What if I simulate / what if I see..." either don't vary with the amount of realityfluid, or presume that the simulating universe exists in the first place.
There are people who claim to be less confused about this than I am. They appear to me to be jumping the gun on what constitutes lack of confusion, and ought to be able to answer questions like e.g. "Would straightforwardly simulating the quantum wavefunction in sufficient detail automatically give rise to sentients experiencing outcomes in proportion to the Born probabilities, i.e., reproduce our current experience?" by something other than e.g. "But people in branches like ours will have utility functions that go by squared modulus" which I consider to be blatantly silly for reasons I may need to talk about further at some point.
I'm not convinced "reality fluid" is an improvement over "qualia".
"Magical reality fluid" highlights the fact that it's still mysterious, and so seems to be a fairly honest phrasing.
So what would you think of "magical qualia"?
It captures my feelings on the matter pretty well, although it also seems like an unnecessarily rude way of summarizing the opinions of any qualiaphiles I might be debating. Like if a Christian selfdeprecatingly said that yes, he believes the reason for akrasia is a magic snake, that seems (a) reasonable (description), whereas if an atheist described a Christian's positions in those terms she's just an asshole.
I suspect I'm misunderstanding the question, because I notice that I'm not confused, and that's usually a bad sign when dealing with a question which is supposed to be complicated.
Is this not equivalent to asking "If one were to simulated our entire universe, would it be exactly like ours? Could we use it to predict the future (or at least the possible space of futures) in our own universe with complete accuracy?"
If so, the immediate answer that comes to mind is "yes...why not?"
Solipsists should be able to dissolve the whole thing easily.
The property you talk about the universe having is an interesting one, but I don't think causality is the right word for it. You've smuggled an extra component into the definition: each node having small fanin (for some definition of "small"). Call this "locality". Lack of locality makes causal reasoning harder (sometimes astronomically harder) in some cases, but it does not break causal inference algorithms; it only makes them slower.
The timeturner implementation where you enumerate all possible universes, and select one that passed the selfconsistency test, can be represented by a DAG; it's causal. It's just that the moment where the timetraveler lands depends on the whole space of later universes. That doesn't make the graph cyclic; it's just a large fanin. If the underlying physics is discrete and the range of timeturners is time limited to six hours, it's not even infinite fanin. And if you blur out irrelevant details, like we usually do when reasoning about physical processes, you can even construct manageable causal graphs of events involving timeturner usage, and use them to predict experimental outcomes!
You can imagine universes which violate the smallfanin criterion in other ways. For example, imagine a Conway's lifelike game on an infinite plane, with a special tile type that copies a randomlyselected other cell in each timestep, with each cell having a probability of being selected that falls off with distance. Such cells would also have infinite fanin, but there would still be a DAG representing the causal structure of that universe. It used to be believed that gravity behaved this way.
Before you feel too proud for postdicting the successors of Newtonian dynamics, I'd like to point out that as soon as Newton proposed his theory of gravitation, it was criticised for proposing instantaneous action at a distance.
The alternate way of computing this is to not actually discard the future, but to split it off to a separate timeline so that you now have two simulations: one that proceeds normally aside for the timetraveler having disappeared from the world, and one that's been restarted from an earlier date with the addition of the time traveler. Of course, this has its own moral dilemmas as well  such as the fact that you're as good as dead for your loved ones in the timeline that you just left  but generally smaller than erasing a universe entirely.
You could get around this by forking the time traveler with the universe: in the source universe it would simply appear that the attempted time travel didn't work.
That would create a new problem, though: you'd never see anyone leave a timeline but every attempt would result in the creation of a new one with a copy of the traveler added at the destination time. A persistent traveler could generate any number of timelines differing only by the number of failed time travel attempts made before the succesful one.
Short jumps (like the 1hour one in the example) look more like erasing a bit of everyone's memories, anyway. At least if you buy Egan's model.
Or maybe also another one, somewhat related to the main post  let the universe compute, in it's own metatime, a fixed point [0] of reality (that is, the whole of time between the start and the destination of time travel gets recomputed into a form that allowed it to be internally consistent) and continue from there. You could imagine the universe computer simulating casually the same period of time again and again until a fixed point is reached, just like the iterative algorithms used to find it for functions.
[0]  http://en.wikipedia.org/wiki/Fixed_point_(mathematics)
A way has occurred to me.
Take the basic program described in the beginning of this post, in which the universe is deterministically computed with a cached series of states of the universe. The change is to make this computation is parallel on a staggering scale, because of how TimeTurners work. I'm going to explain this like there's only one wizard with a TimeTurner that works for one hour, but I'm pretty sure it holds up for the complex case of many Turners that can go back a varying amount of time.
A wizard (Marty McFloat, let's say) carrying a TimeTurner constantly generates a huge number new copies of the universe that differ slightly from the 'real' universe in a way that has gone unobserved because of the anthropic principle. In the 'main track' of the universe, nothing interesting happens, a new state is computed from the previous state. Every other copy of the universe is the same except that a rough copy of the wizard has appeared.
Maybe this copy of Marty has a new life vest, or has a bruise, or just has his head turned slightly to the left and one leg tensed. There are a finite but huge number of these variations, including copies where only a single quark (or whatever the smallest computed unit of manner is) is out of place. But in every variation, this copy of Marty's brain has an extra hour of memories in its head. (More variations!)
Let's follow one of these, the Marty with a new vest. This is a potential future Marty. You can think of this as the appearance of a Marty who went clothes shopping and used his TimeTurner an hour from now, but it's not: it's a variation of the Marty wearing the TimeTurner, not a copy of part of a future computed state. Every possible Martyvariant is generated in a different parallel universe state.
The state of the universe is computed onwards. If, one hour later, Marty does not activate his TimeTurner, the universe fails its consistency check and is deleted. If Marty does activate it, the universe looks back at the Marty that was added an hour ago. If the two Martys are not bitforbit (at whatever the lowest scale of the computation is), the universe fails its consistency check and is deleted. If Marty is identical, the 'younger' one that activated the TimeTurner is deleted and the universe rolls on in a consistent, causal way.
This system has no metatime. Universe computation never has to go back and restart from a previous state, modified or modified. It just requires generating a nearinfinite number of parallel branches for every state of the universe and destroying nearly all of them. (Which I guess is quite a lot of worldkilling, to understate it.)
The universe is causal and can be modeled with a directed acyclic graph. Just imagine that each state of the universe is a DAG, which may include a new node with no parents (the 'arriving' variant wizard), and it's not one DAG but an incredibly thick stack of DAGs, most of which are discarded. The universe never needs to compute (p8pm9pm).
If I correctly understood the prompt (does having multiple copies of the timeline count as "higher order metatime", or does that just mean "no rolling the clock back" as in the example?), I think this perverse solution satisfies the constraints of the question I quoted, but I'd love to hear correction.
As a variation, nothing really requires that universes be computed in parallel; as long as the computer has lots of disk space it could write out the generated parallel universes to disk and continue simulating the current universe until it fails the consistency check or ends, then pick any remaining state from disk and pick up computation from wherever that state left off. This is a infiction way of restating that you can trade off space for parallelism in computation, but I'm not entirely certain what "higherorder" precludes so I wanted to toss it out there as a variation.
Actually, this whole post is an example of the general principle that you can trade off space for time in programs. It just ends up looking really weird when you push this optimization technique to a ridiculous scale. As for who would simulate a universe this way, I would guess some poor sap who was overruled in the design meetings and told to "just make it work".
(On a meta note, I've been wondering for a few years if anything would prompt me to create a LessWrong account and participate. I read this post from my feed reader this morning, went on to have a day that's been very busy and meaningful for my personal life. I didn't think about this post at any point, went to bed, and woke up three hours later with this answer fullyformed except for the onesimulationatatime variation I thought of while typing it up so I can get it out of my head and go back to bed. I guess waking me up with a ridiculous answer to a puzzle I didn't know I was chewing on will prompt it.)
The only story I've seen directly address this issue at all is Homestuck, in which any timeline that splits off from the 'alpha' timeline is 'doomed' and ceases to exist once it diverges too far from the alpha. The three characters with time traveling capabilities are someone who is extremely careful to avoid creating doomed timelines, one who is nihilistically apathetic about death and creates doomed timelines willynilly, and one who is a psychopathic monster bent on using his powers for destruction. Several times, main characters are shown experiencing existential despair over the idea that their own timeline might be a doomed one, and at one point a character with timetraveling capabilities realizes that the only way to prevent the destruction of the universe is to travel back in time, leaving his current timeline doomed. His realization of the implications of dooming that timeline and his efforts to somehow save his timeline's version of his only surviving friend were particularly poignant (to me, at least).
This is a rather confused use of some linguistic terminology. I think "a subject, a verb, and an object" is probably what was intended. (It's worth noting that in academic syntax these terms are somewhat deprecated and don't necessarily have useful meanings. I think the casual meanings are still clear enough in informal contexts like this though.)
