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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 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.[1]
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.
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 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?
[1] 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.)
[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 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"
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Comments (385)
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 coherently-thinkable worlds we could remotely maybe possibly be living in, including worlds with Stable Time Loops and even stranger features?
A start is to choose some language for writing down axiom lists for formal systems, and a measure on strings in that language.
Lowenheim-Skolem is going to give you trouble, unless "coherently-thinkable" is meant of as a subtantive restriction. You might be able to enumerate finitely-axiomatisable models, up to isomorphism, up to aleph-w, if you limit yourself to k-categorical theories, for k < aleph-w, though. Then you could use Will's strategy and enumerate axioms.
Edit: I realised I'm being pointlessly obscure.
The Upwards Lowenheim-Skolem means that, for every set of axioms in your list, you'll have multiple (non-isomorphic) 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 k-categorical 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 k-categoriciticy 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, k-categorical, models.
I don't think it's unfair to put some restrictions on the universes you want to describe. Sure, reality could be arbitrarily weird - but if the universe cannot even be approximated within a number of bits much larger than the number of neurons (or even atoms, quarks, whatever), "rationality" has lost anyway.
(The obvious counterexample is that previous generations would have considered different classes of universes unthinkable in this fashion.)
Why? If the universe has features that our current computers can't approximate, maybe we could use those features to build better computers.
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 non-computable 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 turing-transcendant part must be an integral part of the AI for it to have non-turing-complete hypotheses about the universe, and I have no idea what a turing-transcendant 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 "coherently-thinkable" net widely.)
I don't see how this changes the possible sense-data 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 sense-data 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).
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.
Mostly-causal universes with some time-travel 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...
If this universe contains agents who engage in acausal trade, does that make it partially acausal?
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.
Nope.
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 do--resources and values which will be heavily influenced by what we do today. The structure seems to be at least as similar as self-consistent solutions in plasma physics.
Agents can make choices that enforce global logical constraints, using computational devices that run on local causality.
Thanks, I feel like I grok this answer: There may be higher order acausal structures in the universe, but they run on a causal substrate.
Rationals and integers are both coutable! This is one of my favorite not-often-taught-in-elementary-schools but easily-explainable-to-elementary-school-students math facts. And they, the rationals, make a pretty tree: http://mathlesstraveled.com/2008/01/07/recounting-the-rationals-part-ii-fractions-grow-on-trees/
this is my first time approaching a meditation, and I've actually only now decided to de-lurk 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.
Yes, and I forgot to put it in.
Wait, causal worlds are dense IN acausal ones?
Is that a typo, and you meant "causal worlds were denser than acausal ones" or did I just lose a whole swath of conversation?
I mean the class of causal worlds be dense in the class of worlds, where worlds consists of causal and acausal worlds. The same way we understand a lot of things in functional analysis: prove the result for the countable case, prove that taking compactifications/completions preserves the property, and then you have it for all separable spaces.
Unfortunately, this strikes me as unlikely.
Well, I admit that I had originally considered that Stranger Things would most likely be either causal or acausal; I can't really imagine anything that's neither, given that the words are direct opposites.
In the case of a Stranger Thing that's strange enough that I can't imagine it, we could always fall back on the non-real complex numbers, which are neither rational nor irrational (and are numerous enough to make real numbers look trivial by comparison).
"Non-zero 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 "non-zero probability density." (It's mathematically impossible to assign non-zero 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 infinite-precision real numbers or because they can't solve the halting problem). More generally I'm worried that "coherently-thinkable" implies "not necessarily describable using math," and that would make me sad.
I think you can get around that by defining "describe" to mean "for some tolerance t greater than zero, simulate with accuracy within t". Since computable numbers are dense in the reals, for any t > 0 there will always be a Turing machine that can do the job.
The halting problem is insuperable, though. Universes with initial conditions or dynamics that depend on, e.g., Chaitin's constant are coherently thinkable but not computable.
I don't think your first point solves the problem. If the universe is exponentially sensitive to initial conditions, then even arbitrarily small inaccuracies in initial conditions make any simulation exponentially worse with time.
