by Brian Tomasik
First written: 22 Sep. 2014; last update: 16 Mar. 2017


Special relativity suggests an eternalist picture of time: The universe is a four-dimensional block in which time is another dimension like space. The "arrow of time" is typically said to come from increasing entropy. This view seems to leave out the flowing nature of time, but I suspect that the block universe gives rise to a perception of flowing when viewed from within it. An eternalist view on time has several ethical implications based around the realization that past and future events/minds are as "real" as present ones.


The philosophy of time is a foundational field in (meta)physics. Like many other fundamental ontological topics, it may have deep ethical implications.

Eternalist block universe (with only 2 spatial dimensions). I release this image into the public domain.

Eternalism is the philosophy of time that seems to be required by special relativity. It's also more popular than its presentist alternative among philosophers: The PhilPapers Surveys report that 26.3% of philosophers accept B-theory (eternalism) vs. 15.5% who accept A-theory (presentism or growing block universe), though 58.2% don't accept either.

This essay scratches the surface in exploring eternalism, with a focus on ethics. I'm not an expert on this subject, and probably most of what I say here is unoriginal.


We can imagine a physical system as a series of snapshots, like pages in a flip book or images in a filmstrip. The relations between the snapshots are computed by update rules specified in physical equations, in much the same way video-game objects move according to update rules from one frame to the next. For example, the position p of an object in a video game might update at each time step Δt as

p <- p + v Δt

for some vector v specifying the object's constant velocity, and where "<-" refers to assignment. We can imagine that each game screenshot is printed out, and the collection of pages is made into a flip book.

Of course, there's not necessarily a literal computer calculating the updates of objects in our universe; it's just that the various configurations that exist are conceptually linked by these updates.

Arrow of time

Most of physics is time-symmetric. For instance, given an object's final position, we could run the update rule backwards:

p <- p - v Δt.

Likewise, we can run through a flip book backwards. This leads to the puzzle of why time seems to have a directionality. The standard answer is that entropy provides an "arrow of time" due to the second law of thermodynamics: "Future" can be roughly equated with "higher entropy".

This explains why we can remember the past but not the future. The process of remembering is a computation, typically an irreversible one. But irreversible computations increase entropy. So in order to remember event X, entropy needs to increase, which means that the state of remembering X must have higher entropy than the state when X happened. If "future" means "higher entropy", then remembering X must be in the future relative to when X happened. The same is true not just for episodic memory but also any other implicit forms of memory, such as inclining toward an action in response to a stimulus. (This account is a rough sketch and may require some technical patches. For instance, see "Why We Can't Remember the Future".)

Moments pointing forward

In the eternalist picture, we are just points in a time series -- beads along a temporal string. Each time slice implicitly points toward the next one, like squares on a board game connected by arrows. Our feeling of unity over time consists in these moments of pointing from one time to the next. Like with frames in a movie, different slices of reality feel related to one another because the actors in one slice are anticipating the next slices. Myself now has a feeling that it will become the next time slice's version of that self. But all of the time points actually exist, and which one we find ourselves to be is a matter of indexicality, not fundamental ontology.

In a Facebook comment, Mihnea Maftei explained the "moments pointing forward" view eloquently:

One may ask then what makes your stream of consciousness pass from one moment to the next, in regular fashion, rather than go from the present moment to any random time in the past or future. Well, what would it mean for your stream of consciousness to always leap to random moments? How would it feel? It would feel just the same (or, to put it another way, the question of leaping randomly is meaningless): you one second from now (that is, the "slice" of your self corresponding to what we call "one second from now") remembers your current self and is informationally continuous to it, your current self is in the same relation to your one-second-ago-self, etc. You can say, if you wish, that your consciousness does leap to a random future or past moment. But that slice of yourself (in the future or past) doesn't know or feel that that has happened. It feels its continuity with its what-it-calls-its-past. It's like asking how it would feel if you suddenly switched consciousnesses with one of your friends. You would not notice (because you would switch memories and absolutely everything). Therefore it's meaningless to assert that any switch has happened. (That's why I don't understand what people mean by reincarnation: what's the difference between a person being the reincarnation of another one and that first person not being the reincarnation of the second one?)