Beyond the terminology issue, I'm unconvinced by the actual claim here. Arguments from linguistic usage often turn out to be very bad on scrutiny, and I'm not sure this one holds up too well. What about 'Quirrell secretly followed Harry.'? Seems like a much weaker assertion that Quirrell is causally affecting Harry in some way here. I expect there are more obvious examples  that one took me 10 seconds to come up with.
Quirrell is not causally affecting Harry, but Harry is causally affecting Quirrell.
I'm not saying that your point is necessarily wrong, just that your counterexample isn't really counter.
What about 'Quirrell resembles Harry.'?
Resemblance is evaluated in someone's brain, and causality is very much involved in that evaluation process.
Yep. With lots of transitive verbs, the (syntactic) direct object is that which undergoes a change (the patient) and the subject is that which causes it (the agent)  but not with all of them.
And that's before you even stray outside the Anglocentric perspective and consider ergativeabsolutive oppositions...
BTW, I wonder whether (all other things being equal) speakers of ergativeabsolutive languages tend to exhibit more consequentialistlike thinking and speakers of nominativeaccusative more deontologicallike thinking... Has anybody tested that?
I wonder if testing bilinguals would be the way to go on this, to mitigate a few confounds at least. You could present moral statements for evaluation in each of the languages and see if you got any kind of effect according to which language the statement was presented in.
Hmmm.
As a bilingual person myself (English/Afrikaans, though my Afrikaans is comparatively poor), I have to say that I'd probably treat moral statements in the different languages by mentally translating the Afrikaans to English and then deciding on the basis of the translation. However, here phrasing becomes important.
Consider, for example, the following two statements:
Are these two equally true? In the first case, legal execution of a convicted criminal is included, in the second case it is excluded. Such subtle differences in phrasing could very easily turn up between the two languages, as often a word in one language merely has a close approximation in the other (and not a direct translation).
Yes, they arein as much as two false things are each zero true. What they aren't is equivalent. If you didn't included the absolute modifier "always" then it could perhaps make sense to evaluate "degree of truth".
You are correct; I have edited the grandparent to remove the word "always" from both statements.
There are plenty of sentences that have a noun, a verb, and a subject without having an agent  anything in passive voice or any unaccusative will do the trick. I suspect the argument would be even better worded using semantic roles rather than syntactic categories, eg: "Causality exists when there is an event with an agent". This isn't a very interesting thing to say though, because "agent" is a casual semantic role and so relies on causality existing by definition. You literally cannot have an event with an agent unless there is causality.
Yes, agreed. Semantic roles make the claim much more valid (but also less interesting, it seems to me).
How about "Harry suspected Quirrel"?
That's "Quirrel caused suspicion in Harry's mind", or perhaps "Harry's model of Quirrel caused suspicion to be generated in Harry".
The causality isn't what you would expect from the syntax, going from subject to object, and it isn' implied by the syntax at all, it's in the semantics. Consider "Harry winked out of existence for no reason".
Characters in the novel Pastwatch by Orson Scott Card wrestle with this issue.
Wait, why not ? If people can be encoded as bit strings  which is the prerequisite for any kind of a Singularity  then what's the difference between a bit string that I obtained by scanning a person, and a completely identical bit string that I just happened to randomly generate ?
You make a surprisingly convincing argument for people not being real.
Depends what you mean by "people", and what you mean by "real", really.
I could apply the same argument to rocks, or stars, or any other physical object. They can be encoded as bit strings, too  well, at least hypothetically speaking.
I suppose the difference is knowing to put the number into your bit string interpreter. Whether that be a computer program or the physical universe.
It's kind of like the arguments for "you can't copyright a number". Well sure, but when you stick .mp3 on the end it isn't just a number any more  it now tells you that you should interpret it.
Agreed, but then, I still disagree with Eliezer when he says that when you generate 2^N possible bitstrings of size N, "you wouldn't expect this procedure to generate any people or make any experiences real". If I can generate all these strings in the first place, I could just as easily feed each one to my personemulator, to see which of them are valid personstrings. Then I could emulate these people just as I emulate meatbased people whose brains I'd scanned.
(Apologies for length...)
I doubt this is as relevant as it seems to me, but there is this timetravel strategy game called temporal: http://www.kaldobsky.com/audiogames/ (it's toward the bottom of the page, and the main audience is visually impaired, hence the limited visual design).
The idea is that it is supposed to work similar to time turners, and the easiest way to lose the game is not by getting shot or crushed in security doors, but by losing track of previous instances of yourself and bumping into them to ruin the consistency of the timeline.
Of course, the developer didn't get to the end of the game he had in mind, mostly because the final stage was supposed to be a conflict with an opponent who could also travel through time. I wound up trying to recreate it with a different engine (with the original developer's permission), and got stuck at about the same point.
I also was able to create a paradox that didn't trigger game over (in the original, not my reconstruction, though it works in mine as well). There is a part where you need to get an armed guard to shoot another guard, but nothing is stopping you from then going back in time and killing the armed guard before he could shoot the other... and this does not interfere with anything else you did that relied on the other guard being dead. It seems patchable, but still...
The developer's strategy for the timetraveling boss AI, in as much as he told me, was to calculate where it could be within so many ticks, predict where it would move to, and have "future" instances spawn there. This doesn't sound like it could take into account your actions (only how far you could travel spatially within x ticks), and doesn't account for the fact that the only limits on your abilities are that you can't travel back to before you last woke up, or later than has already occurred naturally. Oh, and it does prevent the sort of past/future interactions we see in HPMoR, or with the patronis in Prisoner of Azkaban. So you strictly avoid observing your future selves, while future you can observe all previous instances of you, provided the universe remains consistent.
So I suppose the difference here is that the timetraveler from the future is the one who experiences the results of the timetravel. Past you has to rescue future you before future you needs rescuing, but future you can do nothing for past you. So it's what time turners would look like if the guidelines from the ministry of magic were strictly followed.
I might try to compute PoA type events by considering all timetravelcapable individuals, or individuals likely to become capable of timetravel within the limits of the ability, then calculate how they are most likely to react to a situation given foreknowledge... at which point this would be the outcome, and that individual would be required to have that outcome happen, or break temporal consistency. So if I knew of a timetraveler in vacinity of a lifethreatening situation, and knew that said entity would try to prevent it if given the chance, I would calculate what they would be most likely to do, and make it happen. So in the case of Temporal, if I was, say, trapped in the presence of several armed guards that I did not believe I could escape, I might have the game try to calculate ways that a future instance could come to the rescue, and have it generate an instance to do just that, but then throw game over if you fail to make it happen.
This doesn't strike me as complete, but I kinda want to try it.
This reminds me of a game/mod (called "Prometheus" IIRC) where you had to complete objectives within a fixed amount of time in a manner impossible to do alone, with guards to kill and multiple switches to press at the same time to open a door... but all you had for help was yourself, in five copies.
The game would basically let you play the first copy, end, play the second copy while the first played out what you had done previously, then the third while the first two kept repeating what you recorded, and so on, and then you could go back and redo earlier copies to account for new actions taken by the later copies, all culminating in one big fiveminute match between You^5 VS (Causally) Impossible Level. Think Portal 2 coop but with timetraveling copies of yourself.
Perhaps some of the inspiration came from those?
I don't understand why it's morally wrong to kill people if they're all simultaneously replaced with marginally different versions of themselves. Sure, they've ceased to exist. But without time traveling, you make it so that none of the marginally different versions exist. It seems like some kind of act omission distinction is creeping into your thought processes about time travel.
Moreso, marginally different versions of people are replacing the originals all the time, by the natural physical processes of the universe. If continuity of body is unnecessary for personal identity, why is continuity of their temporal substrate?
Identity is a process, not a physical state. There is a difference between continuity of body, which is physical, and continuity of identity, which is a process. If I replace a hard drive from a running computer, it may still run all of the same processes. The same could be true of processors, or memory. But if I terminate the process, the physical substrate being the same is irrelevant.
I'm not even certain that identity is a process. The process of consciousness shuts down every time we go to sleep, and gets reconstituted from our memories the next time we wake up (with intermittent consciousnesslike processes that occur inbetween, while we dream).
It seems like the closest thing to "identity" that we have, these days, is a sort of nebulous locus of indistinguishably similar dynamic data structures, regardless of the substrate that is encoding or processing those structures. It seems a rather flimsy thing to hang an "I" on, though.
I'm unclear on your logic; whatever the mechanism, the "cogito" exists. (demonstrably to myself, and presumably to yourself.) Given this, why is it too flimsy? Why does it matter is there is a complex "nebulous locus" that instantiates it  it's there, and it works, and conveys, to me, the impression that I am.
