But if you throw out causality along with time, it is hard to see how a low-entropy terminal condition and high-entropy initial condition could produce the same pattern of similar and dissimilar regions.

Aren't you assuming an expanding universe here? Some physicists speculate that if the universe were to contract in a Big Crunch, quantum decoherence would reverse and macroscopic entropy would decrease as highly correlated quantum fluctuations would be erased by destructive interference. The end effect is that the thermodynamic arrow of time is reversed and such a situation becomes indistinguishable from an expanding universe with increasing entropy. I'm not sure if this is a widely accepted view.

Your comfort with expressing uncertainty, including rather high levels of fundamental uncertainty, is improving your thinking and your writing, in my opinion.

I am uncertain about difficult problems, HA. I refuse to fake modesty on problems that are easy unto me. Even though I know some people find uncertainty reassuring, I will not pretend to be uncertain on straightforward problems; the truly wise would not be impressed. You should realize that being uncertain about a problem yourself, does not mean that uncertainty is the inherently correct attitude.

I refuse to fake modesty on problems that are easy unto me.

It's not a matter of modesty so much as skepticism.

"I am uncertain about difficult problems, HA. I refuse to fake modesty on problems that are easy unto me. Even though I know some people find uncertainty reassuring, I will not pretend to be uncertain on straightforward problems; the truly wise would not be impressed. You should realize that being uncertain about a problem yourself, does not mean that uncertainty is the inherently correct attitude."

This response is a result of a fair and reasonable reading of my comment?

Don't think that any of this preserves time, though, or distinguishes the past from the future. I am just holding onto cause and effect and computation and even anticipation for a little while longer.

What is the difference between a time-like relationship and a causal relationship? How have you not preserved time by preserving causality?

Post hoc ergo propter hoc....

HA, that's what you get for paying compliments around here!

IL, think of it like this. If you simulated a conscious being one moment-slice at a time, presumably you'd think of it as 'conscious'. So if you simulate all those moment-slices at once, why would it be any less conscious? Whatever the detail, we are reasonably certain that The Passage Of Time is not a fundamental element of the universe, but rather the way we seem to experience things.

Has anyone else read Vonnegut's Slaughterhouse-5? Great plotline about alien beings who experience all of their lives simultaneously.

But if you throw out causality along with time, it is hard to see how a low-entropy terminal condition and high-entropy initial condition could produce the same pattern of similar and dissimilar regions.

My intuition differs - but for those who think otherwise this would be well worth trying to show the difference more formally.

Isn't causality strictly a map of a world strictly governed by physical laws? If a billiard ball strikes another ball, causing it to move, that is just our way of describing the motions of the balls. And besides, the universe doesn't even split the world up into individual "objects" or "events," so how can causality really exist?

By the way, any physical system is defined not just by its positions, but by its derivatives and second derivatives as well (I believe this is enough to describe the complete state of a system?). So when you talk about frozen states in a timeless universe, they still have to have time derivatives (in our perception of them). In other words, a sequence of still claymation frames and continuous motion may produce the same movie, but they correspond to very different realities.

Now my mind is blown. Great post, and great response to HA.

There is an old saying: "Correlation does not imply causation." I don't know if this is my own thought, or something I remember hearing, but on seeing this saying, a phrase ran through my mind: If correlation does not imply causation, what does?

"Imply" here means "imply with certainty", making the saying good advice for people who don't understand probability.

It still seems to me that there is some actual connection that makes it more likely for me to wake up tomorrow as Eliezer Yudkowsky, than as Britney Spears.

This, at least, is naive - what is the "me" that is more likely to wake up as EY? If "you" woke up as Britney Spears, "you" would be Britney Spears, with her memories and everything. I'd be very surprised if this sentence proved to mean anything, even if a long-term connected picture is necessary for anticipation. (Incidentally, an intermediate view is possible, where experience-moments supervene on short-but-nonzero-duration causal structures - in order to evade Dust Theory - but nothing (except memory) links the experience-moments.)

IL, to do what you suggest you'd have to actually compute the history of your universe, meaning the causal relations would exist, so there wouldn't be any problem with there being consciousness.

Now my mind is blown. Great post, and great response to HA.