The function exp(x - K) grows exponentially in x, but is nevertheless really, really small for any x << K. Unbounded resources for computing means that the analogue of K may be made as large as necessary to satisfy any fixed tolerance t.
For a fixed amount of time. What if you wanted to simulate a universe that runs forever?
Yes, for a fixed amount of time. I should have made that explicit in my definition of "describe": for some tolerance t greater than zero, simulate results at time T with accuracy within t. Then for any t > 0 and any T there will always be a Turing machine that can do the job.
What about a universe with really mean laws of physics, like gravity that acts in reverse on particles whose masses aren't computable numbers?
How is that different than "within accuracy t, these particles have those computable masses, but gravity acts backwards on them"?
The intention of my example was that you couldn't tell for a given particle which direction gravity went.
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...
I think the problem of enumerating these possibilities is impossible. You should notice that even the conventional possibility, quantum field theory somehow modified to have gravity and cosmology, is incomplete. It describes a mathematical construct, but it doesn't describe how our experiences fit into that construct. It's possible that just by looking at this mathematical object in a different way, you can find a different universe. That's why this point-of-view information is actually important. Looking just at the possibilities where the universe is computable, enumerating Turing machines looks sufficient, but it is not. Turing machines don't describe where we should look for ourselves in them, which is the most important part of the business. If we allow this, we should also allow the universe to be described by finite binary strings, which at times code for a Turing machine where we can be found in a certain point of view, but at other times code for various more powerful modes of computation. We can even say there is only one possibility, the totality of mathematical objects being the universe, which we can find ourselves in in very many different ways (this is the Tegmark level 4 multiverse theory).
So we can't truly enumerate all the possibilities, even assuming a casual universe, since a casual diagram isn't really capable of fully describing a possibility. It might be reasonable at certain times to enumerate these things anyways, and deal with this degeneracy in a ad hoc way. In that case, there would be nothing wrong with also making an ad hoc assumption along the lines of saying that the universe must be Turing computable (in which case you can simply list Turing machines).
This seems an odd question to ask in the comments like this. I know how I'd go about figuring out the answer, but it involves doing lots and lots of really hard math. Coming up with an answer i thee 5 minutes that anyone is going to realistically spend on this seems almost disrespectful, and certainly not very productive.
Or I just misunderstood what you were asking.
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 value-identification 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 utility-maximizing policy/plan. This will involve crazy recursion and turning this whole thing inside-out, 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 half-assed 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.
Since I'm asking about a superintelligent AI's model of the world, and the world of an AI is digital input and output, I first enumerate all possible programs, then enumerate all input strings of finite length, then count diagonally over both.
Then I convert the bits into ASCII, compile them in LOLCODE (since I'm already doing this for the lulz), and throw out the ones that give me compiler errors or duplicates.
Then I sum over the countable number of computable things using inverse squares and divide by pi squared over six (minus whatever I've thrown out).
I hope you didn't want this information to be compiled in a way that is at all helpful to anyone, ever.
But if you did, I guess I might attempt to organize the information as the set of graphs on N vertices for all natural numbers N, or attempt to classify the set of categories of modules of objects with models in Grothendieck's second universe, so that I could do all possible linear algebra. And then I would say that if I can't use linear algebra the object I'm studying doesn't have local consistency and so it doesn't make sense to think about it as a continuous universe and I no longer no what thought means so I have more important issues to deal with.
Hrmm... Well, if the AI is computable, it can only ever arrive at computable hypotheses, so we can enumerate them with any complete program specification language. I feel like I want to say that anything that isn't computable, doesn't matter. What I mean is, if the AI encounters something that is truly outside of its computable hypothesis space, then there’s nothing it can do about it. For concreteness:
TL;DR for paragraph below: our FAI encounters an Orb, which seems to randomly display red or green, and which our FAI really really wants to model accurately.
However, try as it might, our poor computable AI cannot do even an epsilon better than random in predicting the Orb. This is because the Orb is not computable. My point is that this is not distinguishable from a problem that the AI just can’t solve given its current resources. If the prediction problem is really hard, but nevertheless the AI can gain useful information about how the aliens will behave... then either the AI is modelling the alien species, plus a Truly Random variable (in the classical statistics sense) for the Orb, or the AI can do better than random at predicting the Orb.