The "hard problem of time"

It's sometimes claimed that consciousness may be the only "hard problem" for reductionism. David Chalmers suggests ("What are the Problems of Physicalism?") that other puzzles of physicalism may be explicable once we explain consciousness. However, I think the metaphysics of time provides a counterexample to this claim. A few authors talk about a "hard problem of time" in parallel with the "hard problem of consciousness": Why do eternal, static slices in a flip book give rise to the seemingly dynamic flow of time? Wikipedia's article quotes John Lucas opining that "The Block universe gives a deeply inadequate view of time. It fails to account for the passage of time [...]."

In analogy with zombie arguments in the realm of consciousness, I can ideally conceive of a world in which time slices exist, with mathematical relations among them, and yet in which there's no "flow" to the universe. We might call this a "temporal zombie". It might look like a world of snapshots: People and things frozen in motion, without moving from one frame to the next.

Personally, I think such reasoning is mistaken. The universe just works in certain ways, and we're thinking of it wrong when we imagine moments without flow. That would be like, as Daniel Dennett says, "supposing that by an act of stipulative imagination, you can remove health while leaving all bodily functions and powers intact." If we can't understand why, that's our problem, not the universe's. I've seen enough examples of weird reductions like this that I don't find reducing consciousness to functional operations particularly troubling -- at least not uniquely troubling relative to many other puzzles of metaphysics. On the other hand, an anti-reductionist could reach the opposite conclusion: If the essences of both consciousness and time aren't reducible, then reductionism is in trouble.

As we should ask with consciousness, we can inquire how it is, if time is a real flowing property above causal relationships, that we come to learn about the flowing of time. A series of static snapshots should contain beings who believe time is a flowing property just as much as if time really were a flowing property -- in a similar way as phenomenal zombies believe they have phenomenal experiences even though they don't. So Occam's razor removes the need for an actual flowing property. In response to this, a defender of the hard problem of time insists that "I just know time flows", in a similar way as defenders of the hard problem of consciousness insist "I just know I have a what-it's-like-ness property to my experiences."

If we built a video game with highly intelligent, human-like characters, they too would puzzle over why time seems to flow. Yet we can see that they are merely composed of discrete transitions from one state to the next. For instance, if we paused the game for ten years and then resumed it, the players wouldn't know the difference. The state transitions that would represent the characters puzzling over their hard problem of time are logical implications of the mathematical structure of the game's source code, with no reference to some extra flowing property of the universe. I find this argument pretty convincing, along with its parallel argument in the realm of consciousness (namely, that human-like video game characters would puzzle over why they were conscious, even though we could see they were nothing more than a sequence of state transitions). After all, if time's flowing or consciousness's phenomenal texture was something extra, how would that something extra influence the logical state transitions of the characters?

Perhaps Chalmers would claim that consciousness can solve the problem of time because our perception of time's flow is a conscious event. Maybe so. But it seems like our understanding of time's ontology might itself be important for explaining consciousness. Most theories of consciousness postulate things happening over time to produce/constitute consciousness. So it seems that time's ontology might be a more fundamental issue that needs to be explained before we even introduce consciousness, unless someone develops an atemporal theory of consciousness.

One objection to the video-game argument against the hard problem of time could be that the universe running the video game still has a flow of time. It's true that the game can be paused or sped up, but it still moves forward, and maybe the flow of time in the game is inherited from the flow of time in the real world that runs the game? Maybe. But consider that we could theoretically, if the physics of the game was fully reversible, run the game backwards. Suppose that in the forward version of the game, Princess Zelda is kidnapped, and then the hero Link, remembering this, goes off to save her. In the backwards version of the game, Link first remembers Zelda's kidnapping (as judged by neural connections or state-variable settings in his brain) before she's actually kidnapped. If the game's flow of time inherits from our universe's flow of time, then time in the game should flow backwards (Link remembers events before they happen), yet the characters still think time flows forwards. This introduces the possibility of a disconnect between the actual flow of time and in what direction an agent's physical brain thinks the flow of time is going, which seems problematic. In an analogous way, if consciousness is epiphenomenal, then you might actually be in a conscious state of pain even though your physical brain thinks you're in a conscious state of pleasure. The right answer in the face of each of these puzzles is to drop the epiphenomenal entity altogether.

Causation in video games

Historically some philosophers have been puzzled by the question of how mathematical facts can be physical explanations:

For instance, an important debate in the Renaissance, known as the Quaestio de Certitudine Mathematicarum, focused in large part on whether mathematics could play the explanatory role assigned to it by Aristotle. Some argued that lacking causality, mathematics could not be the ‘explanatory’ link in the explanation of natural phenomena [...].