There is an old saying: "Correlation does not imply causation." I don't know if this is my own thought, or something I remember hearing, but on seeing this saying, a phrase ran through my mind: If correlation does not imply causation, what does?

"Imply" here means "imply with certainty", making the saying good advice for people who don't understand probability.

It still seems to me that there is some actual connection that makes it more likely for me to wake up tomorrow as Eliezer Yudkowsky, than as Britney Spears.

This, at least, is naive - what is the "me" that is more likely to wake up as EY? If "you" woke up as Britney Spears, "you" would be Britney Spears, with her memories and everything. I'd be very surprised if this sentence proved to mean anything, even if a long-term connected picture is necessary for anticipation. (Incidentally, an intermediate view is possible, where experience-moments supervene on short-but-nonzero-duration causal structures - in order to evade Dust Theory - but nothing (except memory) links the experience-moments.)

IL, to do what you suggest you'd have to actually compute the history of your universe, meaning the causal relations would exist, so there wouldn't be any problem with there being consciousness.

Now my mind is blown. Great post, and great response to HA.

There is an old saying: "Correlation does not imply causation." I don't know if this is my own thought, or something I remember hearing, but on seeing this saying, a phrase ran through my mind: If correlation does not imply causation, what does?

"Imply" here means "imply with certainty", making the saying good advice for people who don't understand probability.

It still seems to me that there is some actual connection that makes it more likely for me to wake up tomorrow as Eliezer Yudkowsky, than as Britney Spears.

This, at least, is naive - what is the "me" that is more likely to wake up as EY? If "you" woke up as Britney Spears, "you" would be Britney Spears, with her memories and everything. I'd be very surprised if this sentence proved to mean anything, even if a connected picture is necessary for anticipation. (I'm drawn to an intermediate view, where experience-moments supervene on short-but-nonzero-duration causal structures - in order to evade Dust Theory - but nothing (except memory) links the experience-moments.)

IL, to do what you suggest you'd have to actually compute the history of your universe, meaning the causal relations would exist, so there wouldn't be any problem with there being consciousness.

Caledonian: thanks for the reply, but that wasn't what I was getting at. I can see that things in a temporal sequence may not be causally related - e.g. the light flashes and then the bell rings, but the light didn't cause the bell. My question was about the reverse implication: if causality exists, such that A causes B, does that not necessarily imply that A preceded B and that time exists? If not, what aspect of time is not included within the notion of causality such that we can have causality but not time?

The only case I can think of offhand would be a time loop: grampa tells dad a secret, dad tells it to me, then I go back in time and tell it to grampa. In this case causality and time diverge for at least part of the loop. But in Elizier's explanation of causality without time, where you use Bayesian analysis to determine which events in a series caused the others, requires that there be no causality loops. So I don't think my time loop example answers my question: what is the difference between causality-with-time and causality-without-time?

Nick: IL, to do what you suggest you'd have to actually compute the history of your universe, meaning the causal relations would exist, so there wouldn't be any problem with there being consciousness.

I don't think that's correct. You could populate your model with random data, and if that data happens to be an accurate representation of the timeless universe, then poof you have created consciousness with no computation required (unless you believe that acquiring random data and writing it to RAM is "computation" of the kind that should create causality and consciousness).

Granted, most such randomly populated models wouldn't contain causality or consciousness. But a non-zero number of them would.

I think IL's point stands. If the universe is timeless, then a sufficiently large integer is full of conscious beings.

No, because there are no causal relationships, or relationships at all, within the randomly generated memory. If all you know is the prior distribution, not that the large-scale structure is in fact meaningful, there's no mutual information between any of the bits; and even once you know all the bits, since they're independent and random you can't say "this bit is 1 because this bit is 0."

This all smells of Mind Projection Fallacy, now that I think about it.

if causality exists, such that A causes B, does that not necessarily imply that A preceded B

and that time exists?

What is there to support the assumption that the universe generates future values independently of each other?

I feel agreement with "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.", and yet I wonder. Doesn't a configuration space contain the fact that change is occurring, at least in the sense that it contains the informational content of relative velocities, not just of relative positions? Also, I have long asserted that experience associated with static configurations seems to me to be close to isomorphic to experience associated with multiple instantiations of a computation. In any event, even if we have retained causality we have still eliminated change.

