A causality post, for no particular reason
The following question emerged from a conversation with the machine learning theorist Pedro Domingos a month ago.
Consider a hypothetical race of intelligent beings, the Armchairians, who never take any actions: never intervene in the world, never do controlled experiments, never try to build anything and see if it works. The sole goal of the Armchairians is to observe the world around them and, crucially, to make accurate predictions about what’s going to happen next. Would the Armchairians ever develop the notion of cause and effect? Or would they be satisfied with the notion of statistical correlation? Or is the question kind of silly, the answer depending entirely on what we mean by “developing the notion of cause and effect”? Feel free to opine away in the comments section.
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Comment #1 November 2nd, 2012 at 9:09 pm
Is our notion of cause and effect not simply built to fulfill our need for economy of thought? Then, if we were sufficiently smart, and could perform enormous statistical calculations in our minds, would the same question apply equally well to us?
Comment #2 November 2nd, 2012 at 9:14 pm
Bracketing the issues of semantics, it seems to me that one must develop a notion of “(be)cause” roughly as soon as one asks “why?”, and argument-from-lack-of-imagination assures me that any entity that can wonder what will happen could potentially wonder why things did happen.
Comment #3 November 2nd, 2012 at 9:20 pm
Yes, assuming their powers of observation are similar to our own, I think they would develop an idea of causation.
They would notice that grass gets wet after it rains, after someone pours a bucket of water on it, after someone sprays it with a hose, etc. They would also notice that however the grass got wet, it grows better afterwards (if it had been dry for a while before). This is better explained as water causing grass to grow than as rain, buckets, hoses, etc. all being associated with grass growning.
This is more-or-less the idea of “natural experiments” that are used as a subsitute for non-armchair experiments when actual experiments aren’t possible.
On the other hand, if the Armchairians can observe the microstate of a physical system, they would see time-reversible laws, and might not see any need for the non-time-reversible concept of cause and effect.
Comment #4 November 2nd, 2012 at 9:28 pm
The notion of causality is so central to our ideas about scientific predictions, that it is seems unavoidable. Yes, you can sometimes get by with correlations, but even then, people cannot resist giving a causality argument. OTOH, without the ability to do controlled experiments, their science would surely advance much more slowly.
Comment #5 November 2nd, 2012 at 10:09 pm
I don’t understand how they could have evolved without having to be causing and effecting in their past, so it seems hard to imagine experiential, reflexive consciousness without a prior category of cause and effect.
Comment #6 November 2nd, 2012 at 10:29 pm
Doesn’t Pearl claim that he developed graphical models as an armchairian? But does that count, or is there some extra step in declaring this to be cause and effect, which he took because he was contaminated by our culture?
Also, the concept of a causal light cone in some differential equations would certainly come up.
Comment #7 November 2nd, 2012 at 10:55 pm
Suppose the Armchairians did not have any notion other than statistical correlation. Can we imagine a set of events for which humans could produce strictly better predictions than the Armchairians?
I can’t, but that doesn’t mean no such event exists, so I’ll try a bait-and-switch: substitute “a computer program” for “Armchairians”. Computers obviously (?) have only statistical correlation to work with, so this replacement seems acceptable. Can we imagine a set of events for which a human could produce strictly better predictions than a computer?
If we posit that such an event exists, then it follows that there’s something special about human reasoning that can’t be matched by a machine. That’s contrary to my sensibilities though, so my conclusion is that no such event exists and hence that
– either computers advanced enough to match human predictive abilities have a concept of cause and effect
– or that a notion of cause and effect is no more powerful than statistical correlation
– or both of the above (my preference)
Comment #8 November 2nd, 2012 at 11:13 pm
I’d think that every prediction (and subsequent confirmation/disconfirmation) *is* an experiment in causality. Since they don’t interfere, they may not be able to distinguish between competing models of causation, but they are still essentially building causal models.
way I see it, the old saw about “correlation is not causation” is really more of a warning for post-hoc interpretation of already recorded data.
Comment #9 November 3rd, 2012 at 12:51 am
The notion of “cause and effect” is a special example of a statistical correlation and it has always been.
It’s special in two respects. First, when we talk about the “sharp” or “deterministic” cause and effect, the statistical correlation between the cause and effect must be one-side perfect, so the same cause in the initial conditions has to produce the same effect. It isn’t always the case but whether it is the case doesn’t depend on whether the cause was prepared by the Armchairians or someone else.