And this is why we (barely) have checkpointing. If you close you web browser, and launch a saved copy from five minutes ago, is the session a different one?
Because our morality is based on our experiential process. We see ourselves as the same person. Because of this, we want to be protected from violence in the future, even if the future person is not "really" the same as the present me.
Why protect one type of "you" over another type? Your response gives a reason that future people are valuable, but not that those future people are more valuable than other future people.
Mainstream status:
I haven't yet particularly seen anyone else point out that there is in fact a way to finitely Turingcompute a discrete universe with selfconsistent TimeTurners in it. (In fact I hadn't yet thought of how to do it at the time I wrote Harry's panic attack in Ch. 14 of HPMOR, though a primary literary goal of that scene was to promise my readers that Harry would not turn out to be living in a computer simulation. I think there might have been an LW comment somewhere that put me on that track or maybe even outright suggested it, but I'm not sure.)
The requisite behavior of the Time Turner is known as Stable Time Loops on the wiki that will ruin your life, and known as the Novikov selfconsistency principle to physicists discussing "closed timelike curve" solutions to General Relativity. Scott Aaronson showed that time loop logic collapses PSPACE to polynomial time.
I haven't yet seen anyone else point out that space and time look like a simple generalization of discrete causal graphs to continuous metrics of relatedness and determination, with c being the generalization of locality. This strikes me as important, so any precedent for it or pointer to related work would be much appreciated.
The relationship between continuous causal diagrams and the modern laws of physics that you described was fascinating. What's the mainstream status of that?
Showed up in Penrose's "The Fabric of Reality." Curvature of spacetime is determined by infinitesimal light cones at each point. You can get a uniquely determined surface from a connection as well as a connection from a surface.
Obviously physicists totally know about causality being restricted to the light cone! And "curvature of space = light cones at each point" isn't Penrose, it's standard General Relativity.
David Deutsch, not Roger Penrose. Or wrong title.
Page number?
Odd, the last paragraph of the above seems to have gotten chopped. Restored. No, I haven't particularly heard anyone else point that out but wouldn't be surprised to find someone had. It's an important point and I would also like to know if anyone has developed it further.
I found that idea so intriguing I made an account.
Have you considered that such a causal graph can be rearranged while preserving the arrows? I'm inclined to say, for example, that by moving your node E to be on the same level  simultaneous with  B and C, and squishing D into the middle, you've done something akin to taking a Lorentz transform?
I would go further to say that the act of choosing a "cut" of a discrete causal graph  and we assume that B, C, and D share some common ancestor to prevent completely arranging things  corresponds to the act of the choosing a reference frame in Minkowski space. Which makes me wonder if maxflow algorithms have a continuous generalization.
edit: in fact, maxflows might be related to Lagrangians. See this.
Mind officially blown once again. I feel something analogous to how I imagine someone who had been a heroin addict in the OBbookblogging time period and in methadone treatment during the subsequent nonEYnonYvainLW time period would feel upon shooting up today. Hey Mr. Tambourine Man, play a song for me / In the jinglejangle morning I'll come following you.
Seconded.
In computational physics, the notion of selfconsistent solutions is ubiquitous. For example, the behaviour of charged particles depends on the electromagnetic fields, and the electromagnetic fields depend on the behaviour of charged particles, and there is no "preferred direction" in this interaction. Not surprisingly, much research has been done on methods of obtaining (approximations of) such selfconsistent solutions, notably in plasma physics and quantum chemistry. just some examples.
It is true that these examples do not involve time travel, but I expect the mathematics to be quite similar, with the exception that these physicsbased examples tend to have (should have) uniquely defined solutions.
Er, I was not claiming to have invented the notion of an equilibrium but thank you for pointing this out.
I didn't think you were claiming that, I was merely pointing out that the fact that selfconsistent solutions can be calculated may not be that surprising.
There are precedents and parallels in Causal Sets and Causal Dynamical Triangulation
CDT is particularly interesting for its ability to predict the correct macroscopic dimensionality of spacetime:
" At large scales, it recreates the familiar 4dimensional spacetime, but it shows spacetime to be 2d near the Planck scale, and reveals a fractal structure on slices of constant time"
It replaces the exponential time requirement with an exactly analogous exponential MTBF reliability requirement. I'm surprised by how infrequently this is pointed out in such discussions, since it seems to me rather important.
It is rarely appreciated that the Novikov selfconsistency principle is a trivial consequence of the uniqueness of the metric tensor (up to diffeomorphisms) in GR.
Indeed, given that (a neighborhood of) each spacetime point, even in a spacetime with CTCs, has a unique metric, it also has unique stressenergy tensor derived from this metric (you neighborhoods to do derivatives). So there is a unique matter content at each spacetime point. In other words, your grandfather cannot be alternately alive (first time through the loop) or dead (when you kill him the second time through the loop) at a given moment in space and time.
The unfortunate fact that we can even imagine the grandfather paradox to begin with is due to our intuitive thinking that that the spacetime is only a background for "real events", a picture as incompatible with GR as perfectly rigid bodies are with SR.
I've seen academic physicists use postselection to simulate closed timelike curves; see for instance this arXiv paper, which compares a postselection procedure to a mathematical formalism for CTCs.
I tend to believe that most fictional characters are living in malicious computer simulations, to satisfy my own pathological desire for consistency. I now believe that Harry is living in an extremely expensive computer simulation.
I know that the idea of "different systems of local consistency constraints on full spacetimes might or might not happen to yield forwardsampleable causality or things close to it" shows up in Wolfram's "A New Kind of Science", for all that he usually refuses to admit the possible relevance of probability or nondeterminism whenever he can avoid doing so; the idea might also be in earlier literature.
I'd thought about that a long time previously (not about TimeTurners; this was before I'd heard of Harry Potter). I remember noting that it only really works if multiple transitions are allowed from some states, because otherwise there's a much higher chance that the consistency constraints would not leave any histories permitted. ("Histories", because I didn't know model theory at the time. I was using cellular automata as the example system, though.) (I later concluded that Markov graphical models with weights other than 1 and 0 were a less brittle way to formulate that sort of intuition (although, once you start thinking about configuration weights, you notice that you have problems about how to update if different weight schemes would lead to different partition function values).)
I know we argued briefly at one point about whether Harry could take the existence of his subjective experience as valid anthropic evidence about whether or not he was in a simulation. I think I was trying to make the argument specifically about whether or not Harry could be sure he wasn't in a simulation of a trial timeline that was going to be ruled inconsistent. (Or, implicitly, a timeline that he might be able to control whether or not it would be ruled inconsistent. Or maybe it was about whether or not he could be sure that there hadn't been such simulations.) But I don't remember you agreeing that my position was plausible, and it's possible that that means I didn't convey the information about which scenario I was trying to argue about. In that case, you wouldn't have heard of the idea from me. Or I might have only had enough time to figure out how to halfway defensibly express a lesser idea: that of "trial simulated timelines being iterated until a fixed point".
You can do some sort of lazy evaluation. I took the example you gave with the 4x4 grid (by the way you have a typo: "we shall take a 3x3 Life grid"), and ran it forwards, and it converges to all empty squares in 4 steps. See this doc for calculations.
Even if it doesn't converge, you can add another symbol to the system and continue playing the game with it. You can think of the symbol as a function. In my document x = compute_cell(x=2,y=2,t=2)
Yeah, this is one of the most profound things I've ever read. This is a RIDICULOUSLY good post.
The 'c is the generalization of locality' bit looked rather trivial to me. Maybe that's just EY rubbing off on me, but...
Its obvious that in Conways Game, it takes at least 5 iterations for one cell to affect a cell 5 units away, and c has for some time seemed to me like our worlds version of that law
I certainly made a remark on LW, very early in HPMoR, along the following lines: If magic, or anything else that seems to operate fundamentally at the level of humanlike concepts, turns out to be real, then we should see that as substantial evidence for some kind of simulation/creation hypothesis. So if you find yourself in the role of Harry Potter, you should expect that you're in a simulation, or in a universe created by gods, or in someone's dream ... or the subject of a book :).
I don't think you made any comment on that, so I've no idea whether you read it. I expect other people made similar points.
It's more immediately plausible to hypothesize that certain phenomena and regularities in Harry's experience are intelligently designed, rather than that the entire universe Harry occupies is. We can make much stronger inferences about intelligences within our universe being similar to us, than about intelligences who created our universe being similar to us, since, being outside our universe/simulation, they would not necessarily exist even in the same kind of logical structure that we do.
I'm not sure how to respond to this; the ability to compute it in a finite fashion for discrete universes seemed trivially obvious to me when I first pondered the problem. It would never have occurred to me to actually write it down as an insight because it seemed like something you'd figure out within five minutes regardless.
"Well, we know there are things that can't happen because there are paradoxes, so just compute all the ones that can and pick one. It might even be possible to jig things such that the outcome is always well determined, but I'd have to think harder about that."
