This is a pseudo-problem arising from equivocation about the indexical "I". You can either use it to refer to yourself as a continuant (an entire space-time worm) or as a momentary object (a temporal part of the space-time worm). Just make sure you're not mixing the two uses. I think that is what is causing your puzzlement. To dissolve it, let's focus on the momentary object use of "I".
Don't think of your consciousness as somehow moving from step 1 to 2 to 3 and so on. I think it might be better to start out thinking that there are separate objects, separate XiXiDus, at each of these steps. Each one of those momentary-XiXiDu's is fully conscious. When any one of them says "I", they are referring to themselves, so "I" in the mouth of each momentary-XiXiDu refers to a different object. Also, when they say "now" they are referring to different times. Thought of that way, there is no mystery when each momentary XiXiDu says "I am here now." Where else would he (she?) be?
The problem arises because the psychological states of all the momentary-XiXiDu's are related in a way that makes each one think that he is the only one and that he has been moving through time. So the momentary-XiXiDu at step 3 thinks "I was at 1 and I will be at 7, but I'm now at 3. Why?" Really what's going on is that XiXiDu-3's "now" is step 3, just as XiXiDu-1's "now" is step 1. In some sense XiXiDu-3 is right to say he "was" at step 1, if this is interpreted as him bearing a certain relationship to XiXiDu-1. The mistake is that XiXiDu-3 thinks he is identical to XiXidu-1, and so since he is at step 3, XiXiDu-1 can't be at step 1. After all, how can a single momentary object be at both step-3 and step-1? Well, it can't, but this is not a problem, since XiXiDu-3 is not in fact identical to XiXiDu-1.
momentary object
Over short enough time, each bit of me is out of communication with each other bit of me. In light of this, is it still reasonable to think of a momentary consciousness?
I do find myself at 10, and N, and N+1.
That is, I exist in each timeslice, and in each one I have an experience that encompasses that timeslice and no others. (Including the data structures existing in that timeslice that record events in other timeslices.)
Is that not your experience as well?
The only way I can make sense of the question is to rephrase it as something like "Why do I only experience one timeslice at a time? Why don't I experience both N+1 and N simultaneously?" But I'm not sure if that's what you're asking.
If I had to take a guess, I'd say the question is related to "Why do I find myself in my body? Why am I not someone else, say, my neighbor? Why do I have this consciousness and not a random other one?" I'd also say that we're basically talking about how an algorithm feels like from inside.
I'm not at all certain about this, though.
In the computer game The Sims, simulated people (sims) navigate an environment, interacting with other sims. Even if they aren't being directly controlled by a user, sims will do some minimal amount of movement, performing simple actions. They are autonomous simulated agents of a very simple sort.
Suppose that we are watching (but not controlling) a particular sim. If another sim approaches this sim and, say, gets in a fight with it, it will remember this fight, in the sense that its behavior will be influenced by this experience.
So, at any point in time, this sim has some memory of what has happened to it recently. It knows whether a nearby sim has just appeared, and is about to start an interaction, or whether instead this nearby sim just concluded an interaction. In the first case, our sim finds no trace of a recent interaction in itself, while, in the second case, our sim finds itself angry or depressed by a recent fight.
Call the pre-interaction version of our sim "A", and call the post-interaction version "B". Is there any mystery about the fact that A finds itself to be pre-interaction, while B finds itself to be post-interaction?
In Good and Real, Gary Drescher uses the example of a simulated space in which there are large fast-moving balls and small slow-moving balls. Locally, the physics of collision are time-symmetric; if you observe a movie of a collision between just two balls, you cannot tell if the movie is being played forwards or backwards in time.
However, when you look at a movie of the whole simulation, you can easily identify the direction of time's arrow. How? By noticing that the large balls leave wakes behind them: paths that are cleared of small balls by the passage of a large ball. If you run the movie forwards, the large ball pushes small balls out of the way and leaves a wake; if you run the movie backwards, empty paths clear out in anticipation of a large ball coming through, and small balls fill in behind it.
In other words, even though a single collision is time-symmetric, the development of the whole simulation is asymmetric, because the distribution of small balls at any moment is correlated with where the large balls have been but uncorrelated with where they are going next.
Locally, the physics of collision are time-symmetric; if you observe a movie of a collision between just two balls, you cannot tell if the movie is being played forwards or backwards in time.
However, when you look at a movie of the whole simulation, you can easily identify the direction of time's arrow.
I haven't read Drescher's book, but this sounds like the usual Boltzmann-style attempt to explain the arrow of time by starting in a low-entropy state. When you start with many small balls, all moving at similar (because small) velocities, you are in a low entropy state. As the clock advances, you wander from this highly atypical low-entropy region of configuration space into more typical high-entropy regions. This is what gives you all sorts of time-arrows, such as the tracks left by the big balls.
