Causal Reference

I had always thought that our physical universe had this property as well, i.e. the Everett multiverse branches into the past as well as into the future.

Interesting question! I'd say that you could refer to the possibilities as possibilities, e.g. in a debate over whether a particular past would in fact have led to the present, but to speak of the 'actual past' might make no sense because you couldn't get there from there... no, actually, I take that back, you might be able to get there via simplicity. I.e. if there's only one past that would have evolved from a simply-tiled start state for the automaton.

I am unable to see the appeal of a view in which there is no fact of the matter. It seems to me that there is a fact of the matter concerning the past, even if it is impossible for us to know. This is not similar to the case where sneezing alters two shadow variables, and it is impossible for us to meaningfully refer to variable 1 as opposed to variable 2; the past has a structure, so assertions will typically have definite referents.

The Standard Model of particle physics with MWI is time-symmetric (to be precise: CPT symmetric) and conserves information. If you define the precise state at one point in time, you can calculate the unique past which lead to that state and the unique future which will evolve from that state. Note that for general states, "past" and "future" are arbitrary definitions.

This is actually one of the reasons I have to doubt Cryonics. You can talk about nano-tech being able to "reverse" the damage, but it's possible (and I think likely), that it's very hard to go from damaged states to the specific non-damaged state that actually constitutes your consciousness/memory.

Or, a Boltzmann brain that flickered into existence with memories of a past that never happened.

When you "simulate random universes," what distribution are you randomizing over?

Seems like the simulations only help if you somehow already know the true probability distribution from which the actual universe was selected.

How can the version without shadow brains be significantly longer? Even in the worst possible world, it seems like the 2% of non-shadow-brain programs could be encoded by copying their corresponding shadow-brain programs and adding a few lines telling the computer how to garbage-collect shadows using a straightforward pruning algorithm on the causal graph.

That would strongly indicate that something caused the zombies to write a program for generating simulations that was likely to create simulated shadow brains in most of the simulations. (The compiler's built in prover for things like type checking was inefficient and left behind a lot of baggage that produced second tier shadow brains in all but 2% of simulations). It might cause the zombies to conclude that they probably had shadow brains and start talking about the possibility of shadow brains, but it should be equally likely to do that whether the shadow brains were real or not. (Which means any zombie with a sound epistemology would not give additional credence to the existence of shadow brains after the simulation caused other zombies to start talking about shadow brains than it would if the source of the discussion of shadow brains had come from a random number generator producing a very large number, and that large number being interpreted as a string in some normal encoding for the zombies producing a paper that discussed shadow brains. Shadow brains in that world should be an idea analogous to Russell's teapot, astrology, or the invisible pink unicorn in our world.)

Now, if there was some outside universe capable of looking at all of the universes and seeing some universes with shadow brains and some without, and in the the universes with shadow brains zombies were significantly more likely to produce simulations that created shadow brains than in the universe in which zombies had shadow brains they were much more likely to create simulations that predicted shadow brains similar to their actual shadow brains -- then, we would be back to seeing exactly what we see when philosophers talk about shadow brains directly: namely, the shadow brains are causing the zombies to imagine shadow brains which means that the shadow brains aren't really shadow brains because they are affecting the world (with probability 1).

Either the result of the simulations points to gross inefficiency somewhere (their simulations predicted something that their simulations shouldn't have been able to predict) or the shadow brains not really being shadow brains because they are causally impacting the world. (This is slightly more plausible than philosopher's postulating shadow brains correctly for no reason only because we don't necessarily know that there is anything driving the zombies to produce simulations efficiently; whereas, we know in our world that we can assume that brains typically produce non-gibberish because enormous selective pressures have caused brains to create non-gibberish.)

Fair, but quantum mechanics gives us Hawking radiation, which may or may not provide information (in principle) about what went into the black hole.

Also, there are causal arrows from the black hole to everything it pulls on, and those are ultimately the sum of causal arrows from each particle in the black hole even if from the outside we can't discern the individual particles.

Stuff thrown into such a black hole can certainly affect the hypothetical entities living inside. Like a meteor shower from the outside. But the outside is not affected by anything happening inside, the horizon prevents it.