That said, this may just be a difference in background. When I was young, I did a lot of thinking about Conway's Life and in particular "garden of eve" states which have no precursor. Once you consider the possibility of garden of eve states and realize that some Life universes have a strict 'start time', you automatically start thinking about what other kinds of universes would be restricted. Adding a rule with time travel is just one step farther.
On the other hand, the space/time causal graph generalization is definitely something I didn't think about and isn't even something I'd heard vaguely mentioned. That one I'll have to put some thought into.
Isn't that "hint" just an observer selection effect?
Is it surprising that the correlation between "universes that are absolutely/highly causal" and "universes in which things as complex as conscious observers can be assembled by evolution and come to contemplate the causal nature of their universe" is very high? (The fitness value of intelligence must be at least somewhat proportional to how predictable reality is...)
I worry about this "what sort of thingies can be real" expression. It might be more useful to ask "what sort of thingies can we observe". The word "real", except as an indexical, seems vacuous.
It's true that intelligence wouldn't do very well in a completely unpredictable universe; but I see no reason why it doesn't work in something like HPMoR, and there are plenty of such "almostsane" possibilities.
Woudn't HPMoR count as "highly, but not completely, causal"?
It's true that out of the conceivable indeterministic universes, most do not allow for evolvable highlevel intelligence anything like ours. But it's also true that out of the conceivable universes that do allow for evolvable highlevel intelligence like ours, most are not perfectly deterministic. So although the existence of intelligence may be explicable anthropically, I'm not sure the nonexistence of Time Turners (and other causalitybreaking mechanisms) is. Perfect determinism and complete chaos are not the only two options.
I'm not sure we're in a causal universe.
According to the theory of timeless physics, our universe is governed by Schrödinger's timeindependent equation. If the universe can expand without limit, and the potential energy eventually decreases below the total energy, kinetic energy will be driven below zero. This means that the amplitude will change exponentially as the universe expands. There are two ways this can work. Either the amplitude will increase exponentially, in which case we'd expect to be in one of those negativeenergy configuration states, or the amplitude will exponentially approach zero, in which case the universe would look pretty much like it does now. If you just set boundary conditions at the big bang, you'd almost certainly end up in the former case. In order to get the latter case, you have to have part of your boundary conditions that as the universe expands the amplitude approaches zero. This means that the universe is partially governed by how it ends, rather than just how it begins.
There are other explanations, of course. Perhaps amplitude doesn't matter after a while. Perhaps the multiverse is finite. Perhaps timeless physics was wrong in the first place. Perhaps it's something else I haven't thought of. I'm just not sure that the expanding universe boundary condition should be rejected quite yet.
Also, if you accept SSA, the universe is acausal. The probability of being now is dependent on the number of people in the future.
Meditation:
Suppose you needed to assign nonzero probability to any way things could conceivably turn out to be, given humanity's rather young and confused state  enumerate all the hypotheses a superintelligent AI should ever be able to arrive at, based on any sort of strange world it might find by observation of TimeTurners or stranger things. How would you enumerate the hypothesis space of all the coherentlythinkable worlds we could remotely maybe possibly be living in, including worlds with Stable Time Loops and even stranger features?
Hmmm. Causal universes are a bit like integers; there's an infinite number of them, but they pale as compared to thenumber of numbers as a whole.
Mostlycausal universes with some timetravel elements are more like rational numbers; there's more than we're ever going to use, and it looks at first like it covers all possibilities except for a few strange outliers, like pi or the square root of two.
But there's vastly, vastly more irrational numbers than rational numbers; to the point where, if you had to pick a truly random number, it would almost certainly be irrational. Yet, aside from a few special cases (such as pi), irrational numbers are hardly even considered, never mind used; we try to approximate the universe in terms of rational numbers only. (Though a rational number can be arbitrarily close to any given number).
Irrational numbers are also uncountable, and I imagine that I'll end up in similar trouble trying to enumerate all the universes that could exist, given "Stable Time Loops and even stranger features".
Given that, there's only one reasonable way to handle the situation; I need to assign some probability to "stranger things" without being able to describe, or to know, what those stranger things are.
The possibilities that I can consider include:
Alternatively:
The reason why the second is higher than the first, is simply that there are so many more possible universes in which the second would be true (but not the first) in which the observations observed to date would nonetheless be true. The problem with these categorisations is that, in every case, the highest probability seems to be reserved for Stranger Things...
Rationals and integers are both coutable! This is one of my favorite notoftentaughtinelementaryschools but easilyexplainabletoelementaryschoolstudents math facts. And they, the rationals, make a pretty tree: http://mathlesstraveled.com/2008/01/07/recountingtherationalspartiifractionsgrowontrees/
If this universe contains agents who engage in acausal trade, does that make it partially acausal?
Nope. It's just a terrible name.
I almost went with that answer, and didn't ask. But then I thought about trade with future agents who have different resources and values than we doresources and values which will be heavily influenced by what we do today. The structure seems to be at least as similar as selfconsistent solutions in plasma physics.
By 'acausal trade', do you mean:
or
The first is causal (but does not preclude the possibility of the universe containing other acausal effects), the second is acausal.
Agents can make choices that enforce global logical constraints, using computational devices that run on local causality.
"Nonzero probability" doesn't seem like quite the right word. If a parameter describing the way things could conceivably turn out to be can take, say, arbitrary real values, then we really want "nonzero probability density." (It's mathematically impossible to assign nonzero probability to each of uncountably many disjoint hypotheses because they can't add to 1.)
The first answer that occurred to me was "enumerate all Turing machines" but I'm worried because it seems pretty straightforward to coherently think up a universe that can't be described by a Turing machine (either because Turing machines aren't capable of doing computations with infiniteprecision real numbers or because they can't solve the halting problem). More generally I'm worried that "coherentlythinkable" implies "not necessarily describable using math," and that would make me sad.
A start is to choose some language for writing down axiom lists for formal systems, and a measure on strings in that language.
LowenheimSkolem is going to give you trouble, unless "coherentlythinkable" is meant of as a subtantive restriction. You might be able to enumerate finitelyaxiomatisable models, up to isomorphism, up to alephw, if you limit yourself to kcategorical theories, for k < alephw, though. Then you could use Will's strategy and enumerate axioms.
Edit: I realised I'm being pointlessly obscure.
The Upwards LowenheimSkolem means that, for every set of axioms in your list, you'll have multiple (nonisomorphic) models.
You might avoid this if "coherantly thinkable" was taken to mean "of small cardinality".
If you didn't enjoy this restriction, you could, for any given set of axioms, enumerate the kcategorical models of that set of axioms  or at least enumerate the models of whose cardinality can be expressed as 2^2^...2^w, for some finite number of 2's. This is because kcategoriciticy means you'll only have one model of each cardinality, up to isomorphism.
So then you just enumerate all the possible countable combinations of axioms, and you have an enumeration of all countably axiomatisable, kcategorical, models.
Well I suppose starting with the assumption that my superintelligent AI is merely turing complete, I think that we can only say our AI has "hypothesis about the world" if it has a computable model of the world. Even if the world weren't computable, any noncomputable model would be useless to our AI, and the best it could do is a computable approximation. Stable time loops seem computable through enumeration as you show in the post.
Now, if you claim that my assumption that the AI is computable is flawed, well then I give up. I truly have no idea how to program an AI more powerful than turing complete.
Suppose the AI lives in a universe with Turing oracles. Give it one.
Again, what distinguishes a "turing oracle" from a finite oracle with a bound well above the realizable size of a computer in the universe? They are indistinguishable hypotheses. Giving a turing complete AI a turing oracle doesn't make it capable of understanding anything more than turing complete models. The turingtranscendant part must be an integral part of the AI for it to have nonturingcomplete hypotheses about the universe, and I have no idea what a turingtranscendant language looks like and even less of an idea of how to program in it.
Suppose the AI lives in a universe where infinitely many computations can be performed in finite time...
(I'm being mildly facetious here, but in the interest of casting the "coherentlythinkable" net widely.)
I don't see how this changes the possible sensedata our AI could expect. Again, what's the difference between infinitely many computations being performed in finite time and only the computations numbered up to a point too large for the AI to query being calculated?
If you can give me an example of a universe for which the closest turing machine model will not give indistinguishable sensedata to the AI, then perhaps this conversation can progress.
Well, for starters, an AI living in a universe where infinitely many computations can be performed in finite time can verify the responses a Turing oracle gives it. So it can determine that it lives in a universe with Turing oracles (in fact it can itself be a Turing oracle), which is not what an AI living in this universe would determine (as far as I know).
I don't think that's different, unless it can also make infinitely many queries of the Turing oracle in finite time. Or make one query of a program of infinite length. In any case, I think it needs to perform infinite communication with the oracle.
