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 lofty-sounding 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 Time-Turners, of course.
A Time-Turner, 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 time-travel doesn't allow for changing history; whatever you do after you go back, it's already happened. The universe containing the time-travel is a stable, self-consistent 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 Time-Changer 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 Time-Changer 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.
Still, if we don't worry about the ethics or the disk space requirements, then a Time-Changer 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 Time-Changer is the causal descendant of the older universe that just got dumped from RAM.
But what if instead, reality is always - somehow - perfectly self-consistent, 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 sweep-through, without any higher-order 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 Time-Turner used at 9PM, you still couldn't compute the exact state of the time-traveller 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 time-traveller who just arrived.
In a causal model, you can compute p(9pm|8pm) and p(8pm|7pm) and it all starts with your unconditional knowledge of p(7pm) or perhaps the Big Bang, but with a Time-Turner we have p(9pm|8pm) and p(8pm|9pm) and we can't untangle them - multiplying those two conditional matrices together would just yield nonsense.
Does this mean that the Time-Turner is beyond all logic and reason?
Complete philosophical panic is basically never justified. We should even be reluctant to say anything like, "The so-called Time-Turner 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 Time-Turner 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 Time-Turner 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 somewhat-justified conceptual panic which the protagonist of Harry Potter and the Methods of Rationality undergoes upon seeing a Time-Turner, 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 two-dimensional 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 gut-level-understand 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 not-yet-known 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 time-travel 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 brute-force searching through all possible Life-histories, discarding all histories which disobeyed the laws of Life + time travel. If the entire universe were a 4-by-4 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 time-traveling 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 time-travel loops - change their physics to allow Time-Turners - 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 universe-history.
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 time-slice 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 time-traveling 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 self-consistent Time-Turners, 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 Time-Turners, and does appear to have strictly local causality in which each variable can be computed strictly forward-in-time.
And I don't know why that's the case; but it's a likely-looking 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 in-order using local and directional rules of determination, you're vastly narrowing down the possibilities relative to all of Math-space.
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 Pearl-standard causal models. There would be no hypothesis in your hypothesis-space 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.
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.
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 non-causal 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 Time-Turner tomorrow.
Meditation: Suppose you needed to assign non-zero 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 Time-Turners 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?
 Sometimes I still marvel about how in most time-travel 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.)
 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 faster-than-light 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"
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 4-dimensionalist, 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.
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.
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?
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 fan-in (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 time-turner implementation where you enumerate all possible universes, and select one that passed the self-consistency test, can be represented by a DAG; it's causal. It's just that the moment where the time-traveler 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 time-turners 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 time-turner usage, and use them to predict experimental outcomes!
You can imagine universes which violate the ... (read more)
I haven't yet particularly seen anyone else point out that there is in fact a way to finitely Turing-compute a discrete universe with self-consistent Time-Turners 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 self-consistency 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?
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.
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 max-flow algorithms have a continuous generalization.
edit: in fact, max-flows 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 OB-bookblogging time period and in methadone treatment during the subsequent non-EY-non-Yvain-LW time period would feel upon shooting up today. Hey Mr. Tambourine Man, play a song for me / In the jingle-jangle morning I'll come following you.
In computational physics, the notion of self-consistent 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 self-consistent 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 physics-based examples tend to have (should have) uniquely defined solutions.
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 re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d 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.
1) If we ask whether the entities embedded in strings watched over by the self-consistent universe detector really have experiences, aren't we violating the anti-zombie 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?
I think that a correct metaphor for computer-simulating 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".
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?
By the way, how precise must be a simulation to add measure? Did I commit genocide by watching Star Wars, or is particle-level 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 particle-level 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.
"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 pre-packaged 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 m... (read more)
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 Time-Turners work. I'm going to explain this like there's only one wizard with a Time-Turner 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 Time-Turner 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 hug... (read more)
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.
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 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 willy-nilly, 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 time-traveling 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).
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.
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.
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 time-traveler 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.
(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... (read more)
Characters in the novel Pastwatch by Orson Scott Card wrestle with this issue.
Re  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.
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.
My amateur reading of QED: The Strange Theory of Light and Matter left me with the impression that the universe we live in has self-consistent 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... (read more)
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 non-trivial 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.
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 ?
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 cnfg-Rnegu 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".
I'd like to report that images are currently broken. Their URLs have an unnecessary "mediawiki" section in the paths like so:
Current URL: http://wiki.lesswrong.com/mediawiki/images/4/41/WaveCause.jpg
Correct URL: https://wiki.lesswrong.com/images/4/41/WaveCause.jpg
You just made the universe that much less fun for me. ;)
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 not-exist if we don't travel, and "A" will not-exist if we DO travel, it seems morally neutral to make such an exchange - either way there is an equal set of people-who-won't-exist. It's only a bad thing if you have some reason to favor the status-quo of "A exists", or if you're co... (read more)
Suppose you needed to assign non-zero 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 Time-Turners or stranger things. How would you enumerate the hypothesis space of all the coherently-thinkable worlds we could remotely maybe possibly be living in, including worlds with Stable Time Loops and even stranger features?