Second, the “cause and effect” are a pair of statistically correlated events that are timelike separated and by definition, cause is in the past light cone of the effect. Causality actually guarantees that any statistical correlation may only be explained by correlations between timelike separated events in which the later one, the cause, may be uniquely predicted by the previous one, the effect, but not vice versa.
At any rate, none of the special properties has anything to do with the question whether the causes were prepared by the Armchairians or their environment. This is how it works in principle. Of course, in practice, “deliberate” actions and experiments have been very helpful for our understanding because we created environments and situations – like the LHC tube and the collisions in it – that are hard to find naturally, without our actions. But this deliberate preparation of artificial situations only helped us with the technicalities, to get to more extreme realms. Many less extreme realms exist naturally so of course one doesn’t need to produce them again, artificially, if he wants to study them.
Comment #10 November 3rd, 2012 at 1:46 am
In this comment, I’m going to assume that the Armchairians live in a completely classical universe — no quantum, sorry!
If the Armchairians were all powerful beings, then perhaps they would be satisfied by running algorithms (in their heads, I suppose, because they aren’t allowed to build computers) that predict future events based on statistical analyses of all past observations. Their algorithms would output statements such as, “Sunny with 1 – epsilon confidence, based on observed history.” Assuming their algorithms were optimal statistical inference programs, we can imagine that the Armchairians wouldn’t find any compelling reason to try to use any other prediction algorithm.
However, if we placed resource constraints on the Armchairians, such as limits on memory or the number of brain cycles they have available to them, then it seems that they’ll have to be much more clever in their prediction strategies. Suppose they had very limited memory; e.g. they can’t hope to keep track of all atom movements in the atmosphere. Instead, they’ll have to develop ways of succinctly explaining the patterns that they’ve seen over time, and storing those instead. General rules of thumb such as “it’s usually warm and sunny in the summer” are much easier to store and process than all weather data since the dawn of time. While the predictions produced by these heuristics may not be as detailed as those produced by the mega statistical inference engine of the previous scenario, these Armchairians will have to perform some “sparsification” of their observations if they hope to predict anything with their limited resources.
I’ll boldly claim that in the process of finding these succinct theories of their world, the Armchairians *must* develop a notion of cause and effect. What do I mean by a “notion of cause and effect”? In hand wavy terms, it’s the concept of an ordering relation on events: some events MUST precede other events; e.g. a glass cup does not shatter before it is manufactured. In their (efficient) prediction algorithms, the Armchairians will have to prune away ridiculous possibilities such as “glass cup shatters before it is manufactured”, though in a purely statistical mindset, they’d have to at least consider the probability.
Whatever their pruning method is, I’d call that a notion of “cause and effect”.
Comment #11 November 3rd, 2012 at 1:52 am
Sure they can do whatever we do, at worst with some (exponential?) slow down. whenever they would have wanted to do an experiment, they wait until the same experiment occurs naturally. (E. g If you wait long enough, a monkey doing random actions will perform Nobel prize winning experiments..)
so they should have the same notion of causality as us, only develop a much smaller set of inferences in the same time period.
Comment #12 November 3rd, 2012 at 5:24 am
Well, the fact they never take any actions does not mean there will no be actions of the world on them … Can an apple fall on the help of an Armcharian ?
Another question is can they observe without intervening ?
Comment #13 November 3rd, 2012 at 5:47 am
My first thought is that “making a prediction” based on having the goal of making an “accurate prediction” is a kind of action. But I suppose the point is that this is a kind of action that itself produces no effects? But wouldn’t a “more-accurate” prediction lead to subsequent more-accurate predictions? Perhaps this race would learn to design controlled “experiments” where such prediction-streams (initial more-accurate vs. initial less-accurate predictions) are isolated from one another to compare the “effects” of good and bad initial predictions on subsequent ones?
My second thought is that cause-effect reasoning is built into our perceptual systems. We cannot help but to experience perceptual causality even when temporal-spatial correlation is all we have to go on. But I suppose this is not a given because in the thought experiment we are talking about a hypothetical race…although its hard to imagine “intelligence” without understanding simple causal relations. Then again, human infants can do it without explicit understanding. But maybe this is your point? If this hypothetical race could not perceive causality implicitly would they never discover it explicitly?
Comment #14 November 3rd, 2012 at 5:50 am
Yes, they would develop the notion of cause and effect as it carries additional information and has better utility for making predictions over statistical correlations.
Of course originally all causation is inferred from statistical correlations but it also carries information about time ordering and the presence of a local chain (of similarly ordered pairs) of events linking cause and effect. Both pretty important when one wants to model reality.