I'll grant that it seems likely that a universe with infinite computation capability will also have infinite communication capability using the same primitives, but I don't think it's a logical requirement.
As mentioned below, we you'd need to make infinitely many queries to the Turing oracle. But even if you could, that wouldn't make a difference.
Again, even if there was a module to do infinitely many computations, the code I wrote still couldn't tell the difference between that being the case, and this module being a really good computable approximation of one. Again, it all comes back to the fact that I am programming my AI on a turing complete computer. Unless I somehow (personally) develop the skills to program transturingcomplete computers, then whatever I program is only able to comprehend something that is turing complete. I am sitting down to write the AI right now, and so regardless of what I discover in the future, I can't program my turing complete AI to understand anything beyond that. I'd have to program a transturing complete computer now, if I ever hoped for it to understand anything beyond turing completeness in the future.
Ah, I see. I think we were answering different questions. (I had this feeling earlier but couldn't pin down why.) I read the original question as being something like "what kind of hypotheses should a hypothetical AI hypothetically entertain" whereas I think you read the original question as being more like "what kind of hypotheses can you currently program an AI to entertain." Does this sound right?
Yes, I agree. I can imagine some reasoning being concieving of things that are transturing complete, but I don't see how I could make an AI do so.
Enumerate mathematical objects by representing them in a description language and enumerating all strings. Look for structures that are in some sense indistinguishable from "you". (taboo "you", and solve a few philosphical problems along the way). There's your set of possible universes. Distribute probability in some way.
Bayesian inference falls out by aggregating sets of possible worlds, and talking about total probability.
In the same stroke with whch you solve the "you"identification problem, solve the valueidentification problem so that you can distribute utility over possible worlds, too. Excercising the logical power to actually observe the worlds that involve you on a close enough level will involve some funky shit where you end up determining/observing your entire future utilitymaximizing policy/plan. This will involve crazy recursion and turning this whole thing insideout, and novel work in math on programs deducing their own output. (see TDT, UDT, and whatever solves their problems).
Approximating this thing will be next to impossible, but we have an existence proof by example (humans), so get to it. (we don't have prrof that lawful recursion is possible, though, if I understand correctly)
Our current halfassed version of the inference thing (Solominoff Induction) uses Turing Machines (ick) as the description language, and P'= 2^(L), where L is the length of the strings describing the universes (that's an improper prior, but renorm handles that quick).
We have proofs that P' = 1 does not work (no free lunch (or is that not the right one here...)), and we can pack all of our degrees of freedom into the design of the description language if we choose the length prior. (Or is that almost all? Proof, anyone?)
This leaves just the design of the description langauge. Computable programming languages seem OK, but all have unjustified inductive bias. Basically we have to figure out which one is a close approximation for our prior. Turing machines don't seem particularly priveledged in this respect.
EDIT: Bolded the Tl;dr.
EDIT: Downvotes? WTF? Can we please have a norm that people can speculate freely in meditation threads without being downvoted? At least point out flaws... If it's not about logical flaws, I don't know what it is, and the downvote carries very nearly no information.
this is my first time approaching a meditation, and I've actually only now decided to delurk and interact with the website.
One way to enumerate them would be, as CCC has just pointed out, with integers where irrationality denotes acausal worlds and rationality denotes causal worlds.
This however doesn't leaves space for Stranger Things; I suppose we could use the alphabet for that. 1 If, however, and like I think, you mean enumerate as "order in which the simulation for universes can be run" then all universes would have a natural number assigned to them, and they could be arranged in order of complexity; this would mean our own universe would be fairly early in the numbering, if causal universes are indeed simpler than acausal ones, if I've understood things correctly.
This would mean we'd have a big gradient of "universes which I can run with a program" followed by a gradient of "universes which I can find by sifting through all possible states with an algorithm" and weirder stuff elsewhere (it's weird; thus it's magic, and I don't know how it works; thus it can be simpler or more complex because I don't know how it works).
In the end, the difference between causal and acausal universes is that one asks you only the starting state, while the other discriminates between all states and binds them together.
AAAAANNNNNNNND I've lost sight of the original question. Dammit.
It would be nice if there was some topology where the causal worlds were dense in the acausal ones.
Unfortunately, this strikes me as unlikely.
Well, I appear to be somewhat confused. Here is the logic that I'm using so far:
If:
1: A hypothesis space can contain mathematical constants,
2: Those mathematical constants can be irrational numbers,
3: The hypothesis space allows those mathematical constants to set to any irrational number,
4: And the set of irrational numbers cannot be ennumerated.
Then:
5: A list of hypothesis spaces is impossible to enumerate.
So If I assume 5 is incorrect (and that it is possible to enumerate the list) I seem to either have put together something logically invalid or one of my premises is wrong. I would suspect it is premise 3 because it seems to be a bit less justifiable then the others.
On the other hand, it's possible premise 3 is correct, my logic is valid, and this is a rhetorical question where the answer is intended to be "That's impossible to enumerate."
I think the reason that I am confused is likely because I'm having a hard time figuring out where to proceed from here.
If you ever plan on talking about your hypothesis, you need to be able to describe it in a language with a finite alphabet (such as English or a programming language). There are only countably many things you can say in a language with a finite alphabet, so there are only countably many hypotheses you can even talk about (unambiguously).
This means that if there are constants floating around which can have arbitrary real values, then you can't talk about all but countably many of those values. (What you can do instead is, for example, specify them to arbitrary but finite precision.)
Only if you live in a universe where you're limited to writing finitely many symbols in finite space and time.
Point.
If I lived in such a universe, then it seems like I could potentially entertain uncountably many disjoint hypotheses about something, all of which I could potentially write down and potentially distinguish from one another. But I wouldn't be able to assign more than countably many of them nonzero probability (because otherwise they couldn't add to 1) as long as I stuck to real numbers. So it seems like I would have to revisit that particular hypothesis in Cox's theorem...
It looks like you're right, but let's not give up there. How could we parametrize the hypothesis space, given that the parameters may be real numbers (or maybe even higher precision than that).
It really seems you need to taboo "real" here, and instead ask some related questions such as:
which types of universes could observe which other types of universe (an universe which can observe you you can also, obviously, "travel" to)? Which universes could trade, in the broadest senses of the word, with which other universe? What types of creatures in which types of universes are capable of consistently caring about things in what types of universes?
Specifically it seems likely that your usage of "real" in this case refers to "things that humans could possibly, directly or indirectly, in principle care about at all.", which is the class of universes we must make sure to include in our priors for where we are.
Yep. Gary Drescher in Good and Real makes the point that there's no inherent difference between the real universe and other mathematically possible universes (essentially Tegmark's MUH, but put in a more comprehensible (for me at least) way), and “real” is just a deictic, meaning ‘contained in the universe the speaker is in’. (But if we found that the Kolgomorov complexity of this universe is much larger than what would suffice for sentient beings to arise in it, that might mean that there's something else that makes this universe real other than the fact that we are in it.)
I'm having trouble with this usage of the world "universe". Can't you call it "timeline" or "plane" or something?
Whether the manyworlds hypothesis is true, false, or meaningless (and I believe it's meaningless precisely because all branches you're not on are forever inaccessible/unobservable), the concept of a universe being observable has more potential states than true and false.
Consider our own universe as it's most widely understood to be. Each person can only observe (past) or affect (future) events within his light cone. All others are forever out of reach. (I know, it may turn out that QM makes this not true, but I'm not going there right now.) Thus you might say that no two people inhabit exactly the same universe, but each his own, though with a lot of overlap.
Time travel, depending on how it works (if it does), may or may not alter this picture much. Robert Forward's <i>Timemaster</i> gives an example of one possible way that does not require a manyworlds model, but in which time "loops" have the effect of changing the laws of statistics. I especially like this because it provides a way to determine by experiment whether or not the universe does work that way, even though in some uses of the words it abolishes cause and effect.
So, there's direct, deterministic causation, like people usually talk about. Then there's stochasitic causation, where stuff has a probabilistic influence on other stuff. Then there's pure spontenaity, things simply appearing out of nowhere for no reason, but according to easily modeled rules and probabilities. Even that last is at least theorised to exist in our universe  in particular as long as the total energy and time multiply to less than planck's constant (or something like that). At no point in this chain have we stopped calling our universe causal and deterministic, no matter how it strains the common use meaning of those terms. I don't see why time turners need to make us stop either.
To take your Game of Life example, at each stage, the next stage can be chosen by calculating all selfconsistent futures and picking one at random. The game is not acausal, it's just more complicated. The next state is still a function of the current (and past) states, it's just a more complicated one. A timeturner universe can also still have the property that it has a current state, and it chooses a future state taking the current state as (causal) input. Or indeed the continuous analogue. It just means that choosing the future state involves looking ahead a number of steps, and choosing (randomly or otherwise) among selfconsistent states. The trick for recovering causation is that instead of saying Harry Potter appearing in the room was caused by Harry Potter deciding to turn the time turner in the future, you say Harry Potter appearing in the room was caused by the universe's generateaconsistentstory algorithm. And if you do something that makes selfconsistentstories with Harry Potter appearing than otherwise then you are having a stochastic causal influence on this appearance. Causality is intact, it's just that the rules of the universe are more complicated.