That is not entirely true: stuff thrown into the black hole increases the horizon area and possibly modifies its geometry, and in return the horizon affects the spatial infinity (the area around the horizon). The debate is about how much information the horizon deletes in the process. The same is for the cosmological horizon, which is effectively just another kind of singularity.

The last nodes are never observed by anyone, but they descend from the same physics, the same F(physics), that have previously been pinned down, or so I assume. You can thus meaningfully talk about them for the same reason you can meaningfully talk about a spaceship going over the cosmological horizon. What we're trying to avoid is SNEEZE_VARs or lower qualia where there's no way that the hypothesis-making agent could ever have observed, inducted, and pinned down the causal mechanism - where there's no way a correspondence between map and territory could possibly be maintained.

Following this reasoning, if there is a finite causal state machine, then your pruning operation would eventually remove me, you, the human race, the planet Earth.

Now, from inside the universe, I cannot tell whether your hypothesis of a finite state graph universe is true or not - but I do have a certain self-interest in not being removed from existence. I find, therefore, that I am scrambling for justifications for why the finite-state-model universe nodes containing myself are somehow special, that they should not be removed (to be fair, I extend the same justifications to all sentient life).

Even if the Universe is infinite...

Okay, I can see that I need to spell out in more detail one of the ideas here - namely that you're trying to generalize over a repeating type of causal link and that reference is pinned down by such generalization. The Sun repeatedly sends out light in individual Sun-events, electrons repeatedly go on traveling through space instead of vanishing; in a universe like ours, rather than the F(i) being whole new transition tables randomly generated each time, you see the same F(physics) over and over. This is what you can pin down and refer to. Any causal graph is acyclic and can be divided as you say; the surprising thing is that there are no F-types, no causal-link-types, which (over repeating time) descend from one kind of variable to another, without (over time) there being arrows also going back from that kind to the other. Yes, we're generalizing and inducting over time, otherwise it would make no sense to speak of thingies that "affect each other". No two individual events ever affect each other!

So... the past can affect the future, but the future cannot affect the past (barring things like tachyons, which may or may not exist in any case). Taking this in context of the article could lead to an interesting discussion on the nature of time; does the past still exist once it is past? Does the future exist yet in any meaningful way?

It seems that you get similar questions as a natural outgrowth of simple computational models of thought. E.g. if one performs Solomonoff induction on the stream of camera inputs to a robot, what kind of short programs will dominate the probability distribution over the next input? Not just programs that simulate the physics of our universe: one would also need additional code to "read off" the part of the simulated universe that corresponded to the camera inputs. That additional code looks like epiphenomenal mind-stuff. Using this framework you can pose questions like "if the camera is expected to be rebuilt using different but functionally equivalent materials, will his change the inputs Solomonoff induction predicts?" or "if the camera is about to be duplicated, which copy's inputs will be predicted by Solomonoff induction?"

If we go beyond Solomonoff induction to allow actions, then you get questions that map pretty well to debates about "free will."

Pretty much the same reason religion needs to be talked about. If no one had invented it wouldn't be useful to dispute notions of god creating us for a divine purpose, but because many people think this indeed happened you have to talk about it. It's especially important for reasonable discussions of AI.

Because epiphenomenalist theories are common but incorrect, and the goal of LessWrong is at least partially what its name implies.

It's good practice for seeing how the rules play out; and having a clear mental visualization of how causality works, and what sort of theories are allowed to be meaningful, is actually reasonably important both for anti-nonsense techniques and AI construction. People who will never need any more skill than they currently have in Resist Nonsense or Create Friendly AI can ignore it, I suppose.

Philosophers have a tendency to name pretty much every position that you can hold by accepting/refusing various "key" propositions. Epiphenomenalism tends to be reached by people frantically trying to hold on to their treasured beliefs about the way the mind works. Then they realise they can consistently be epiphenomenalists and they feel okay because it has a name or something.

Basically, it's a consistent position (well, Eliezer seems to think it's meaningless!), and so you want to go to some effort to show that it's actually wrong. Plus it's a good exercise to think about why it's wrong.

People don't like epiphenomenalism per se, they feel they are forced into it by other claims they find compelling. Usually some combination of

1. Qualia exist in some sense

2. Qualia can't be explained reductively

3.The physical world is causally closed.

In other words, 1 and 2 jointly imply that qualia are non physical, 3 means that physical explanations are sufficient, so non physical qualia must be causally idle.