By picturing the universe as a video game, we can clarify this point. The source code of a video game embodies a mathematical structure that defines how the components of the game move and update. Physical behavior in games doesn't require one thing to bump into another (a brute "physical" explanation) but only that the physical updates obey the mathematical regularities specified in the source code (a mathematical explanation). Movement of objects in a video game has a sort of causal structure in the sense that when, say, Mario hits his head on a question-mark block, this causes the block's contents (a coin, mushroom, flower, etc.) to come out of the block. But this causation lies implicit in the way the source code's update rules generate successive world snapshots, not from an ontologically distinct property of "causal power" underlying Mario's block-hitting action.

The universe as a whole appears to behave much like a (huge) video game, the only difference being that the complete universal game apparently can't be run in some higher realm of physics, because that too should count as part of the physical universe. Rather, at bottom, our universe's behavior appears to just exist with certain regularities, without being explicitly generated as physical computations within a larger structure. However, physical dynamics show regularities as if they had been so generated; this relates to the observation that the universe can be modeled (Einstein: "the eternal mystery of the world is its comprehensibility"). Indeed, if this weren't the case, complex intelligence could not have evolved, since predictive brain mechanisms would have been futile.

In general, almost all philosophical confusions can be alleviated by picturing ourselves as video-game characters in an elaborately detailed virtual world. The only inscrutable mysteries left open are why this game exists and what it could even possibly be, at its ontological core.

Indexicality and philosophy of time

Blaise Pascal said, I "am astonished at being here rather than there; for there is no reason why here rather than there, why now rather than then." Let's consider some possible answers to this puzzle.

1. Only here and now exists?

Presentism aims to answer the question of why I'm now rather than then by suggesting that only "now" exists, and the past and future don't. But there's an analogous question with respect to space: Why is "here" here rather than there? Benj Hellie calls this the vertiginous question: Why are my experiences in particular the ones that are "live"? If we accept the intuitive argument for presentism, it seems we should also accept an intuitive argument for a kind of solipsism -- that only our experience-moment is currently "live". Personally, I take this as a reductio against the intuition for presentism.

Hellie himself considers the vertiginous question more unsettling than the question of why now is now. In "Against egalitarianism", he claims that he can dissolve the puzzle about time by imagining his life as "a long string of points of view". His "total stream of consciousness is available as a higher legislator, in a position to conclusively rule this 'disagreement' [among different temporal perspectives] purely indexical". In contrast, he says, the same will not work between different minds.

This strikes me as nonsense. There's no fundamental distinction between myself at different times and different people. My past self is someone other than my present self, just like you are someone other than my present self. The degree of difference is larger in the latter case, and I happen not to have memories of you, but otherwise the relation is the same. If memories of your childhood were implanted into Hellie's brain, would Hellie then say he could understand what it had been like to be you in the past?

2. Reality is serially computed?

We might think that another answer to why "here and now" are here and now could be that reality is run on a serial computer, which calculates updates at each location of space one after another, one slice of time after another. For instance, the game of life running single-threaded on a laptop computes one cell update at a time.

But this answer appears unhelpful, because even if reality were instead computed in parallel, our physical beliefs would presumably look exactly the same. In general, an account of indexicality should explain why the truth of that account makes us feel intuitively that it's true. For instance, do our evolved or culturally developed intuitions about "here and now being privileged" track the metaphysical truth of the matter for some reason?

3. All here-and-now's are equally real?

I think this explanation is the right one.

Picture a room with different objects in different locations. Our thoughts about ourselves and about this question are physical processes occurring in some specific location, like objects in the room. Of course some objects have to be in some places while others are in other places. And we can explain why some objects are here and others there: The laws of physics evolved so as to yield that particular configuration of matter and energy.

It feels like there's a further question: Why am I this object instead of that one? But there is no additional meaning to what "I" am beyond being that particular set of physical processing. You are not a disembodied soul that could occupy different organisms without changing the identity of your soul. The exact physical processes that constitute "me" are those that are occurring here, just like an object must be where it is. Of course, it does make sense to ask why, say, a chair is in the corner of the room rather than the center, and such questions can have answers (e.g., the owner of the chair would trip over it if he had put it in the center). But beyond these physical facts about object location, there's no further question that needs to be answered. It only seems like there is if we picture ourselves as more than clumps of matter.