Therefore, if our AI ever encountered something Truly Random or otherwise Really Weird (that is, something that is coherent in whatever way it has to be in order to be real, but not computable), then the AI would not and could not do better than it would by just reacting as though it was a problem too hard to solve, and modelling it as a random variable. For things that seemed random or weird but that were actually computable, the AI would naturally (if we’ve done our job) become smart enough or think long enough to solve the problem, or at least work around it. For things that were really truly unpredictable by a computable hypothesis, the same thing would happen. It’s just a special case where the AI never gets around to solving it.
Declaring uncomputable things irrelevant hopefully isn’t too crippling in practice; the universe looks computable, Time Turners can maybe be brute-forced, etc. Now, that doesn’t really answer the question. What do we do about uncomputable universes? Again, nothing... except if there is a chance of hypercomputation. But even if an AI is trying to somehow harness a hypercomputation to do better than chance at dealing with an uncomputable facet of reality, it still has to do figure out how to do the harnessing using its current computable hypotheses and the rest of its computable self.
In other words, hypercomputation isn’t a special case. It’s still a part of reality that correlates in some way with another part of reality (right? I’m, like, totally out of my depth here, but as long as we’re speculating...). The AI can notice and use this, while still only working from computable hypotheses. It should do this naturally, even operating under computable hypotheses, if it sees some way of expanding its (hyper)computational abilities.
TL;DR: whether or not the universe is computable, the AI can’t do better than computable hypotheses. The differences between reality and the best hypotheses that the AI can muster will be unavoidable, since the AI is computable. It can harness hypercomputation, but it still does so working from its computable hypotheses. Unless we program an uncomputable AI. Are you trying to ask how the AI should write an uncomputable extension of itself if it encounters hypercomputation?
Mainstream status:
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?
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.
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.
Page number?
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.
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.
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 self-consistent solutions can be calculated may not be that surprising.
The Novikov self-consistency principle has already been invented; the question was whether there was precedent for "You can actually compute consistent histories for discrete universes." Discrete, not continuous.
Yes, hence, "In computational physics", a branch of physics which necessarily deals with discrete approximations of "true" continuous physics. It seems really quite similar, I can even give actual examples of (somewhat exotic) algorithms where information from the future state is used to calculate the future state, very analogous to your description of a time-travelling game of life.
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"
I was going to reply with something similar. Kevin Knuth in particular has an interesting paper deriving special relativity from causal sets: http://arxiv.org/abs/1005.4172
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)
Fixed.
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 human-like 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.
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's also interesting how few people seem to realize that Scott Aaronson's time loop logic is basically a form of branching timelines rather than HP's one consistent universe.
I know that the idea of "different systems of local consistency constraints on full spacetimes might or might not happen to yield forward-sampleable 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 Time-Turners; 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".
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.
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'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.
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.
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.
Short jumps (like the 1-hour 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 meta-time, 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)
As good as dead, until you jump back, right? As long as you jump back to a point after you originally jumped from.
That would imply that any changes you made in the past never had any effect on the time you had come from. Which is certainly logically consistent, but not the way most time travel stories work.
(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.)
Rowling is on record as stating that prophecies can be just-walked-away-from which makes their dynamics less clear and not obviously a self-consistency thing.
Oh, I didn't know that, thanks.
What does this even mean?
I think it means that prophecies may be merely "very good magically-derived estimations of the future" -- we are not sure they bind the past with the future as tightly as Time-Turners seem to do.
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.
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".
And it does it on a routine basis. After all, most of the critters are returned to the moment they were taken.
Why would the old timeline deserve to exist more than the new one?
Suppose I destroy the timeline, and create an identical one. Have I committed a moral evil? No, because nothing has been lost.