The rationalist world doesn't have a clear refutation of of the above. Some try to refute 1, the Dennett approach of qualia denial. Others try to refute 2, in ways that fall short of providing a reductive explanation of qualia. Or just get confused between solving the easy problem and the hard problem.

In other words, "Yes"?

Where in the causal diagram does "meaning" go?

So does the Mediation link.

As bryjnar points out, all the stuff you say here (subtracting out the Pearl stuff) is entailed by the causal theory of reference. The reason quick summaries of that view will seem unfamiliar is that most of the early work on the causal theory was primarily motivated by a different concern -- accounting for how our words acquire their meaning. Thus the focus on causal chains from "original acts of naming" and whatnot. However, your arguments against epiphenomenalism all hold in the causal theory.

It is true that nobody (that I know of) has developed an explicitly Pearlian causal theory of reference, but this is really accounted for by division of labor in philosophy. People working on reference will develop a causal theory of reference and use words like "cause" without specifying what they mean by it. If you ask them what they mean, they will say "Whatever the best theory of causation is. Go ask the people working on causation about that." And among the people working on causation, there are indeed philosophers who have built on Pearlian ideas. Christopher Hitchcock and James Woodward, for instance.

You've got a more sophisticated notion of causality, but otherwise this is very similar to the causal theory of reference. For example, the way they would describe what's going on with the shadow sneeze variables is that when you name "SNEEZE_VAR", there was no causal link that allowed you to pick out the actual SNEEZE_VAR: there would need to be a causal arrow going the other way for that to be possible. (and then any later uses of "SNEEZE_VAR" would have to be linked causally to your earlier naming: if we wiped your brain and rebooted it with random noise that happened to be the same, then you wouldn't succeed in referring) I'm pretty sure I've seen someone use a similar kind of example where you can't decide which of two possible things you're referring to because of the lack of a causal link of the right kind.

They also use pretty similar examples: a classic one is to think of an being on the other side of the galaxy thinking about Winston Churchill. Even if they have the right image, they even happen to think the right things about where he lived, what he did etc. it seems that they don't actually succeed in referring to him because of the lack of a causal link. It's just a coincidence.

With that in mind, there are probably arguments made against the causal theory of reference that may apply to you to, but I don't know any off the top of my head.

We know that there are qualia, for the obvious reason that we are not p-zombies: and we know that consciousness is created via neurons in the brain, for we can map a correspondence between qualia and brain states

Some questions here. How do you know that other people are not p-zombies? Presumably you believe them when they say they have qualia! But then those speech acts are caused by brain states, and if qualia are epiphenomenal, the speech acts are not caused by qualia. Similarly, the correspondence you describe is between brain states and reported qualia by other people: I doubt you've ever managed to map your own brain states to your own qualia.

Related, how do you know that you were not a p-zombie every day of your life up to yesterday? Or that if you had qualia yesterday, how do you know that you didn't have a green quale when looking at red (stop) traffic lights? Well because you remember having qualia, and you remember them being the same as the qualia you have today! But then, aren't those memories encoded in brain states (neural connections and synaptic strengths)? How could qualia cause those memories to become encoded if they were epiphenomenal to brain states?

Stuff like this makes me pretty sure that epiphenomenalism is false.

That's the point, I believe. To call something 'real', and yet say in principle it couldn't affect us causally, is to contradict yourself. If you're contained in a set of nodes that are causally linked, then that is your reality. Any other sets of nodes that can't contact you just don't matter. Even if there was, say, a causal structure beside our universe, of puppies and kittens running around, it wouldn't matter in the slightest, if in principle we could never interact with them. If we could deduce from the laws of physics that they had to exist, then we would be causally linked. The point I am (and perhaps Eliezer is) trying to emphasise is that our reality is everything that can, and does, affect us.

...doesn't the structure or contents of the uncausing stuff cause me to...

Um...

...the uncausing stuff cause me...

-.-

It seems to me that the structure of your epiphenomenal model causes you to think about it in the same way that the structure of arithmetic "causes" you to think about arithmetic. So you can infer the existence of an epiphenomenal self as a sort of Platonic form. If you take modal realism seriously, maybe you should infer the "existence" of the epiphenomenal self.