So what's the answer to Hellie's vertiginous question? It's that all experiences are "live" to whatever mind is having them -- whether in the past, present, or future, and whether nearby or far away. Since experiences are just chunks of physics, this is no more mysterious than the fact that all chunks of physics exist. I agree the question can indeed feel vertiginous if imagined in a certain way, but this is because of an egocentric perspective in which we feel that our own experiences are somehow special, which leads us to wonder why nature has privileged our experiences over everyone else's. The answer is simply that we're not special. All experiences exist, and we just happen to be whichever one we happen to be.

The moral status of flip books

Suppose someone took a highly detailed film recording of a person at a rate of quadrillions of frames per second and then stacked these frames one by one next to each other. Would the resulting collection contain a conscious playing-out of the person? (Thanks to Mihnea Maftei for originally coming up with this thought experiment.)

Note that a temporal reductionist is not committed to saying "yes", because (A) compiling spatially contiguous frames within a small subset of a temporal slice of physics is not ontologically the same thing as (B) compiling full snapshots of the universe as a whole across time slices. Note that in case (B), the snapshots don't "exist within" anything because there can't be anything outside the universe. That would be like having a positive real number outside the range [0, infinity).

That said, I do wonder whether I would consider a highly elaborate flip book to have a nonzero degree of moral importance. After all, the successive snapshots that it contains would be best described by the same kinds of physical update rules as the successive moments of real physics are, which suggests that the same sort of causal relationships exist between the snapshots as exist between real physical moments.

Actually, this isn't necessarily true for two-dimensional (2D) snapshots, because they lose a lot of detail by projecting three dimensions down to a flat sheet of paper. As I discussed in "Appearance vs. implementation", mere 2D images don't always tell us about the underlying algorithms. An actor in a movie might feign suffering, and the resulting film strip could be atom-for-atom identical with a film of a real person actually suffering. To capture the algorithms within brains, it seems we'd need three-dimensional (3D) snapshots -- i.e., blocks of physics that contain replicas of the neural/atomic structures of the person at each time slice. Needless to say, it would be extremely difficult to produce such slices, even to a low degree of resolution. Scanning 3D brains across time is a long-term goal of connectomics, but it appears many decades away.

If we do grant some moral concern to static 3D flip books, we can ask how this concern changes as we vary certain parameters. For instance, how much does it matter that the 3D blocks are spatially adjacent? How much does it matter if they have a resolution of 1000 frames per second vs. 100? How does the (dis)value vary with the coarseness of the approximation to the real physics being represented? If we copy the data in the 3D blocks using another method than the running algorithm that originally produced them, does this copying process matter? And so on.

In any case, this issue may not be highly relevant in practice because I don't expect the future to be filled with massive numbers of 3D flip books in the way I do expect it to be filled with massive numbers of digital agents running through time. Rather, this topic is more important as a thought experiment to test our intuitions and conceptions of the eternalist view of the universe.

And there may be some practical applications. For instance, if rapidly successive brain dumps are stored to allow for backups, do they matter morally by just existing in the database? Do they matter more if their physical addresses or locations on disk are contiguous? Or if they're stored for a longer time? In general, there's a space-time tradeoff in computer science, in which more storage allows for less recomputation. If future civilizations must run some morally unpleasant computations for the greater good (e.g., digital lab rats), it would be helpful to have a handle on how the moral disvalue of recomputing compares with storing existing computations. My sense is that if only one or two brain states are stored, this doesn't matter very much, and reusing them is much better than recomputing them. On the other hand, if a lot of successive brain states are stored for a long time, the tradeoff becomes less obvious. (I still would probably go with storage over recomputation, but my intuitions on this could change.)

Other ethical implications

It's tempting to see philosophy of time as a playful distraction from serious work. Asking about time seems like the kind of thing that college students stereotypically do in dorms at 3:00 am. But like many other areas of metaphysics, time's ontology matters for ethics. Following are a few examples.

Importance of the far future

Some people have the intuition that currently nonexistent beings matter less than currently existing beings. In some axiologies, nonexistent beings may not matter at all. But in an eternalist picture, all beings that will ever exist do exist, just in a different part of spacetime. Luke Muehlhauser suggests this line of argument. Of course, one could modify one's ethical theory to place greater weight on beings at this indexical temporal location, but I feel like eternalism makes such a weighting scheme less morally plausible than presentism.