Suppose I destroy the timeline, and restart from an earlier point. Have I committed a moral evil? Very much yes. What was lost? To give only one person's example from Flight of the Navigator out of a planet of billions, out of a whole universe, the younger brother who was left behind had spent years - of personal growth, of creating value and memories - helping his parents with their quixotic search. And then bonding with the new younger "older" brother, rejoicing with his parents, marvelling at the space ship. And then he was erased.
I don't disagree that things are lost. But on the other hand, there are things that the new timeline has that the old timeline didn't as well. In the new timeline, the younger brother also has experiences that his counterpart in the old timeline did not.
By choosing not to destroy the timeline to create a new one, you deny the new-timeline younger brother his experiences, as well as everyone else in the new universe. Either way, something is lost. It seems that the only reason to treat the original universe as special is status-quo bias.
Suppose I have the opportunity to end literally all suffering in the universe, and choose not to.
Its okay. In the new timeline, the nurse went on to be a sex columnist.
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.
How about "Harry suspected Quirrel"?
That implies the existence of some X and Y in the sentence "Harry suspected Quirrel of X because Y", e.g., "Harry suspected Quirrel of secretly being some variety of uplifted rodent because Harry had suffered organic brain damage that impaired his ability to think rationally." As long as Harry is (being modeled as) subject to causal influences, such a sentence can't escape implying causes.
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".
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).
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 Anglo-centric perspective and consider ergative-absolutive oppositions...
BTW, I wonder whether (all other things being equal) speakers of ergative-absolutive languages tend to exhibit more consequentialist-like thinking and speakers of nominative-accusative more deontological-like thinking... Has anybody tested that?
That's a really interesting question. I've never heard of any research on it.
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 are---in 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".
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".
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 "almost-sane" 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 high-level intelligence anything like ours. But it's also true that out of the conceivable universes that do allow for evolvable high-level intelligence like ours, most are not perfectly deterministic. So although the existence of intelligence may be explicable anthropically, I'm not sure the non-existence of Time Turners (and other causality-breaking mechanisms) is. Perfect determinism and complete chaos are not the only two options.
Characters in the novel Pastwatch by Orson Scott Card wrestle with this issue.
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).
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?
This.
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?
it does add measure, but probably a tiny fraction of it's total measure, making it more of "making it slightly more real" then "creating" it. But that's semantics.
Edit: and it may very well be the case that other types of "looking at" also add measure, such as accessing a highly optimized/cryptographically obscuficated simulation through a straightforward analog interface.
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?
"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 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 "anti-zombie principle".
Edit: this is why I don't believe in the "anti-zombie principle".
Why? Seems like the simulated universe gets at least as much additional reality juice as the simulating universe has.
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.)
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.
Of course, there's no reason to strictly believe that what you thought was a future version of yourself wasn't either lying or a simulacrum of some kind, or that any note you receive after intending to send a note back to yourself hasn't been intercepted and subverted.
Which leads to interesting stories when those expectations are subverted, but only after they've been established.
Yes, that's a type 3 plot.
Such numbering isn't however very meaningful or intuitive... I'd just say "timeline-overwriting".
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 ?
It's not too hard to write Eliezer's 2^48 (possibly invalid) games of non-causal-Life to disk; but does that make any of them real? As real as the one in the article?
I am having trouble figuring out what the word "real" means when applied to the game of Life. I do know, however, that if my Life game client had a "load game" function, then it would accept any valid string of bits, regardless of where they came from -- a previously saved game, or a random number generator.
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.
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
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 sums-over-histories as mathematical abstractions only. From this perspective they don't describe processes that are actually happening out-there-in-the-world, 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 many-worlds.)
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.
Me too, but almost all of it would be concentrated at "sums over histories are inaccurate descriptions of what happens." Sums-over-histories 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."
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 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 otherwise-equal 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.
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 not-killing 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 time-travel, Universe A still existed once, and contrary to the preferences of the people there was then extinguished. The preferences of the people in not-yet-existent meta-future 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.
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 long-term 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 world-state, not just the desirability of the world-state. 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.
I probably would, but the choice is very different. I happen to know what did happen, including all the things that didn't happen. By changing that I am abandoning the gauruntee that something at least as good as the status quo occurs. Most critically, I risk things like delaying a nuclear war such that a war occurs a decade later with superior technology and so leads to an extinction outcome.