Then it's not uncausing. It has caused you to think in this way rather than that way.

PA proves "2 + 2 = 4" using the associative property. PA does not prove "2 + 2 = 3". "2 + 2 = 4" is actually shorthand for "((1+1) + (1+1)) = (((1+1)+1)+1)". Moving stuff next to other stuff in our universe happens to follow the associative property; this is why the belief is useful.

  S(S(0)) + S(S(0))
= S(S(S(0))) + S(0)
= S(S(S(S(0)))) + 0
= S(S(S(S(0))))

2+2=4 isn't a cause. It's a tautological description. Describing things is useful, though.

I think this example brings out how Pearlian causality differs from other causal theories. For instance, in a counterfactual theory of causation, since the negation of a mathematical truth is impossible, we can't meaningfully think of them as causes.

But in the Pearlian causality it seems that mathematical statements can have causal relations, since we can factor our uncertainty about them, just as we can other statements. I think endoself's comment argues this well. I would add that this is a good example of how causation can be subjective. Before 1984, the Taniyama-Shimura-Weil conjecture and Fermat's last theorem existed as conjectures, and some mathematicians presumably knew about both, but as far as I know they had no clue that they were related. Then Frey conjectured and Ribet proved that the TSW conjecture implies FLT. Then mathematician's uncertainty was such that they would have causal graphs with TSW causing FLT. Now we have a proof of TSW (mostly by Wiles) but any residual uncertainty is still correlated. In the future, maybe there will be many independent proofs of each, and whatever uncertainty is left about them will be (nearly) uncorrelated.

I also think there can be causal relations between mathematical statements and statements about the world. For instance, maybe there is some conjecture of fluid dynamics, which if true would cause us to believe a certain type of wave can occur in certain circumstances. We can make inferences both ways, for instance, if we observe the wave we might increase our credence in the conjecture, and if we prove the conjecture, we might believe the wave can be observed somehow. But it seems that the causal graph would have the conjecture causing the wave. Part of the graph would be:

[̶P̶r̶o̶o̶f̶ ̶o̶f̶ ̶c̶o̶n̶j̶e̶c̶t̶u̶r̶e̶ ̶-̶>̶ ̶c̶o̶n̶j̶e̶c̶t̶u̶r̶e̶ ̶-̶>̶ ̶w̶a̶v̶e̶ ̶<̶-̶ ̶(̶f̶l̶u̶i̶d̶ ̶d̶y̶n̶a̶m̶i̶c̶s̶ ̶a̶p̶p̶l̶i̶e̶s̶ ̶t̶o̶ ̶w̶a̶t̶e̶r̶)̶ ̶]̶

[Proof of conjecture <- conjecture -> wave <- (fluid dynamics applies to water) ]

It is meaningful to talk about mathematical facts causing other mathematical facts. For example, if I knew the complete laws of physics but did not have enough computing power to determine all their consequences (which would be impossible anyways, as I'm living inside of them), my uncertainty about what is going to happen in the universe would be described by the exact same probability distribution as my uncertainty about the mathematical consequences of the laws of physics, and so both distributions would satisfy the causal Markov condition for the same causal graph* (modulo any uncertainty about whether the laws that I believe to be correct actually do describe the universe).

This works the same way with any other set of mathematical facts. I believe that if the abc conjecture is true, then Szpiro's conjecture is also true and I believe that if the abc conjecture is false, then Shinichi Mochizuki's proof of it is flawed. All of these facts can be put into one probability distribution which can then be factored over a Bayesian network. There is no need to separate the mathematical from the nonmathematical.

* Depending on how exactly you phrase the question, I would even say that these distributions are describing my uncertainty about the same thing, but that isn't necessary here.

While it seems viable to say that mathematical truths exert causal (albeit time-invariant) influence on the universe, you might think it prima facie unlikely that we could causally influence them. However, it perhaps we can causally affect the outputs of decision algorithms.

On its own, mathematics is just the study of various systems of rules for symbol manipulation. The "unreasonable effectiveness of mathematics" in more practical areas like physics allows us to conclude something about the structure of physical law. Whatever the true laws of physics are, we conclude, they seem to be well described by certain systems of rules for symbol manipulation.