I am now starting to REALLY lament my lack of formal education, because I JUST NOW managed to grasp why the whole "speed of light" thing makes sense. Stupid poverty, ruin my fun. :D
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 follow-up 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".
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.
I think that's because people change into their analog in the new timeline, rather than disappearing in a butterfly eff... (read more)
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, Quantum Mechanics looks a great deal like this. The existence of objects like time turners creates the opportun... (read more)
I'm not sure we're in a causal universe.
According to the theory of timeless physics, our universe is governed by Schrödinger's time-independent 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 negative-energy configuration states, or ... (read more)
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 no-where 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 caus... (read more)
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 n... (read more)
I'd rather not have this.
Instead of making up a high-status 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 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.)
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...
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 ca... (read more)
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.
"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 Time-Turner 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 ;)
But didn't you already answer this? The computer needed to find-and-mark a universe with closed time loops is much, much larger, computationally speaking, than the one you need to, say, find-and-mark 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.
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... (read more)
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.
(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 obviously-causality-violating thing, there's much less call to be extremely suspicious of other, apparently-causality-violating things.)
Guys, I am not a physicist but I have problems with understanding this:
Is that a proven known thing that space is really continuous and indefinitely divisible?
(An ex-physicist here) Quantization of measured energy levels in a bound system has nothing to do with the potential discontinuity of spacetime. The latter is hypothesized, but by no means proven or even tested. As for the original quote, it states that one has to leave room for models other than "a discrete causal graph".
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.
Perhaps something is simply wrong with my moral processing module, but I really don't see any morality issues associated with this sort of thing. Morality is, in my opinion, defined by society and environment; sure, killing people in the here and now in which we live is (in general) morally wrong, but if you go too away from that here and now, morality as we know it breaks down.
One area where I feel this applies is the "countless universes" arena. In most of... (read more)
Any inference about "what sort of thingies can be real" seems to me premature. If we are talking about causality and space-time 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... (read more)
I am having my doubts that time travel is even a coherent concept. Actually, I have my doubts about time itself. At non-relativistic 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.
This whole post strongly reminds me of "A New Kind of Science" , 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.
 - http://www.wolframscience.com/nksonline/toc.html
One of the neat things the Fringe TV show does is a thing with the part of time travel where the previous timeline and all the people in it get eradicated.
Here's my problem. I thought we were looking for a way to categorize meaningful statements. I thought we had agreed that a meaningful statement must be interpretable as or consistent with at least one DAG. But now it seems that there are ways the world can be which can not be interpreted even one DAG because they require a directed cycle. SO have we now decided that a meaningful sentence must be interpretable as a directed, cyclic or acyclic, graph?
In general, if I say all and only statements that satisfy P are meaningful, then any statement that doesn't ... (read more)
I'm not sure this is necessarily correct. We typically model quantum configurations as functions defined over a continuous domain, but it's yet possible that quantum configurations could be representable by a finite set of numbers (more precisely: that all possible configurations of our universe could be expressed as f(x) for some... (read more)
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... (read more)
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, the Kids, are playing an immersive video game called Sburb, a... (read more)
One thing this model ignores, so far as I could tell, is the reflective point of view of third person / past tense narration. Both Rowlings HP and Eliezer's HPMOR are past tense narrations, stories told progressively, but always reflectively ("Harry said" instead of "Harry says").
So, what if the causal links are already updated to the new information introduced with a 9pm|8pm turn, and this in turn updates the memories of agents within the universe, including the narrator (note: Narrator and Author are seperate entities in this concept;... (read more)
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 sce... (read more)
You can apply the brute-force/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 linear-time subregions of CGoL+timetravel. So I might guess that the execution of such a filter ... (read more)
Re your checking method to construct/simulate an acausal universe, won't work near as I can tell.
Specifically, the very act of verifying a string to be a life (or life + time travel or whatever) history requires actually computing the CA rules, doesn't it? So in the act of verification, if nothing else, all the computing needed to make a string that contains minds actually contain the minds would have to occur, near as I can make out.
One model for time travel might be a two dimensional piece of paper with a path or paths drawn wiggling around on it. If you scan a "current moment" line across the plane, then you see points dancing. If a line and its wiggles are approximately perpendicular to the line of the current moment, then the dancing is local and perhaps physical. Time travel would be sigmoid line, first a "spontaneous" creation of a pair of points, then the cancellation of one ("reversed") point with the original point.
An alternative story is of a li... (read more)