Very good points Nick T!

Michael: could you elaborate on "Also, I have long asserted that experience associated with static configurations seems to me to be close to isomorphic to experience associated with multiple instantiations of a computation."?

Ricky: I don't think that assumption is being made; rather, you have to transform causal hypotheses with intramoment dependencies into ones without (this seems like it should always be possible).

Eliezer: this may indicate I missed the point of that section, but you can generate a high→low entropy history by computing a low→high entropy history and reversing the frames. It looks to me like Bayesian causality naturally accompanies increase in entropy, since (very handwavingly, this is hard for me to verbalize) P(M2|R1,R2) ≠ P(M2|M1,R1,R2) is more likely to hold if R has higher entropy than M. (Is there a different standard term?)

This definition of causality doesn't seem to work, since the universe clearly doesn't generate future values independently of each other. Consider the following story:

On Monday I decide to buy 2 windows of the same mass. Suppose I want to buy the biggest windows I can afford, and I have money in two bank accounts that I can use for this purpose. On Tuesday a couple of cute little vandals break both of my windows. Some of the glass falls inside my home, and rest outside. Now let:

L1 = how much money I had in bank 1 L2 = how much money I had in bank 2 M1 = mass of window 1 M2 = mass of window 2 R1 = mass of glass that fell inside my home R2 = mass of glass that fell outside my home

Intuitively it seems pretty obvious that the arrow of causality runs from left to right, but if you use the definition Eliezer gave, you'd get the opposite result. Quoting Eliezer:

if we see:

P(M2|L1,L2) ≠ P(M2|M1,L1,L2) P(M2|R1,R2) = P(M2|M1,R1,R2)

Then we can guess causality is flowing from right to left.

Well, P(M2|L1,L2) ≠ P(M2|M1,L1,L2) because M2 depends on the price of glass as well as L1 and L2, but knowing M1 gives us the precise value of M2 (remember that I wanted to buy 2 windows of the same mass). P(M2|R1,R2) = P(M2|M1,R1,R2) since M2=(R1+R2)/2 and M1 doesn't give any more information on top of that.

Nick: What is there to support the assumption that causal hypotheses with intramoment dependencies can always be transformed into ones without?

Dynamically Linked, that's cheating because M1 always equals M2. It's like those division by zero proofs.

Regardless, Eliezer's point here is utterly beautiful and blew my mind, but I just want to check it's applicability in practice:

Suppose that we do know L1 and L2, but we do not know R1 and R2. Will learning M1 tell us anything about M2?

That is, will we observe the conditional dependence

P(M2|L1,L2) ≠ P(M2|M1,L1,L2)

to hold? The answer, on the assumption that causality flows to the right, and on the other assumptions previously given, is no.

True if we're sure we're perfectly reading L1/L2 and perfectly interpreting them to predict M2. But if not then I think the answer's yes because M1 provides additional implicit evidence about L1/L2 than we get from an imperfect reading or interpretation of L1/L2 alone.

Then again, you still get evidence about the direction of causality by how much P(M2|L1,L2) and P(M2|M1,L1,L2) tend to approximately equality in each direction, so even very imperfect knowledge could be got around with statistical analysis. I haven't read Judea Pearl's book yet so sorry if I this is naive or already discussed.

RI, what if I wanted to buy two windows such that one is twice the mass of the other. Is that still cheating?

Nick, how would you transform my causal hypothesis (in the comment above) with intramoment dependencies into one without?

Caledonian: What I mean by "time" is whatever Eliezer means by it, and what I mean by "exist" is that thing that Eliezer says causality does but time doesn't. It seems to me that time and causality are so intertwined that they are surely the same thing; if you have causality but not time, then I don't understand what this "time" thing is that you don't have.

When Eliezer says things like "Our equations don't need a t in them, so we can banish the t and make our ontology that much simpler", perhaps I need a better understanding of exactly what he's proposing to banish.

Perhaps my first clue is your point that causality loops are logically possible. Perhaps time loops aren't logically possible, and that's one way in which the two are not the same. Perhaps I'm using a different mental dictionary than everyone else in these threads.