That said, Daniel Carrier noted an important rejoinder: "Considering that any action we take will only affect the future, any [consequentialist] system of ethics that does not involve the future is worthless." This doesn't rule out A-theories of time from taking on ethical commitments, but we at least need an account of what "making the future better" means in these frameworks. If presentists do care about the near-term future, presumably they should also care about the far future.

Still, I think the eternalist picture does have some impact as an intuition pump, perhaps because it draws a close analogy between time and space. It seems wrong to most (but not all) philosophers to discount the welfare of more spatially distant organisms, and eternalism makes more palpable the parallel with temporally distant organisms.

Eternal existence of good deeds

One reason so many people hope for eternal life is that they feel as if merely temporary things don't count. "If everything I do will just be undone later, why does it matter?" The book of Ecclesiastes is an exquisite expression of this sentiment:

"Utterly meaningless! Everything is meaningless." What does man gain from all his labor at which he toils under the sun? Generations come and generations go, but the earth remains forever. [...]

man has no advantage over the animal. Everything is meaningless. All go to the same place; all come from dust, and to dust all return.

In reply, Aesop says "No act of kindness, no matter how small, is ever wasted." Peter Singer echoes the sentiment in How Are We To Live?:

We should not, however, think of our efforts as wasted unless they endure forever, or even for a very long time. We can make the world a better place by causing there to be less pointless suffering in one particular place, at one particular time, than there would otherwise have been. As long as we do not thereby increase suffering at some other place or time, or cause any other comparable loss of value, we will have had a positive effect on the universe.

Eternalism accentuates this anti-meaninglessness argument by pointing out that every act of kindness, no matter how small, exists "forever" in our block universe (where "forever" refers to timeless existence, in the way that God is often thought to exist outside of time). The points of spacetime where a kind act occurred don't go away. Of course, very long world lines of kindness matter more than short ones, but even the short ones eternally matter to some degree.

Eternalism thus implies a sort of immortality. It's not the immortality of an infinitely long subjective world line but the timeless existence of a finite world line. If we think of "the universe" as "God", then this picture is strikingly similar to that of Charles Hartshorne, who held "that people do not experience subjective (or personal) immortality, but they do have objective immortality because their experiences live on forever in God, who contains all that was."

Eternal existence of pain

Occasionally I hear people claim that pain before death doesn't really matter because soon the organism won't be around to feel bad about it. For example:

Why does it really matter that their death is painful? Death is not pleasant either way and once they're dead, whatever they went through no longer matters, as it can only truly matter to them and they are not.

It's clear enough to most of us that this reasoning is wrong. We would not regard it as morally neutral if we knew our death within the next 24 hours would be agonizing rather than peaceful. But eternalism helps clarify why the badness of pain doesn't "disappear" from moral radar once an organism is dead.

Impossibility of eliminating suffering

Past suffering, such as Stegosaurus being eaten alive by Allosaurus, exists eternally. Even if we could eliminate all suffering on Earth going forward (which itself seems nigh impossible), we couldn't eliminate suffering in the past.

My main lesson from this is that we should avoid perfectionism in reducing suffering. We shouldn't seek a Hail Mary way to abolish all suffering, since often the perfect is the enemy of the good. Instead we should recognize that some suffering is inevitable, and we should focus on reducing suffering by the biggest amount we can.

Past and future preferences

Preference utilitarians typically aggregate the preferences of present agents. For instance, a social welfare function is defined over the individuals within a society. But given eternalism, granting special status to present preferences seems less justified. Why not also count the preferences of cave men and pterosaurs, as well as those of post-humans? Unless we adopt an A-theory of time, it's not clear what agents we should consider as simultaneous.

Eternalism + accelerating universe = actual infinity

One troubling implication of eternalism is that it seems to require us to believe in actual infinities, which is a metaphysical leap that not everyone is willing to take. It appears that the universe will expand forever rather than collapsing back in on itself. This implies that the temporal dimension of the universe must be infinite at least into the future. If all of time exists as a fixed mathematical object, then this object must be absolutely infinite in at least one direction.

That said, because the universe also seems to be spatially infinite, even a presentist arguably needs to admit of actual infinities, so maybe eternalism's commitment to them is less drastic. And of course, it's also possible that the universe will actually end after some finite time not predicted by current equations of physics, which would also deflate the issue.

What is the ontological primitive?

I've compared time slices with pages in a flip book. Presumably this conception takes the pages (moments) as real and the relations between them as conceptual. But could it be the other way around? What if the relations were real and the snapshots were conceptual? Instead of board-game squares connected by implicit arrows, we'd have arrows connecting implicit board-game squares.