Egg falling and breaking are correlated but while predicting that a falling egg will likely break makes sense predicting that a broken egg will likely fall does not.
Comment #15 November 3rd, 2012 at 6:19 am
A summary of my answer would be as follows.
1. In order to make accurate predictions, they would need explanations.
2. Explanations generally take the form “A happened because B happened”.
3. The word “because” implicitly suggests more than mere statistical correlation — something like a statistical correlation that fits into a theoretical picture — which it is reasonable to call a notion of causation.
4. What I’ve said above depends on what I mean by “developing the notion of cause and effect”, so somebody could agree with most of it but prefer not to call it a notion of causation. But I’m ready to defend my notion …
Comment #16 November 3rd, 2012 at 6:45 am
>> who never take any actions
Is it really possible to observe the world and not take any actions? I am not even talking about fancy collapse models in quantum theory, just the act of moving your eyes, paying attention to one sound and not another etc. and also
observing your own body as it breathes in and out …
Comment #17 November 3rd, 2012 at 7:13 am
reminds me of the cargo cultists.
purely based on observations, the armcharians would have made very wrong assumptions about those events.
so i’m afraid they would pile up invalid models of nature’s mechanisms.
some of their models would be correct, because they observed cause and effect directly.
but of course this does not exclude correct models, born from observing perfectly correlated events, which is a superset of the cause-and-effect events.
would they be able to see the difference between cause and effect observations, and observing perfectly correlated events?
but i guess that was the question.
Comment #18 November 3rd, 2012 at 7:15 am
OK, so I assume these armchairians would use a language different from ours. Let’s say we happened, in our galactic travels, on a library of writings of the armchairians. I think it would be very hard to decipher their language based on your assumptions, but maybe some of the books would incorporate pictures and somehow we would be able to translate some of it into english. Now let’s make one more assumption, namely that there are apple trees on the planet they live on. Then I think eventually we would find a book in the armchairians library which contains a sentence that *we* would translate like this: “If I put my armchair under an apple tree, then an apple will fall on my head eventually.”
See what I am saying?
Comment #19 November 3rd, 2012 at 8:54 am
First, observing is an action, it requires at least focusing one’s attention. Further, figuring out the underlying structure of reality requires even more action (breaking things and so on). I think this principle is involved even in our most basic concepts (see the importance of manipulation for educating children) and I am not sure that having a cognitive system like ours could happen to armchairians if they really do not act at all.
So depending on how passive they are, I suppose armchairians would have a very superficial knowledge of the world and a very primitive conceptual framework, and indeed correlations might suffice. For example, say you want to explain the movement of planets and stars: you can do that very passively, and incenditally don’t need a notion of causality for that, for the movement of stars might well be explained in terms of cosmic cycles.
Comment #20 November 3rd, 2012 at 9:24 am
This is a valid philosophical question — you might want to look at the discussions about ‘teleosemantics’ and the notion of the functional content of representations. Broadly speaking the claim is that it isn’t enough for a representation merely to have an information theoretic correlation with events in the real world, but must also be causally coupled in the sense that the representations must be attached to actions.
David Papineau and especially Nick Shea at KCL work on these issues.
Comment #21 November 3rd, 2012 at 10:25 am
Here’s my spout:
The only way to avoid having to take any actions is to exist outside of space and time and be able to view the whole 4-dimensional enchilada in one go in which case they would observe patterns but wouldn’t necessarily be motivated to postulate laws of physics – they might just be happy to explore this pretty thing called the universe and be content with correlation and their ability to observe a sample at time=t and predict what a sample at time=t+1 would look like. Of course if they have access to the whole of 4d-esty then they don’t need prediction because they can get 100% accuracy just by sampling, therefore we suppose that they want to do prediction as some form of playing a game to amuse themselves.
But maximising accuracy of prediction and also wanting to play the game of minimising the amount of sampling are conflicting goals – but let’s say a good result is to get high accuracy from low sampling rate.
If some armcharian compressed all of 4d into a minimal set of deterministic physical laws that generated everything then all they would need is to sample the starting conditions and they would get total accuracy therefore that would be a good result.
And there’s the rub – perhaps the universe isn’t very compressible due to quantum probabilistic effects.
Even without non-deterministic effects, compressibility is also limited by chaos – but wait – if the armchairians can generate the universe exactly and precisely then there is no chaos – their calculations are in effect an exact simulation of the universe. (assuming the 4d universe is described by finite information and hence also finitely generated)
Comment #22 November 3rd, 2012 at 10:53 am
To continue my previous comment: Chaos would be reintroduced if in addition to maximising accuracy and minimising sampling they also wanted to minimise number of computations by not doing an exact simulation.