RI, nice catch. Ricky and DL, replied offsite.

Causal loops are a problem....

I'm not sure that the "arrows" are more real in all cases.

Well, first, as far as bijective deterministic thing, I'm going to say that there is no prefered direction, no "true" internal causality direction, given that the rule in all candidate directions is equally simple in either direction and equally local. In that case, claiming any arrows would seem to be epiphenomenal. I mean, it looks like the only thing it could mean there is if something external to the system violated its fundamental rules, reaching in and altering the system somewhere. Then the direction in which the change would propagate would be the causality direction. But then, that just brings in a larger external system and one can ask about the total causality of that...

Perhaps from there we ought take the idea that a simple discrete unique direction of causality is simply a fundamentally wrong model?

Now, if you have some deterministic system which is not bijective, then it does seem pretty clear that the direction in which it's deterministic would perhaps the the most objectively valid direction for "objective causality"

A refinement: Bijective and local, but if we consider a step in some direction, A -> B, such that to determine the state of a neighborhood in B of size x, you need a neighborhood in A of size y, but if going in the B -> A direction, to determine state of neighborhood of size x in A you need neighborhood of size z > y in B, then I think I'd say A -> B is the "natural" direction of causality.

Frankly, I'm semi suspecting that perhaps the concepts of locality and causality are deeply tied to one another.

Anyways, let's consider Barbour's universe for a moment... What would we consider ultimate cause and effect? The basic rule for the amplitude field + boundry conditions = ultimate cause of everything going on, right?

Perhaps we mean "given that, and given some other thing, but changing some other thing, what happens?"

It looks like perhaps some notion of "relative causality" or "conditional causality" may be in order, rather than simply being tied to a single absolute causality.

Sorry some of this is vague, I'm still thinking it through.

Oh... With Barbour's Platonia, there actually would be something that fits with some of the above: The whole thing about neighborhood size. I THINK the direction away from the origin may be the prefered direction based on that criteria, at least if one starts with a neighborhood as "wide" as it needs to be to hit the boundries.

On the other hand, what if someone started midPlatonia with a hyperspherical shell shaped neighborhood of known values? Then away from the origin of that would be the locally prefered direction... until one hit the boundries. Then stuff would start getting odd.

As I said, I'm still thinking it through, but it does look like some form of notion of relative of conditional causality is really needed.

Consider our brain states... Given that and the physics, there's presumably a natural "forward" direction, or group of prefered directions. (There can't be a single prefered direction in Platonia anyways... I mean, you've got effective branching into the decoherent worlds and all that...)

Now, given some locally prefered direction, we might ask if we held fixed the "tag"/dimensions representing us, but varied some other factors/dimensions that we're curios about, then peek ahead in whatever the "obvious relative to us" prefered directions are for each of the states we're testing, what would be different in each? That would tell us something about what the changing thing causally affects, relative to us.

Sorry this is a bit rambling. I'm confused on this issue too, I'm just here poking and prodding at it and hoping I get out some useful insight.

Infotropism: There may be some other things which are conserved in Life, some abstract properties maybe. I dunno, anyone here know? Anyways, does Noether's theorem even apply to it? I thought it just applied to things that had lagrangians or something analogous. Can Life be represented in any mathematical form that ends up with sufficient lagrangian or whatever structure that Noether's theorem can even begin to talk about it?

Also, I think Eliezer was hinting at that possibility, he was partly suggesting something along the lines of "am sticking with this notion until I have something better and less confusing to replace it with."

Nick: Casually, either experience is a property of the math, in which case it only comes from a single instance of a computation (or even from zero instances) or it's a property of the existence of the physical state, in which case it comes from multiple instances, but equally much from one instance that endures for as long as those multiple instances do. Timeless physics may make a third path possible, and there may be other work-arounds, but those two possibilities seem to be the default.

Caledonian: It doesn't need to be a simple sum. What I meant was maybe something a bit more abstract. Perhaps something with some form of "directionality", analogous to momentum, such that different sections can cancel out.