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.
I agree. That does seem to be a key point in the disagreement.
There doesn't seem to be an obvious way to compute the relevant utility function segments of the participants involved.
So is the argument that we should give up utilitarianism? (If so, what should replace it?) Or is there some argument someone has in mind for why annihilation has a special disutility of its own, even when it is a necessary precondition for a slight resultant increase in utility (accompanying a mass creation)?
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?
It depends. As for universes, so too for individual human beings: Is it moral (in a vacuum — we're assuming there aren't indirect harmful consequences) to kill a single individual, provided you replace him a second later with a near-perfect copy? That depends. Could you have made the clone without killing the original? If an individual's life is good, and you can create a copy of him that will also have a good life, without interfering with the original, then that act of copying may be ethically warranted, and killing either copy may be immoral.
Similarly, if you can make a copy of the whole universe without destroying the original, then, plausibly, it's just as wicked to destroy the old universe as it would be to destroy it without making a copy. You're subtracting the same amount of net utility. Of course, this is all assuming that the universe as a whole has positive value.
Regarding universes, there's a discussion of this in Orson Scott Card's Pastwatch novel, where future people debate traveling back in time to change the present, realizing that that means basically the elimination of every person presently exisiting.
Regarding individuals, I once wrote a short story about a scientist who placed his mind into the body of a clone of himself, via a destructive process (scanned his original brain synapse by synapse after slicing it up, recreated that in the clone via electro stimulation). He was tried for murder of the clone. I hadn't seen the connection between the two stories until now, though.
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 line next to a loop - spontaneous creation of two "virtual" particles, one reversed, followed by those two cancelling.
Would J.K. Rowling's book be causal if we add to the lore that Time Turners are well understood to cause (unasked) "virtual bearers" very like their bearers? The virtual bearers could be reified by the real bearer using the time turner, or if they are not reified, they will "cancel" themselves by using their own, virtual, time turner.
I think this addition changes the time turner from a global / acausal constraint on possible universes to a local / causal constraint, but I could very well be mistaken. Note that the reversed person is presumably invisible, but persuasive - perhaps they are a disjunctive geas of some sort.
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...
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.
Larry Niven once commented that, if past-changing time travel is possible, the most stable universes will be those in which time travel is never invented...
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.
Of course, if you also assigned a probability of zero to the event you just observed, now you have 0/0 error, which is more awkward to deal with. The case of having a posterior probability of zero in contradiction to the evidence is not particularly problematic for the agent's thinking, it just isn't very useful. But a true 0/0 event might well cause serious issues.
In practice, you conclude you hallucinated the event.
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 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.
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?
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.
Yeah. Basically, I'm trying to figure out how subjective probabilities would work consistently in the "parallel timelines" model, e.g. the probability of meeting a time traveler vs becoming that time traveler, when everyone's decisions can also be probabilistic. The question interests me because in some cases it seems to have a unique but non-obvious answer.
Last time I tried reasoning on this one I came up against an annoying divide-by-infinity problem.
Suppose you have a CD with infinite storage space - if this is not possible in your universe, use a normal CD with N bits of storage, it just makes the maths more complicated. Do the following:
If nothing arrives in your timeline from the future, write a 0 on the CD and send it back in time.
If a CD arrives from the future, read the number on it. Call this number X. Write X+1 on your own CD and send it back in time.
What is the probability distribution of the number on your CD? What is the probability that you didn't receive a CD from the future?
Once you've worked that one out, consider this similar algorithm:
If nothing arrives in your timeline from the future, write a 0 on the CD and send it back in time.
If a CD arrives from the future, read the number on it. Call this number X. Write X on your own CD and send it back in time.
What is the probability distribution of the number on your CD? What is the probability that you didn't receive a CD from the future?
The Novikov Self-Consistency Principle can help answer that. It is one of my favorite things. I don't think it was named in the post, but the concept was there.