In our causal models, this is an arrow between "laws of physics" and "observations about the behavior of collections of objects" [subject to Eliezer's caveat about a "laws of physics" node]. Once we include this arrow, we can do neat tricks like counting the numbers of rocks in piles A and B, encoding those numbers in symbols, manipulating those symbols, and finally using the result to correctly predict how many rocks we will have once we combine the two piles.

Unfortunately I accidentally looked at some of the other answers first, but I think my answer would have been this anyway:

The fact "2+2=4" is a fact about the products of certain systems of thought and computation. It is also a abstract description of a certain property of objects in reality (namely, that taking two sets of two objects and combining the sets results in a set of four objects), at least at the classical level.

There seem to be all sorts of reasons that our distant ancestors' development of a number sense was useful enough to be evolutionarily favored. Do we still have everyone in the tribe? Do we outnumber the enemies? How many predators were chasing me? Are these all of my children? A number sense that told us "2+2=3" could be quite maladaptive.

I see it as being in the causal graph - not as a node, but as an arrow (actually, a whole class of arrows). If I have two stones, and I put two more stones with them, then this will cause me to have four stones. Note that this doesn't apply in all cases - if I have two piles of sand and I put them together with two more piles of sand, the result is one really big pile of sand and not four piles - but it applies in enough cases that the cases in which it does not apply can be considered exceptions for various reasons.

'2+2=4' can be causally linked to reality. If you take 2 objects, and add 2 others, you've got 4, and this can be mapped back to the concept of '2+2=4'. Computers, and your brain, do it all the time.

This argument falls when we start talking about things which don't seem to actually exist, like fractions when talking about indivisible particles. But numbers can be mapped to many things (that's what abstracting things tends to do), so even though fractions don't exist in that particular case, they do when talking about pies, so fractions can be mapped back to reality.

But this second argument seems to fall when talking about things like infinities, which can't be mapped back to reality, as far as I know (maybe when talking about the number of points in a distance?). But in that case, we are just extrapolating rules which we have already mapped from the universe into our models. We know how the laws of physics work, so when we see the spaceship going of into the distance, where we'll never be able to interact with it again, we know it's still there, because we are extrapolating the laws of physics to outside the observable universe. Likewise, when confronted with infinity, mathematicians extrapolated certain known rules, and from that inferred properties about infinities, and because their rules were correct, whenever computations involving infities were resolved to more manageable numbers, they were consistent with everything else.

So our representations of numbers are a map of the territory (actually, many territories, because numbers are abstract).

Mathematics is a lower, actually the lowest, tier.

but my effect on the Andromeda Galaxy is the sort of thing we tag "epsilon"

For now.

Maybe I'm misunderstanding something. I've always supposed that we do live in a multi-tiered causal universe. It seems to me that the "laws of physics" are a first tier which affect everything in the second tier (the tier with all of the matter including us), but that there's nothing we can do here in the matter tier to affect the laws of physics. I've also always assumed that this was how practically everyone who uses the phrase 'laws of physics' uses it.

So you mean we live in a multitier universe with no bridging laws and the higher tiers are predictable fully from the lower tiers? Why not just call it a single tier universe then? Especially because your hypothesis is not distinguishable from the single-tier, which is simpler, so you have no good reason to ever have encountered it. "Such and such is true, but that has no causal consequences, but it's truth is still somehow correllated with my belief". (note that that statement violates the markov-whatsit assumption and breaks causality).

Forgive me if I misunderstood.

E.g., we discover that physics tells us that for every particle, there is a cooresponding shadow particle that has no effect on regular ones.

And how, exactly, would we discover that?

If we discovered this meaningfully, then it means that at least one bit in the entire universe is different than it would be if there were no shadow particles. In this case, the existence of shadow particles is inevitably causally linked to that one bit. As such, they are no longer epiphenomenal, because they do have an effect on that one bit of data, which has its own effect on the rest of the universe.

If we discover this without any such things, then AFAICT it's a meaningless discovery, because we can make a discovery of absolutely anything if there is no information.

If you send data somewhere and it disappears once it affects the lower level, then that is an interaction from the lower level to the upper level, since the upper level would have been different if the lower level wasn't there (the data would not have disappeared). Then again, I'm not entirely sure about this. Maybe this is how you'd build a p-zombie detector: Find the ones that don't have random bits of data randomly blink out of existence.