Comment #23 November 3rd, 2012 at 11:17 am
There seems to be substantial agreement above that causal relations are a special type of stronger (more deterministic, more rule-like, more “if-then”-like) correlation that one arrives at by shedding or pruning away all the “weaker” correlations.
There also seems to be substantial agreement that causal relations are really useful, almost indispensable, to any person or machine who wants to make lots of predictions, because they are a sort of “approximation” that yields a substantial speedup and simplification in “approximate” inference.
So, have causal relations been studied before in quantum mechanics? Perhaps “consistent histories” is the study of causal relations in quantum mechanics? If so maybe Judea Pearl’s tools for studying causal relations in classical probability and “consistent histories” in QM are connected theories that could cross-pollinate?
Comment #24 November 3rd, 2012 at 11:25 am
I understood this as saying the answer is “yes, there is a notion of cause and effect in the data”: http://lesswrong.com/lw/ev3/causal_diagrams_and_causal_models/
Comment #25 November 3rd, 2012 at 12:22 pm
maybe I misunderstood the question and it’s not whether they would be *able* to infer casual relations but whether they would *want* to.
It’s hard to guess the culture of a hypothetical race. However it does not seem to be the case that people try to learn the laws of nature only because they want to exploit them by taking active actions.
If anything it seems like the other way around : if your goal is to find what actions will be most useful for you, then statistical correlations are good enough. The only reason we want to know “why” is our curiosity, which apparently is shared by the armcharians.
Comment #26 November 3rd, 2012 at 12:50 pm
At first sight the answer is straightforward: assuming strong AI and mind uploading are possible (I have discovered a truly marvelous proof of this, which this margin is too narrow to contain), we could ourselves live in virtual word, say within a computer lying in an armchair, and access slowed-down time through some window. The question then reduce to whether we still understand causality when watching a screen.
But in a sense this is to miss the point. The question is not whether Armchairians could be built by Movians, the question is wether Armchairians could develop the notion of cause and effect by themself (here we should add “with high probability/in time short engouh”, to specifically forbid random generators filling some lookup table).
If we take for granted that the answer is yes, then we have to explain why the following beliefs, once shared by many, turned false:
“I believe that in about fifty years’ time, it will be possible to programme computers (…) to make them play the imitation game so well that an average interrogator will not have more than 70 percent chance of making the right identification after five minutes of questioning” (Turing, 1950)
“machines will be capable, within twenty years, of doing any work a man can do.” (Simon, 1965)
Obviously, something turned bad. Obviously, Scott’s question is not interesting by itself (if we could already program Movians that do understand causality, who would actually cares if there exists a path for Armchairian to do so?), but as to suggest a road to the building of a true AI: let it experiment, let it see the consequences of it’s own actions, that’s may well be one of the keys we have missed. At least that what neuroscientists would suggest from the evidences of mirror systems.
Comment #27 November 3rd, 2012 at 1:25 pm
It seems like models where the statistical significance of variables changes over time would be the rub. I suspect that cause and effect and experimentation would do better at predicting the outcome.
An organism that has to rely only on large sets of data is going to be at a disadvantage in a rapidly changing system when the historical data is not predicting the current model. With only statistical correlation and no prediction of cause and effect, it seems that you could only understand that change was happening and wait for enough data to come in that predicts the new situation.
If on the other hand you were an organism that had made efforts to predicted possible causes and expected effects on top of your statistical models, you would be able to check those predictions against your changing system and see which were the most successful, while you waited for more data to support your predictions.
If you expand that and you are now an organism that can experiment with your predictions ahead of time, then you should be able to weight your predictions without having to wait for a change event to occur.
The general premise is that at any given time the universe around us is only displaying a small fraction of the potential of what is possible, so if we have to rely only on observed data, it seems unlikely that we would be able to predict how things can change. The sharpest curve can look like a line if you zoom in far enough.
Comment #28 November 3rd, 2012 at 1:29 pm
What exactly is a ’cause’? More importantly, is our scientific reasoning really based on an interplay of cause and effect?
I like the earlier example of water putting out fire. This is quite certainly a relationship between typical events of our every day experience. We start with the situation of a small fire (let’s say a candle that is lit) and a quantity of water (say, a full drinking glass). After observing this situation many times, we find that the fire ceases to exist if enough water is poured on it. I think the only difference between the Armchairians and us is that we are capable of finding this out faster, because we can leave our chair and pour the water ourselves.