Which brings me to the meditation. Dealing with the idea of a universe with time turners is no different to a universe with psychics. In either case, the universe itself would need to be substantially more complicated in order for these things to work. Both involve a much larger increase in complexity required than they intuitively seem to, because they're a small modification to the universe "as we see it", but making that change requires a fundamental reworking of the underlying physics to something subtantially more complicated. Thus until substantially strong evidence of their existance comes to light, they languish in the highKolmogorovcomplexity land of theories which have no measurable impact on an agent's choices, nonzero probability or otherwise.
Who's to say there aren't timeturners in the universe by the way? Positrons behave exactly like electrons travelling backwards in time. A positronelectron pair spontaneously appearing and soon annhiliating could also be modelled as a timeloop with no fundamental cause. You can make a timeturner situation as well out of them, going forward then backwards then forwards again. Of course, information isn't travelling backwards in time here, but what exactly does that mean in the first place anyway?
Just a general comment on how to make people think harder about what you write, given the multitude of poorly thought out comments. There is a standard technique in quality control, where a small amount of defective products is inserted into the stream in order to keep the controller's focus. (Can someone find a link for me, please?) There is a similarly standard, though rarely used technique in teaching, where the instructor gives a false statement in the course of a lecture and the students are expected to find it (in some variations sometimes there is none).
The material you describe is fairly involved and nontrivial, so making people sift through all your statements and how they fit (or do not fit) together by inserting an occasional intentional falsehood (and being upfront about it, of course), then fixing it a few days later, while leaving a trace of what got edited and when) strikes me as a reasonable way to make sure that your readers pay attention.
I'd rather not have this.
Instead of making up a highstatus rationalization, let's just say that I am neither the brightest nor the most diligent reader, and thus the article without intentional errors gives me more value that an article with intentional errors. I would probably just not notice the error.
I'm... really shocked to hear this from you, so maybe I'm missing something:
Yes, you're destroying Universe A, but also creating Universe B. Given that "B" will notexist if we don't travel, and "A" will notexist if we DO travel, it seems morally neutral to make such an exchange  either way there is an equal set of peoplewhowon'texist. It's only a bad thing if you have some reason to favor the statusquo of "A exists", or if you're concerned about the consent of the billions of people whose lives you alter (in which case you should be equally concerned about getting their consent before killing evil villains, fixing the environment, or creating FAI, neh?)
Once you're viewing it as an otherwiseequal exchange, it's just a matter of the specifics of those universes. It's generally given in time travel stories that, at least from the protagonist's view, "B" has a higher expected utility than "A", so it would seem that time travel is the right choice.
If we use phrases like "extinguished the world", then people will get bothered, because most people view that as a "bad thing", and then people would choose "A" instead, so it seems like a useful policy (in a world with time travel) to not really draw attention to this.
My morality has a significant "status quo bias" in this sense. I don't feel bad about not bringing into being people who don't currently exist, which is why I'm not on a longterm crusade to increase the population as much as possible. Meanwhile I do feel bad about ending the existence of people who do exist, even if it's quick and painless.
More generally, I care about the process by which we get to some worldstate, not just the desirability of the worldstate. Even if B is better than A, getting from A to B requires a lot of deaths.
If you could push a button and avert nuclear war, saving billions, would you?
Why does that answer change if the button works via transporting you back in time with the knowledge necessary to avert the war?
Either way, you're choosing between two alternate time lines. I'm failing to grasp how the "cause" of the choice being time travel changes ones valuations of the outcomes.
Of course.
Because if time travel works by destroying universes, it causes many more deaths than it averts. To be explicit about assumptions, if our universe is being simulated on someone's computer I think it's immoral for the simulator to discard the current state of the simulation and restart it from a modified version of a past saved state, because this is tantamount to killing everyone in the current state.
[A qualification: erasing, say, the last 150 years is at least as bad as killing billions of humans, since there's essentially zero chance that the people alive today will still exist in the new timeline. But the badness of reverting and overwriting the last N seconds of the universe probably tends to zero as N tends to zero.]
But the cost of destroying this universe has to be weighed against the benefit of creating the new universe. Choosing not to create a universe is, in utilitarian terms, no more morally justifiable than choosing to destroy one.
That seems to be exactly the principle that is under dispute.
Values are not up for grabs. If they turn out to be asymmetrical and inelegant (like, for example, really caring more about people not getting killed than people getting born) then, well, they are asymmetrical and inelegant. Maybe the distinction between notkilling and creating is incoherent but I haven't yet seen an argument trying to demonstrate that without appeals to philosophical parsimony.
If you time travel, "Universe A" doesn't exist. If you don't, then "Universe B" doesn't exist.
They're BOTH universes which fail to exist if you chose the other one. No one dies  there's just a universe that doesn't exist because you didn't choose it.
If you timetravel, Universe A still existed once, and contrary to the preferences of the people there was then extinguished. The preferences of the people in notyetexistent metafuture Universe B don't matter to me yet, because they may never exist.
Once Universe B is created, and if there was some way to restore Universe A, it'd be then that the preferences of the residents of the two universes (past and present) would weigh equally to my mind, having been equally real.
Obligatory JRPG references ho!
In Chrono Cross, n fvtavsvpnag cybg gjvfg vagebqhprf guvf pbaprcg naq ersenzrf gur tnzr nf orvat nobhg svkvat gur qvfnfgre pnhfrq ol Puebab Gevttre'f cebgntbavfgf' abg guvaxvat bs vg.
In Star Ocean: The Last Hope (in one of the only good bits of a largely terrible game), gur cebgntbavfg nppvqragnyyl qrfgeblf na nygreangr cnfgRnegu va n fvzvyne jnl, naq npghnyyl ernpgf gb guvf nccebcevngryl ol orvat pehfurq jvgu qrcerffvba naq thvyg. Tnzref, bs pbhefr, ungrq guvf naq pnyyrq uvz "rzb".
Re [1] I totally noticed that "Flight of the Navigator" is a story about a kidnapped, returned boy who forges a new relationship with his older parents and ex younger, now older brother, and a cute nurse at the government facility, and then kills them all.
To say understanding this spoiled the story for me is an understatement. That movie has more dead people than Star Wars. It's a fricken' tragedy.
Its okay. In the new timeline, the nurse went on to be a sex columnist.
Um. Doesn't Star Wars (I take it we're talking about the movie otherwise known as "Episode IV" rather than the whole series) more or less begin with the destruction of an entire planet? And ... is it actually clear that the only way to implement time travel is the one Eliezer describes, and that it's best described as killing everyone involved? It doesn't look that way to me.
But I haven't seen Flight of the Navigator so maybe there are details that nail things down more.
The Star Wars series is about the tragic destruction of one planet and two death stars, and the childish bickering that caused it.
Flight of the Navigator ends the timeline. It destroys every planet, every star, every wandering spaceship billions of light years into the dark, total universal omnicide. And a reboot into a new timeline from a previously existing history.
Upvoted for "omnicide".
Why would the old timeline deserve to exist more than the new one?
Tentative answer: It was presumably more of a collaborative process than a timeline chosen by one person.
Any opinions about Asimov's The End of Eternity? An organization attempts to optimize the timeline. The book might be a good starter for discussion of CEV, terminal values, and such.
Has anyone read Garfinkle's *All of an Instant"? I've never finished it, but the premise is that time travel is a biological capacity, and when many people discover it, all chaos ensues.
And it does it on a routine basis. After all, most of the critters are returned to the moment they were taken.
Alright. To preface this, let me say that I'm sorry if this is a stupid issue that's been addressed elsewhere. I'm still working my way through the sequences.
But... the jump from discrete causality to continuous causality seems to be hiding a big issue for the argument against time travel. It's not an insoluble issue, but the only solution that I see does pose problems for the locality of this definition of "causal universe".
To start from the beginning: the argument in the discrete case relies heavily on the computability of the universe. In a causal universe, we can compute time t=8 based on complete knowledge about time t=7, and then we can compute time t=9 on our newly found knowledge about time t=8.
But as far as I can see, there's not similar computability once we move into a continuous universe. In particular, if we have complete knowledge about a subspace K of spacetime, even with infinite computing power we can only find out the state of the universe along what I'll call the "future boundary" of the space K: in particular, we can only compute the state of points P in spacetime whose past light cone of height d lies entirely inside K, for some d. That means that we can never compute time t=8 based on knowledge that we can have at time t=7, in fact, we can't compute time t=8 unless we have complete knowledge about time t<8.