Or maybe some more abstract property, perhaps some completely non local property that turns out to be conserved. Again, I'm not saying there is such a property in Life, merely that it's not obvious to me that there isn't, and that as far as I know, Noether's theorem doesn't apply to this sort of system.

(If I'm wrong about the last, well, someone lemme know? :))

Nick, here's what Judea Pearl wrote on this topic. On page 59 of his book:

This suggests that the consistent agreement between physical and statistical times [i.e., the direction of time and the direction of causality] is a byproduct of the human choice of linguistic primitives and not a feature of physical reality. ... Pearl and Verma (1991) speculated that this preference represents survival pressure to facilitate prediction of future events, and that evolution has evidently ranked this facility more urgent than that of finding hindsighted explanation for current events.

Eliezer wants to go from timeless physics to causality, to computation, to anticipation. He admits being unsure about the latter two steps, but even the first step doesn't seem to work. And besides, timeless physics (and relational physics, which timeless physics builds on top of) itself is highly speculative and problematic. Is the intention to actually convince us of the correctness of these ideas, or just to make us "think outside the box" and realize that these possibilities exist?

I don't see the point in all this.

We have this mathematical Platonia object and the relation across the time dimension is not symmetric: in what we call increasing values of time slices of the Platonia get larger. If you want to talk about some of the structures in the Platonia as "timeless causation" or "computation" then, sure, I have no problem with that. But I don't see that you've created or rescued anything, you've just defined existing words in terms of the Platonia's structure.

I certainly don't see why you are being "forced to grind up reality into disconnected configurations". Why not continuous time? Then you don't need "glue between them" as there is no between. Speaking of which, your example is in discrete time, but does it hold in continuous time? From mathematical finance I've learnt that many counter intuitive things can happen in continuous time stochastic processes. Unfortunately, I'm only just coming to terms with discrete time martingale theory and haven't yet progressed to the continuous case - so I can't answer this question myself.

Yes, the discrete vs. continuous time issue calls into question the conclusions drawn from the example. This is related to my question above: "What is there to support the assumption that the universe generates future values independently of each other?"

Configuration vs computation: Storing a configuration depends on the representation. To say that you're storing a configuration of Conway's Life, rather than some other 2d cellular automaton, requires some commitment that this is the intended computation. I have no idea what such a commitment would look like. Actually doing the computation sounds pretty good, but otherwise?

There is no t coordinate, and no global now sweeping across the universe. Events do not happen in the past or the present or the future, they just are. But there may be a certain... asymmetric locality of relatedness... that preserves "cause" and "effect", and with it, "therefore"

Not to trivialize this, but Phillip Fry helps me think about it, by going back in time and being his own grandfather:

http://en.wikipedia.org/wiki/Roswell_That_Ends_Well

for him, whether he was prior to his father is an unanswerable question, but the story is causally consistent.

I'm just curious: Is there an intentional double-meaning of L, M, R (Light, Me, Rock)?

Do you know that it doesn't work if we use a deterministic rule, or have you just not tried? Cause I'm trying right now.

"To compute a consistent universe with a low-entropy terminal condition and high-entropy initial condition, you have to simulate lots and lots of universes, then throw away all but a tiny fraction of them that end up with low entropy at the end. With a low-entropy initial condition, you can compute it out locally, without any global checks. So I am not yet ready to throw out the arrowheads on my arrows."

Here's the problem with this argument. Your simulations are occurring as a sub-history of a universe where the second law of thermodynamics already holds. A simulation of a universe with increasing entropy will be a sub-history where entropy increases, and will therefore be more likely to occur than a simulation of a universe with decreasing entropy (i.e. a subhistory where entropy decreases.)

That is, unless your simulation finds a way to dump entropy into the environment. The usual way to do this is by erasing information cf: http://en.wikipedia.org/wiki/Von_Neumann-Landauer_limit . Throwing out the simulations where entropy increased would be one example. Likewise, simulating non-information preserving rules (e.g. Conway's game of life) will also allow entropy to decrease within the simulation -- for example, most random fields of a reasonably small size will settle into a pattern of stable oscillators. This can happen because it is perfectly possible for two ancestor states to go to the same descendent state within the rules of Conway's game, and when this happens, entropy must leak into the environment according to the second law.