The problem with using this as a global arrow of time is that, if you run the simulation backwards from the initial low-entropy state, you will again almost surely wander into a high-entropy state. From the point in time when entropy is minimized, both directions in time will look like futures (almost surely).
Imagine that you start with a big 2D box. Assume that all collisions are elastic. In the initial configuration, the box is evenly filled with a bunch of nearly-stationary little balls, and one big ball with large initial velocity. As you run the simulation forwards, you'll see the big ball clear out a path behind itself as it moves through the little balls, just as you said.
But now run the simulation backwards from that same initial configuration. You'll see exactly the same time-arrow-indicating phenomena as the simulation runs backwards. Only now, the time-arrows will be pointing into the past (towards which the simulation is running).
After running the simulation backwards for a while, stop, and rerun the simulation forwards from that time in the past. It will seem uncanny as the balls arrange themselves just so, but something strange had to happen for the balls to end up in the wildly improbable initial configuration with which we began.
Drescher actually deals with this — from an initial configuration, positive or negative movement both work as time arrows; time can be measured as distance in accumulated correlation from that initial state in any particular direction. At zero, moving along the positive or negative direction is equally "forward in time"; but at +42, it isn't.
Oh, okay. Then Drescher has it right:
Viewed from a very local level (encompassing just a single collision), there's no arrow of time, because entropy doesn't change significantly.
Taking a middle-level view (encompassing more balls for a greater span of time), there's a unique time arrow as you pass from the low-entropy initial configuration to a higher one.
But taking a global view, encompassing all balls for all time, you lose the unique arrow of time again, because you are just as likely to leave low-entropy states as time runs "backwards" as you are when time runs "forwards".
In other words, even though a single collision is time-symmetric, the development of the whole simulation is asymmetric, because the distribution of small balls at any moment is correlated with where the large balls have been but uncorrelated with where they are going next.
It would be fascinating to observe an instance of this universe that was symmetric. It is certainly possible. With the right starting conditions you could have a universe that runs forward but looks like it is being played backward. With another set of starting conditions a universe could be found that looks just as plausible running forward as backwards.
I have another question. For timeless physics to be true does that mean Einstein was wrong? Like, does timeless physics contradict the idea of time as a fourth dimension, space-time, etc.
This isn't really a question of timeless physics. It applies in classical physics too, or in any other possible universe with more than one mind.
There is no reason why you fond yourself now instead of somewhen else. That is, it's just as likely to find yourself now as an anytime else.
I think you're reasoning from the idea that there is a source of I-ness which is somehow separate from your physical self. Why, you seem to be asking, is this I-ness attached to this particular body at this particular time?
Firstly, there is no direct evidence that there is such an I-ness. Secondly, if there are other selves at other places and times, there's no reason to suppose that they don't have a similar experience to the one you have here and now.
For every one of those causal steps, you will find a person surprised that they are at that particular causal step. So this surprise is not information about the world - it's a diagnostic sort of surprise that comes from a contradiction in your definitions. As pragmatist says, said contradiction is probably between the 'I's in "I am here now" and "I exist in spacetime." And, personally, I think you should go with "I am here now."
Why do I find myself at N rather than 10 or N+1?
Well, t=10 is probably a time at which the universe was still quark soup, so you're rather unlikely to show up as a conscious being then.
As for appearing at t=N vs t=N+1, the explanation I remember hearing has two parts: Firstly, if you check out your physical state at any given time, it will necessarily not contain memories of the future; memory formation generates a lot of entropy, and time tends to progress from low-entropy to high-entropy states. So regardless of what time you find yourself at, you'll remember the past but not the future. Secondly, if we treat your personal sampling of time as random versus in a linear fashion, since at each point in your personal experience your memory satisfies this property you'll perceive time as flowing linearly (or at least in a forwards fashion) at any point.
So basically, as near as I can tell, there's no good way to tell the difference between any type of sampling from the time distribution; your subjective experience would be very similar in any case. You find yourself at t=N because you have to find yourself at some t, and t=N is about as likely for you to sample as any other.
This seems to repeat the confusion in the original post. In what sense are "you" sampling different times? What is this "you" doing the sampling? Is there some sort of disembodied consciousness flitting randomly from time slice to time slice?
This seems to repeat the confusion in the original post. In what sense are "you" sampling different times?
There is a difference between the standard "timeless physics" of the 4D block universe, and the specific kind of "timeless physics" advocated by Julian Barbour, which Eliezer was referencing in that post. Your explanation was a good reply within the context of the 4D block universe. And there, there is no issue of "sampling".