So computability doesn't seem to pose a problem for Time Turners, because even without Time Turners the (nonlocal) future is not computable. To put it another way, continuous causality has been defined in an entirely local way, which means that nonlocal cycles don't seem to be a problem. In fact, positing a TimeTurner jump from times t<9 to time t=8 merely requires redefining the topology of time in such a way that point P at times t<9 is in the past light cone of the same point P at time t=8.
The obvious reply is that (by definition) point P at time t=8 must be in the past light cone of the same point P at all times 8<t<9. So we have the past light cone of point P intersecting the future light cone of point P. So should our definition of a "causal universe" exclude that? That seems perfectly reasonable, but doing so seems to destroy the locality of our definition of a causal universe. Because the intersection of the light cones that we're objecting to is not a local phenomenon: for a point P at time t<9 arbitrarily close to 9 (i.e. in the local past time cone of P at t=8), point P at time t=8 is only its nonlocal past time cone.
Does the issue I'm trying to get at make any sense? I can rephrase if that would help, and I'd be happy to read anything that addresses this.
The fact that you can't think of a way to compute the behavior of such a universe is no reason to conclude that it can't be done.
In particular, it's easy enough to come up with simplistic billiard ball models where you can compute events without 'backtracking'. Now such models are certainly weird in the sense that in order to compute what happens in the future one naturally relies on counterfactual claims about what one might have done.
However, <B>Quantum Mechanics looks a great deal like this</B>. The existence of objects like time turners creates the opportunity for multiple solutions to otherwise deterministic mechanics and if microscopic time turners were common one might develop a model of reality that looked like wave functions to represent the space of possible future paths that can interfere constructively/destructively via interaction from time turner type effects.
That's the transactional interpretation, right?
You just made the universe that much less fun for me. ;)
This probably sounds like a dumb question but given the assumptions of many worlds, timeless physics, no molecular identity and then adding that time travel is possible, why would that even be specially interesting?
In particular, why would that be different than 2D land that suddenly works out that instead of always having to move forward in the Z dimension you can move backwards as well.
I would very much like to see an abstract at the beginning of this article. It is interesting, but rather long, and when the Game of Life example started, I was kind of lost what the intention of the article is supposed to be. I admit that I haven't read the post this is a followup to, but given that one of the largest criticism for the sequences is their inaccessibility to newcomers, there might be room for improvement in this new series of posts.
The Ed stories by Sam Hughes might be interesting to you. (Warning: long.)
Edit: If you want to skip to the bit that your post reminded me of, that's the chapter titled "Hotel Infinity", specifically starting at the first instance of the words "Time travel".
I might be some kind of monster but: I don't see what is bad about my timeline ending. There's no suffering involved (indeed, much less than the timeline continuing.) It's not like we had a civilizational fuckup that lowers our status relative to our modal counterparts; what we would have gone on to do remains unchanged. People would be denied experiences but I don't see how you can endorse that without coming to the repugnant conclusion (which does seem genuinely horrific.)
This whole post strongly reminds me of "A New Kind of Science" [0], where Stephen Wolfram tries to explain the workings of the universe using simple computational structures like Cellular Automata, network systems, etc. I know that Wolfram is not highly regarded for many different reasons (mostly related to personal traits), but I got a very similar feeling when reading both NKS and this post  that there is something in the idea, that the fabric of the universe might actually be found to be best described by a simple computational model.
[0]  http://www.wolframscience.com/nksonline/toc.html
My amateur reading of QED: The Strange Theory of Light and Matter left me with the impression that the universe we live in has selfconsistent time travel. Summing over histories involves summing over histories in which particles go back in time.
For example, on page 97, the caption to Figure 63 says
Over the page
I vaguely assumed that the reason we don't observe macroscopic time travel drops out of the principle of stationary phase. All the lumps of high amplitude arise from paths such that minor deviations don't really change the phase, allowing a bunch of similar paths to add coherently. But try to travel back in time and you create a loop. Pull the loop a little tighter and the phase changes a lot. Loops never have stationary phase and the amplitudes of similar paths fail to add coherently, averaging out to pretty well zero.
Several mathematicians I know (and, I would guess, a sizable population of physicists as well) regard Feynman sumsoverhistories as mathematical abstractions only. From this perspective they don't describe processes that are actually happening outthereintheworld, they're just mathematically convenient and maybe also intuitively useful. (I haven't thought about whether or how this position can be reconciled with what I think is the standard LW position on manyworlds.)
My limited impression of physics is that there is a tendency for mathematically convenient but "not real" descriptions to turn out to be either subtly inaccurate, or to actually correspond to something real. For example, negative frequency photons seem to have some element of reality to them, along with the quantum wave function and virtual particles. I assign some nontrivial probability weight to "either sums over histories are inaccurate descriptions of what happens, or they correspond to something that acts a lot like a real thing", even when knowledgeable physicists say they aren't a real thing.
Me too, but almost all of it would be concentrated at "sums over histories are inaccurate descriptions of what happens." Sumsoverhistories are conceptually unsatisfying to me in that they use the classical concept of a history in order to describe quantum phenomena. My vague intuition is that a truer theory of physics would be more "inherently quantum."
Is there a word for time travel that works like this? I'm writing a novel that has it, and would like to be able to succinctly describe it to people who ask what it's about or how the time travel works.
(I'm not invoking computer simulation, but the effects as far as the characters see are like this  or rather, the characters see time travelers from the future but never get to see the versions of the universe where they get to remember seeing someone leave to travel to the past.)
Yes, that's a type 3 plot.
Such numbering isn't however very meaningful or intuitive... I'd just say "timelineoverwriting".
This is the standard model of time travel / prophecy in Greek myths, isn't it? Maybe I'm overgeneralizing from Cassandra.
[edit] Eliezer calls it Stable Time Loops, which is a term I've seen before.
My understanding is that Stable Time Loops work differently: basically, the universe progresses in such a way that any and all time traveling makes sense and is consistent with the observed past. Under the above model, you will never witness another copy of yourself traveling from the future, though you might witness another copy of yourself traveling from an alternate past future that will now never have been. With STL, you can totally witness a copy of yourself traveling from the future, and you will definitely happen to travel back in time to then and do whatever they did. That's my understanding, at least.
There is a hugely successful webcomic called Homestuck (maybe you've heard of it; it raised over $2 million in one month to make a game out of it) and a significant part of the comic's events are reliant on time travel. The comic itself is dense and insanely complex, so I will do my best to spoil as little as possible, because to my knowledge there are no plot holes, and in the end it all makes sense if you keep reading through to Act 5 and beyond.
The basic idea is that the four main characters are playing an immersive video game called Sburb, and the game takes place within their universe. In Act 4, Dave is shown in a Bad Future where something happened and made the game unwinnable. At some point he had created timetables that let him go back and forth in the timeline, became the Knight of Time, and eventually decided to go back and Make Things Right. We then learn that Sburb, the gameuniverse, encourages the use and abuse of stable time loops, but punishes those who try to change fate by killing the errant traveler. This leads to a handful of dead Daves piling up, the equivalent to Dumbledore discovering his own sticky notes, except more gruesome.
The biggest mystery of Act 4 was the fact that the Dave from the Bad Future came from a Doomed timeline, but his interference in the Alpha timeline was critical to winning the game. In fact, his interference caused a grandfather paradox, as he prevented the events that caused him to go back. Normal causality had to be thrown out the window. This caused a hurricane of argument on the MSPA forums over which time travel theory used Occam's Razor the best.
My personal favorite was developed by myself and BlastYoBoots, and we called it Wobble Theory. It worked like a turing machine: Sburb steps through the initial seed of the universe and tries to see if certain conditions are met, chief among them being the WIN or LOSE condition, but there are additional caveats <rot13>fhpu nf erdhvevat gung nyy vagrefrffvba pbairefngvbaf gnxr cynpr, gur cynagvat bs gur Sebt Grzcyr, gur cnffntr bs Wnpx Abve naq gur Pebfolgbc/Srqben, rgp</rot13>. If these conditions were not met, the universe would mark down places where things had gone right (i.e. adhered to the Alpha timeline as decided), constrain those, and see what else it could tweak. The mostoften changed variable would be a Time player's decisions, as they were literal butterfly effects who could bring huge changes back to the present after their decisions had propagated into a Doomed future. In this way, the Alpha timeline was like a vigorously shaken wet noodle, grabbed from one end and pinched along its length until it stopped wobbling.
Eventually, the comic explained that Immutable Timeline Theory was the winner. Sburb had literally calculated the entire timeline AND all of its offshoots in one go; that something happened was "AN IMMUTABLE FACT THAT WE ARE STATING FOR THE RECORD." The various problems with this are explained away with a turtlesallthewaydown demeanor, and going into those explanations would only spoil more than I want to.