If the idea that time stems from the second law is true, and we apply the principle of eliminating variables that are redundant because they don't make any difference, we can collapse the notions of time and entropy into one thing. Under these assummptions, in a universe where entropy is decreasing (relative to our external notion of 'time'), the internal 'time' is in fact running backward.

As also noted by some other commenters, it seems to me that the expressed conditional dependence of different points in a universe is in some way equivalent to increasing entropy.

Let's assume that the laws of the universe described by the LMR picture are in fact time-symmetric and that the number of states each point can be in is too large to describe exactly (i.e. just as is the case in our actual universe, as far as we know). In that case, we can only describe our conditional knowledge of M2 given the states of M1 and R1,2 using very rough descriptions, not using the fully detailed descriptions describing the exact states. It seems to me that this can only be usefully done if there is some kind of structure in the states of M1,2 (a.k.a. low entropy) that matches our coarse description. Saying that the L or M part of the universe is in a low entropy state is equivalent to saying that some of the possible states are much more common for the nodes in the L or M part than other states. Our coarse predictor will necessarily make wrong predictions given some input states. Since the actual laws are time symmetric, if the input states to our predictor were randomly distributed over all possible states, our predictions would fail equally often predicting from left to right or from right to left. Only if on the left the states we can predict correctly happen more often than on the right will there be an inequality in the number of correct predictions.

...except that I now seem to have concluded that time always flows in the opposite direction of what Eliezers conditional dependence indicates, so I'm not sure how to interpret that. Maybe it is because I am assuming time symmetric laws and Eliezer is using time-asymmetric probablistic laws. However, it still seems correct to me that in the case of time symmetric underlying laws and a coarse (incomplete) predictor, predictions can only be better in one way than the other if there is a difference in how often we see correctly predicted input relative to incorrectly predicted input, and therefore if there is a difference in entropy.

Okay so the tldr; of this could be : In a nondeterministic universe, effects imply at least one cause, but a cause does not imply an effect, therefore a causal model implies some kind of time like asymmetry. Correct?

So then it seems to me you can make the obvious extension into a quantum universe by subsituting probability mass for amplitudes. So that in our quantum, deterministic universe, the asymmetry comes from the way amplitude spreads down everett branches, and our confinement to a single one. A dead cat in schroedinger's box now implies a live one a certain time in the past, a live one now does not necessitate a dead one at any given time in the past.

well, for me is still an enigma how statistical series, any statistical series, wich is by definition defined as pairs of time|numbers series can be in any logical way ... timeless

you have that string of naked numbers, pure numbers ... and its timecoded by its very pure defined nature! 1rst value, second value, third value etcaetera ... that is already time coded and that can't be changed unless you are alowed to work with statistical series where you can randomly permute series members and still pretend that it is still statistical series .. and that, i think, will defeat any statistical analisis of anything because you will work with nothing more than pure and random numerical garbage if you are serios and use real randomness ;-p

so for me timeless causality is just another logical and random pure garbage and nonsense

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.

This also lets me keep, for at least a little while longer, the concept of a conscious mind being connected to its future Nows, and anticipating some future experiences rather than others.  Perhaps I will have to throw out this idea eventually, because I cannot seem to formulate it consistently; but for now, at least, I still cannot do without the notion of a "conditional probability".

I wrote a long comment, but the main question is: Why do you guess an answer here, instead of "Shut up and calculate"?

Why are/were you favouring the hypothesis? Considering what I have read so far from you, I find it more likely that I have missed something, than there being no reason, but I can't find it....

If you look into the brains of Alpha and Betty in the morning, as well as the weather forecast, the attitude of each girl to the food that their parents will give them today (that is, how much one of them will deteriorate/elevate their mood) and into the brains of their parents (how they will interact with each other and with their daughters) etc., you will have the conditions to understand which of the girls is more likely to throw a stone.

I haven't made my way through your article yet, though I hope to. But I was a little surprised when you discussed how correlation does not prove causation that you did not mention David Hume who basically says, at least in my reading of him, that no matter how many times one observes lightning and thunder you can not say with absolute certainty that lightning causes thunder.