However, under Barbour's account, what exists is bigger than a single 4D block universe. What exists is a configuration space (called "Platonia") in which each point represents a possible state for a 3D spatial universe. Conversely, every such possible state is represented by a point in Platonia. In addition, this configuration space supports a static complex scalar field (something like a stationary state solution to the Schrödinger equation in quantum mechanics). Using the Born rule, this scalar field can be interpreted as a fixed probability distribution assigning high probability to some regions in Platonia and low probability to others. Barbour does appeal to this probability distribution to explain why we never "find ourselves" in highly "improbable" configurations of the macroscopic universe.
For example, Platonia contains a point (i.e., a 3D universe) containing people just like us, except that they are looking up into the sky and seeing two suns where their memories say that there was only one sun moments before. That is, they are witnessing what appears to be a flagrant violation of the laws of physics. Barbour's explanation for why we never have this experience is that such configurations get practically no probability mass from the complex scalar field.
So, there is a sort of sampling going on in Barbour's account. He would admit, I think, that this "sampling" is just as mysterious as the Born rule is in the usual many-worlds interpretation of quantum mechanics.
I was referring to the set of all experiences that identify as being XiXiDu as "you" for simplicity's sake; the sampling is the selection of a particular timeslice to experience (ie, XiXiDu was presumably experiencing t=N when he wrote this).
Maybe it would make more sense to frame this differently; the laws of physics dictate that XiXiDu will experience conscious thought at times t=a, a+1...b (assuming consciousness is non-magical and is a result of physics), so those timeslices contain conscious experiences by an entity self-identifying as XiXiDu. As I understand it, timeless physics predicts that they will all experience simultaneously (so to speak), so there will be b-a instances of XiXiDu running at the same time, giving a 1/(b-a) chance that a given instance will be experiencing t=N.
Related to: lesswrong.com/lw/qp/timeless_physics/
Why do I find myself at this point in time, configuration space, rather than another point? In other words, why do I have certain expectations rather than others?
I don't expect the U.S. presidential elections to have happened but to happen next, where "to happen" and "to have happened" internally marks the sequential order of steps indexed by consecutive timestamps. But why do I find myself to have that particular expectation rather than any other, what is it that does privilege this point?
So you seem to remember Time proceeding along a single line. You remember that the particle first went left, and then went right. You ask, "Which way will the particle go this time?"
My question is why I find myself to remember that the particle went left and then right rather than left but not yet right?
But both branches, both future versions of you, just exist. There is no fact of the matter as to "which branch you go down". Different versions of you experience both branches.
Yes, but why does my version experience this point of my branch and not any other point of my branch?
I understand that if this universe was a giant simulation and that if it was to halt and then resume, after some indexical measure of causal steps used by those outside of it, then I wouldn't notice it. Therefore if you remove the notion of an outside world there ceases to be any measure of how many causal steps it took until I continued my relational measure of progression.
But that's not my question. Assume for a moment that my consciousness experience is not a causal continuum but a discrete sequence of causal steps from 1, 2, 3, ... to N where N marks this point. Why do I find myself at N rather than 10 or N+1?
This is a pseudo-problem arising from equivocation about the indexical "I". You can either use it to refer to yourself as a continuant (an entire space-time worm) or as a momentary object (a temporal part of the space-time worm). Just make sure you're not mixing the two uses. I think that is what is causing your puzzlement. To dissolve it, let's focus on the momentary object use of "I".
Don't think of your consciousness as somehow moving from step 1 to 2 to 3 and so on. I think it might be better to start out thinking that there are separate objects, separate XiXiDus, at each of these steps. Each one of those momentary-XiXiDu's is fully conscious. When any one of them says "I", they are referring to themselves, so "I" in the mouth of each momentary-XiXiDu refers to a different object. Also, when they say "now" they are referring to different times. Thought of that way, there is no mystery when each momentary XiXiDu says "I am here now." Where else would he (she?) be?
The problem arises because the psychological states of all the momentary-XiXiDu's are related in a way that makes each one think that he is the only one and that he has been moving through time. So the momentary-XiXiDu at step 3 thinks "I was at 1 and I will be at 7, but I'm now at 3. Why?" Really what's going on is that XiXiDu-3's "now" is step 3, just as XiXiDu-1's "now" is step 1. In some sense XiXiDu-3 is right to say he "was" at step 1, if this is interpreted as him bearing a certain relationship to XiXiDu-1. The mistake is that XiXiDu-3 thinks he is identical to XiXidu-1, and so since he is at step 3, XiXiDu-1 can't be at step 1. After all, how can a single momentary object be at both step-3 and step-1? Well, it can't, but this is not a problem, since XiXiDu-3 is not in fact identical to XiXiDu-1.
momentary object
Over short enough time, each bit of me is out of communication with each other bit of me. In light of this, is it still reasonable to think of a momentary consciousness?