Eliezer Yudkowsky says:

I would sooner associate experience with the arrows than the nodes, if I had to pick one or the other! I would sooner associate consciousness with the change in a brain than with the brain itself, if I had to pick one or the other.

I agree. This doesn't imply that the arrows rather than the nodes must be the ontological primitive, since I think consciousness can be a relation without being made of explicit primitives. But I don't see an obvious reason why an arrow-based conception couldn't work either. Maybe this is naive, and if I understood physics better the ontology would look more clear.

Fortunately, exactly what counts as the primitive doesn't seem to affect the broad thrust of eternalism. All of the previous ethical implications would remain unchanged, although maybe 3D flip books would seem less morally important if time slices aren't ontologically primitive, since this would weaken the analogy between the flip book and real physical time.

Is time fundamental or emergent?

In "A Universe from Nothing?", Sean Carroll reviews two possibilities:

  1. the universe actually evolves in time
  2. time emerges from relations in a fixed block universe.

#2 seems more aligned with eternalism, though maybe #1 could fit into that framework too. I don't know enough about this and should learn more.

Time travel

There's much debate about whether and in what senses time travel is logically, physically, and practically possible. Conventionally, presentists deny the possibility of time travel because the past and future don't exist. Eternalism seems more tolerant of time travel. However, some modern presentists also consider time travel to be coherent.

Causal loops are situations in which an event A causes B, which causes C, which causes D, ..., which causes A again. Even though the whole sequence seems to have no external cause, an uncaused object may not be physically impossible, judging from the fact that the big bang (or maybe the multiverse out of which the big bang arose) was uncaused. Closed timelike curves, if they exist, might be self-caused loops. If we take Yudkowsky's view on causality based on Judea Pearl, in which causation refers to certain asymmetric relationships among structures, it seems quite sensible to imagine a closed causal loop, for the same reason we can imagine closed loops of other kinds within physics. (Or does a loop prevent Pearl's definition from working? I haven't thought enough about this.)

Consider a loop in which A causes B, which causes C, which causes A. As Wikipedia explains, "A temporal causality loop [...] implies that the same events can be repeated identically and eternally [...]." Suppose, implausibly, that a person were in that loop. Would we then say the person "lived forever" because she was constantly repeating herself? Would her experiences have infinite (dis)value? Without being an expert on the underlying physics, my guess is that we should treat this situation the same as a non-circular world line of the same length. After all, eternalism tells us that non-looping world lines also have a kind of immortality. Viewed from the outside, two world lines of the same length containing similar experiences seemingly should count the same amount?

In practice, I don't expect anyone to carry out macroscopic time travel, other than trivial time travel into the future, including by differential amounts as in the twin paradox. The scenarios for time travel to the past seem to require physically implausible set-ups. That said, time travel by macroscopic agents is not yet 100% certain to be impossible, and even if it is, thought experiments about it can nonetheless be instructive.

Time travel of the kind seen in fiction is quite feasible in virtual worlds. Take the grandfather paradox. Start the virtual world off with a young man who will later become a grandfather. Save the state of the system S to disk while he's young. Keep running the world forward until the grandfather has a grandson. That grandson finds a time machine. As the grandson presses the button to go back, save the state of the grandson's mind and body, load up the state S, and stitch the grandson's mind and body into the virtual world of S. Now run forward. In this new situation, it's perfectly coherent for the grandson to kill his grandfather and still exist. This "virtual world" version of time travel is a way to excuse soft science fiction like Terminator that otherwise seems self-contradictory. (Indeed, virtual worlds can realize almost any fiction story. In a certain sense, books and movies already are coarse-grained virtual worlds, and futuristic digital manifestations of them are just more precise and detailed.)

See also "Analyzing Time Lapse from the Perspective of Fixed-Point-Finding Algorithms".

Caring about past suffering

Is there any practical reason to care about suffering in the past? Sure, eternalism may make it look like past suffering is timelessly important, but does this change our actions at all? If we were designing an artificial general intelligence, would we have any reason to include the badness of past suffering in its utility function? The answer is "yes" for at least two reasons.