The idea is that contradictions have probability zero. So the first scenario, the one with the paradox, doesn't happen. It's like the Outcome Pump if you hit the Emergency Regret Button. Instead of saying "do the following," it should say "attempt the following." If it is one self-consistent timeline, then you will fail. I don't know why you'll fail, probably just whatever reason is least unlikely, but the probability of success is zero. The probability distribution is virtually all at "you send the same number you received." (With other probability mass for "you misread" and "transcription error" and stuff).
If your experiment succeeds, then you are not dealing with a single, self-consistent universe. The Novikov principle has been falsified. The distribution of X depends on how many "previous" iterations there were, which depends on the likelihood that you do this sequence given that you receive such a CD. I think it would be a geometric distribution?
The second one is also interesting. Any number is self-consistent. So (back to Novikov) none of them are vetoed. If a CD arrives, the distribution is whatever distribution you would get if you were asked "Write a number." More likely, you don't receive a CD from the future. That's what happened today. And yesterday. And the day before. If you resolve to send the CD to yourself the previous day, then you will fail if self-consistency applies
Have you read HPMoR yet? I also highly recommend this short story.
These are pretty strong arguments, but maybe the idea can still be rescued by handwaving :-)
In the first scenario the answer could depend on your chance of randomly failing to resend the CD, due to tripping and breaking your leg or something. In the second scenario there doesn't seem to be enough information to pin down a unique answer, so it could depend on many small factors, like your chance of randomly deciding to send a CD even if you didn't receive anything.
Seconding A113's recommendation of "Be Here Now", that story along with the movie Primer was my main inspiration for the model.
Scott Aaronson's model, that Eliezer refers to here is basically this.
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 small-fanin criterion in other ways. For example, imagine a Conway's life-like game on an infinite plane, with a special tile type that copies a randomly-selected 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 fan-in, but there would still be a DAG representing the causal structure of that universe. It used to be believed that gravity behaved this way.
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.
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 "n-dimensionalist" about the "meta-time" concept in Eliezer's story, the future people who are lopped off the timeline still exist in the meta-timeless eternity of the "meta-timeline," 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 at-least-conceivable stuff that is disconnected from our local universe.
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 well-being 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.
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
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.
But none of those things is what he means by 'real.' Else it would be nonsense to ask, 'Can completely boring, completely unobservable things be real?'; the answer would be 'Trivially, they cannot be real.'
What we mean by 'real' is similar to what we mean by 'exists' and 'actual' and 'territory' (in the map-territory sense). You could argue that the existential quantifier is too general to be meaningful, that we should make it more anthropocentric, make it mean 'something we could observe' or 'something we could observe or imagine observing' or similar. But this would simply be a semantic non-starter. As a linguistic fact, that is not what we mean by 'reality' or 'existence.' We mean the most general category to which instantiated things can belong -- a highly disjunctive property, perhaps, but not on that account a meaningless one.
Whether the many-worlds 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 many-worlds 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.
I'm having trouble with this usage of the world "universe". Can't you call it "timeline" or "plane" or something?
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.)
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.
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; most literature students would not argue with this. At least, not too much)
As such, it's not a cycle of updating information that the universe has to remain consistant; the new universe continues on from 8pm as normal, but new information is added to the collective memories of anyone who interacts with the Time Traveller, as well as the Time Traveller themselves.
The only way this doesn't work is with Harry in MOR pulling a Bill and Ted with the Remembrall. Anyone with better maths want to tackle that one?
Ooops, shouldn't have posted before reading the whole thing. Still, my arguement stands; what defines the "goodness" or "badness" of universe being destroyed and immediately replaced with another identical to it in all the most miniscule ways (the memories of agents interacting with the time machine), or for that matter the "betterness" of the previous universe.
Technically, this means "time travel" is less accurate that "history re-writer", but to me, that doesn't sound any worse.
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.)
The question is simply whether annihilating the universe has higher expected value than letting it continue. To determine that, you can't just compare the expected suffering of our future survival against the zero-level suffering of our nonexistence. You also have to factor in the positive experiences that are attainable should we survive, but not if we die.
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.
(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 timetravel-capable 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 life-threatening 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.
"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 ;)
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 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.
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 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.