The short version is that Andrew Hussie literally exists inuniverse as the author of the comic, and if he says the timeline ought to go this way, it will.
I just got an idea for an interesting fictional model of time travel, based on a combination of probabilities and consistent histories.
The simplest example would go like this. Imagine you step into the time machine, travel a minute into the past, and kill your younger self. At the moment of your arrival, the universe branches into two. Since the number (total weight?) of killers should be equal to the number of victims, the branches have probability 50% each. In one branch you live and become a killer, in the other you die.
Now let's take a more complex scenario. You flip a coin to decide whether you should step into the time machine, and another coin to kill or spare your past self. (Of course you have to travel to the moment before the first coinflip, otherwise this reduces to the previous scenario.) To figure out the probabilities, imagine that n people survive to flip the first coin. Then n/2 of them will step into the time machine and n/4 will become killers, which gives us n/4 victims. So you have a 1/5 chance of dying in this situation.
Is this model new? How far can we extend it consistently? What kinds of paradoxes can arise?
Scott Aaronson's model, that Eliezer refers to here is basically this.
I fail to see how this is different from the standard "parallel timelines" model. It seems like you just applied probabilistic reasoning to figure out the relative occurrences of certain timelines.
Perhaps I'm misinterpreting what you mean by branching, but for all intents and purposes in the first example there are two parallel timelines which happen to be identical until in one of them a copy of the you from the other appears and kills you in this timeline, and later you disappear from the other one the killer came from.
Question  isn't the sheer abundance of cyclic graphs something of a large argument we are in an acausal universe? If time travel is simply very difficult it's probable that we'd never see it in our past light cone by chance (or at all barring intelligent intervention), and locally such a universe looks causal: events have causes even if they don't have a First Cause.
How did you decide that our prior regarding the causal structure of the universe should be a somewhat uniform distribution over all directed graphs??
I didn't  but I did do a backoftheenvelope calculation, which predicts that there are something like a googolplex times more graphs with one cycle than there are acyclic paths, assuming 10^60 nodes (the number of Planck times since the beginning of the universe.)
And I don't have a prior that says that an acausal universe should have a probability penalty of one over googolplex.
(I assume you meant "acyclic graphs")
If this sort of reasoning worked, you could find strong arguments for all sorts of (contradictory) hypotheses. For instance:
or
or
or
I mean, your observation is interesting, but I don't think it constitutes a "large argument". You can't just slap reasonableish priors onto spaces of mathematical objects, and in general using math for long chains of inference often only works if it's exactly the right sort of math.
Any inference about "what sort of thingies can be real" seems to me premature. If we are talking about causality and spacetime locality, it seems to me that the more parsimonious inference regards what sort of thingies a conscious experience can be embedded in, or what sort of thingies a conscious experience can be of.
The suggested inference seems to privilege minds too much, as if to say that only the states of affairs that allow a particular class of computation can possibly be real. (This view may reduce to empiricism, which people like, but stated this way I think it's pretty hard to support! What's so special about conscious experience?)
EDIT: Hmm, here is a rather similar comment. Hard to process this whole discussion.
EDIT EDIT: maybe even this comment is about the same issue, although its argument is being applied to a slightly different inference than the one suggested in the main article.
I am having my doubts that time travel is even a coherent concept. Actually, I have my doubts about time itself. At nonrelativistic speeds and over small distances we can kid ourselves that two events not in the same place can both happen "at" a particular time. But we know that in general that's only a convenient simplification. There's no objectively real "t" axis in spacetime independent of the observer's frame of reference.
There's no x,y, or z axis independent of the observer's frame of reference either. Does that mean that spatial travel is not a coherent concept?
If the coherent concept is 'spacetime travel', why is it required that there exist an ordering over all points in spacetime? Every pair of points (A,B) falls into one of three categories: events at point A can directly or indirectly have an effect/be observed at point B, but not vice versa; events at point A cannot have an effect or be observed at point B, directly or indirectly; events at point B can be observed or have an effect at point A, directly or indirectly.
It is difficult for different observers to communicate where points are, but they divide all points in spacetime into the same three categories.
But Eliezer gave you a constructive example in the post!
OK then, I am having doubts that my mind is coherent enough to discuss time travel usefully.
Understandable. Your brain shipped with a builtin module that models time as a property of reality in order to simplify other processes. Most people have to bludgeon it to neardeath in order to just barely avoid the basic failure modes of thinking about time travel.
"But if you were scared of being wrong, then assigning probability literally zero means you can't change your mind, ever, even if Professor McGonagall shows up with a TimeTurner tomorrow."
Doesn't this assume that every mental state of mine has to be causally connected to a prior mental state? If we live in an acausal reality, I'm willing for my beliefs to be more related to a causal events than to Beysian updating. I don't know how clear that is, but it is your fault for bringing up time travel ;)
P(A)=0; P(B)=0 P(AB)=1
If we define probability to be continuous on [0,1], the math works. In practice, however, the probability of Professor McGonagall showing up with a TimeTurner tomorrow, given that I see and talk to her and try out the timeturner myself and it has the expected results, including being able to solve NPcomplete problems in constant time, remains zero. The odds of spontaneous creation of Professor McGonagall and a device which causes me to perceive that I have traveled through time and which solves any NPhard problems that I choose to give it in finite time is epsilon. The odds of a selfconsistent hallucination that the above events have happened is an epsilon of a higher order.
Therefore, given impossible evidence one should conclude that one is insane. Once one has concluded that one is insane, one should reconsider all of one's prior judgements in light of the fact that one cannot tell real evidence from hallucinatory evidence which brings all of the evidence regarding the impossibility of any event into question.
In other words, there is epsilon chance that all of your experience is fake, and therefore at least epsilon uncertainty in any prediction you make, even predictions about pure hypothetical situations where mathematical proof exists.
But didn't you already answer this? The computer needed to findandmark a universe with closed time loops is much, much larger, computationally speaking, than the one you need to, say, findandmark our universe. If you give me no information other than "a computer is simulating a universe", I'll still rate it more likely that it's doing something that doesn't require iterating the totality of predecessor search space.
But if the computer simulating operates in an acausal universe, the limitations on complexity we see in our causaluniverse computers may not hold, and so the point may be selfdefeating.
I'd suggest that if this is a meaningful question at all, it's a question about morality. There's no doubt about the outcome of any empirical test we could perform in this situation. The only reason we care about the answer to such questions is to decide whether it's morally right to run this sort of simulation, and what moral obligations we would have to the simulated people.
Looked at this way, I think the answer to the original question is to write out your moral code, look at the part where it talks about something like "the wellbeing of conscious entities," taboo "conscious entities," and then rewrite that section of your moral code in clearer language. If you do this properly you will get something that tells you whether the simulated people are morally significant.
You can apply the bruteforce/postselection method to CGoL without timetravel too... But in that case verifying that a proposed history obeys the laws of CGoL involves all the same arithmetic ops as simulating forwards from the initial state. (The ops can, but don't have to, be in the same order.) Likewise if there are any lineartime subregions of CGoL+timetravel. So I might guess that the execution of such a filter could generate observers in some of the rejected worlds too.
There are laws of which verification is easier than simulation, but CGoL isn't one of them.
Why can't you change your mind ever? Is this because of the conservation of expected evidence?
No. This isn't conservation of expected evidence but a simple consequence of Bayes theorem. If your prior probability is zero, then you end up with a zero in the numerator of the theorem (since P(A) is zero). So your final result is still zero.
My hypothesis is that universes that allow macroscopic time travel are very unlikely to have life intelligent enough to exploit the time travel. The hypothesis depends on two points: 1) policing time travel is likely to be extremely difficult or impossible, and 2) at least some members of the species will want to cause trouble with a time machine, including the sort of trouble that causes the entire species to have never evolved in the first place. Therefore I take the fact that we exist as evidence that arbitrary amounts of time travel aren't possible in our universe...
Larry Niven once commented that, if pastchanging time travel is possible, the most stable universes will be those in which time travel is never invented...
Doesn't follow. The fact that you exist in a certain way isn't evidence about prior probability of your existing in this way. (Your points (1) and (2) are arguments about prior probability that don't have this problem; using observations that depend on the value of prior probability also works.)
Hm. It looks like my intuition has a bug. I'll have to think about it more.
(There's also a prophecy. True, a prophecy could simply indicate a Meddling Force that nudges events in a particular direction, rather than someone receiving information from the future, but once you have one obviouslycausalityviolating thing, there's much less call to be extremely suspicious of other, apparentlycausalityviolating things.)
Rowling is on record as stating that prophecies can be justwalkedawayfrom which makes their dynamics less clear and not obviously a selfconsistency thing.
What does this even mean?
I think it means that prophecies may be merely "very good magicallyderived estimations of the future"  we are not sure they bind the past with the future as tightly as TimeTurners seem to do.