  1. Speculative possibilities: Future intelligences may discover weird methods of reducing past suffering, and if so, we would want them to act on these discoveries. One example would be if time travel works, though my guess is that even if time travel is possible, it would only allow trivial changes to the past. But perhaps there are other ways to influence the past that we haven't yet discovered.
  2. Non-causal decision theories: Decision theories that one-box on Newcomb's paradox allow for the possibility of (non-causally) influencing the past without time travel. Consider the following variant of Newcomb's problem. The setup is the same as in the regular Newcomb problem, except that in this case, if you choose just one box, the Predictor will have anticipated this and will have prevented 1,000,000 units of suffering already in the past (in a manner not yet visible to you, just like the $1 million in the regular Newcomb box isn't yet visible to the chooser), while if you choose both boxes, the Predictor will prevent 1,000 units of suffering in the future. If you didn't care about past suffering, you'd choose both boxes. But you can (non-causally) "prevent" 1000 times more suffering by taking only one box. This example may seem contrived, but there are probably real-world applications where non-causal decision theories allow for "preventing" past suffering.

If we think of "You" as "the collection of copies of your cognitive algorithms and (less so) near copies of those algorithms", then the modified Newcomb example seems less mysterious. "You" are both (A) the copy of your body that makes a choice in the ordinary physical world of the Predictor and (B) the model of your brain that the Predictor used to simulate what you would choose. Both (A) and (B) produce functionally the same outputs upon getting the same inputs. The Predictor's decision about whether to reduce 1,000,000 units of suffering is in the future light cone relative to (B), just not relative to (A). Since "You" are both (A) and (B), the Predictor's action was in "Your" future light cone even if it wasn't in (A)'s future light cone.

Relativity of simultaneity and consciousness

Magnus Vinding raises an interesting question of whether and how our thinking about consciousness should change in light of the fact that different spacelike separated events, such as distributed computations in a brain, can be interpreted as happening in different orders depending on one's reference frame. For example, we could imagine a distributed conscious mind, in which some computations are done in New York and others in Tokyo, and the results of those computations are periodically shared with each other city over the Internet. Computations that are simultaneous relative to the Earth's reference frame would not be simultaneous relative to the reference frame of someone flying from New York to Tokyo.

To me, this observation suggests a possible principle that we could try to maintain when attributing consciousness: The moral value of a mind should be (as far as possible) independent of the reference frame from which it's viewed. One example of where this principle might matter is the following scenario. Suppose you maintain that a mind only actually suffers if it experiences more pain computations than pleasure computations at a single instant; otherwise, the pleasure "swamps" the pain, and so there's not actually suffering going on. Suppose that the Tokyo and New York computers compute neutral hedonic experiences at all times except for 1 millisecond at 00:00:00 UTC time, when the New York computers generate -4 hedonic units (suffering) and the Tokyo computers generate +5 hedonic units (happiness). If you maintain that pleasure swamps pain, then the net balance is 5 - 4 = 1 > 0, so there's no suffering here. But someone flying from New York to Tokyo would see the suffering computation happen at a different time than the happiness computation.

My rough, unreflective intuition is that most attributions of moral value to minds won't depend heavily on one's reference frame, because what matters most is the functional/causal behavior of the system, which is independent of reference frame. The inputs, processing steps, and outputs of a computation don't change based on reference frame, and it doesn't seem especially important to me when different computations happen. As an analogy, suppose we're simulating a human brain on a computer. The brain performs many distributed computations in parallel, but imagine that the computer has only a single core and computes everything serially. It doesn't seem to me to make much moral difference in what order the computer calculates different parts of the simulation. A high-level temporal ordering from start to finish will be preserved because, for example, when the output A of one brain area combines together with the output B of another brain area, you need to have already computed A and B. Computing a result, call it C, based on A and B means that C is causally dependent on A and B and hence comes after A and B in all reference frames. (C is timelike or at most lightlike separated from A and B.)

'Trick Slattery offers another observation: Different parts of a distributed brain can move independently from one another. For example, part of the brain could be on a fast-moving train, while another part is stationary on the Earth. This raises the question of whether time dilation has moral relevance. My sense is that, as with relativity of simultaneity, time dilation should generally not affect our moral valuations because it's relative to reference frame. Moreover, functionalists who consider consciousness to consist in various computational processes needn't pay attention to wall-clock time; they just focus on how much progress the system has made on its computational task. This is similar to the idea that the moral importance of a mind is determined by its "subjective speed" rather than how long the computation runs in wall-clock time. If computation A is identical to computation B but computation A is run twice as fast on a faster computer, the moral value of A and B remains the same (or at least approximately the same) because A "perceives itself" to be running as fast as B does (although the external world runs slower for A than for B).