But where is the cause and effect? All we really have is a sequence of situations:
1) a glass of water and a lit candle,
2) the pouring of water on the candle, and
3) less water and an unlit candle that is also wet.
Situation (3) can, of course, come about in a variety of ways. I think the sense in which we generally consider (2) to be a cause is not in the sense that there is an event that follows that could not have occurred without (2), but rather that the temporal path between events (1) and (3) cannot exist without event (2) or something similar. With no external influence, and in a reasonably small amount of time, situation (1) will not become situation (3).
Scientifically speaking, I don’t think we care about causality. Teleology, as far as I can tell, doesn’t really play a role in our reasoning process beyond a convenient fiction used to describe processes. We don’t worry about exactly how the chemicals in a beaker were prepared, only that they are presented to us and are somewhat understood. We might say that titration causes the liquid in the beaker to change colour, but this statement only has colloquial meaning. It’s really a complex interplay between various chemicals of diverse origins (you may have prepared the titrand, but maybe you bought the titrant from a lab somewhere), and no action is really identifiable as a ’cause’ (which drop caused the change in colour?). I think all scientific explanations bear this view out.
If our science is not really causal, then I don’t think the Armchairians will need causality either. I think ’cause’ and ‘effect’ is a crude and unnatural way to describe the interrelationship of different situations. The universe doesn’t yield to such elementary analysis. Effects have multiple causes, and causes have multiple effects.
Comment #29 November 3rd, 2012 at 2:46 pm
No because instead of saying that A causes B, they are content to say that “A at time t” is highly correlated with “B at time t+1.”
This is, I think, naive. I’m going with:
Yes because if they are smart as we are, and we can imagine Armchairians, then they can imagine non-Armchairian actors, and their accurate models of the world should include (crude) representations of non-Armchairian thought processes, which include models of cause and effect. e.g. even little kids can explain why a dog would do some behavior (running after a squirrel) in order to attempt to achieve some effect (catching the squirrel). So a moderately intelligent Armchairian, living in a world with hungry dogs, should be able to do the same.
Comment #30 November 3rd, 2012 at 3:14 pm
hmm, interesting question and awesome blog!
it could be that causality is a consequence of our appreciation of the privileged nature of 3+1 spacetime [1], which case the Armchairian might potentially derive a similar concept?
correlations focusing on other dimensions might have different names (perhaps displacement, conservation of mass).
hmm, but why do we perceive reality as a having 3 spatial and 1 temporal dimensions? perhaps that allows macro-phenomenon to be approximated with simple heuristics, giving that mental model an evolutionary advantage [2]?
or one can fall back to the idea that: “time is nature’s way of keeping everything from happening at once.” [3]
scott aaronson is the master!
[1] http://en.wikipedia.org/wiki/Spacetime#Privileged_character_of_3.2B1_spacetime
[2] http://en.wikipedia.org/wiki/Evolutionarily_stable_strategy
[3] http://books.google.com/books?id=39KQY1FnSfkC&pg=PA98
[disclaimer: yes, much of this comment is mumbo-jumbo and i’m drunk…]
Comment #31 November 3rd, 2012 at 3:30 pm
My answer is not just yes, but heck yes! (Pardon my harsh language.)
Even a mind only concerned with statistical correlations is going to need an efficient way of representing them and storing them. And if their universe has the kind of structure necessary for prediction to work at all, then there will be more efficient ways of storing it than the super-exponentially large table of entries that say “Ai is correlated with Aj when you condition on/control for Ak, Am, An …, but not when you control for Bk, Bm, Bn …”.
And the best way (IIRC) we know of summarizing this information is with a Bayes net, which requires the minimum (or at least a polynomial) amount of space to represent all of those conditional (in)dependencies, as it removes all the entries you would otherwise need to store when the Markov condition holds (i.e. when you only need to look at a finite set of variables, “neighbors”, to infer all correlations).
And implicit in a Bayes net is a concept isomorphic to (our best understanding of) causality: the direction of (i.e. asymmetry in) the arrows: if A and B are correlated when you don’t condition on H, but uncorrelated when you do condition on H, then you should draw arrows from H to A and B. But if the opposite is true (A and B are correlated when you do condition on H but not when you don’t), then you draw the arrows from A and B to H. (And so on for the various other kinds of relationships.)
So even if they don’t call it causality, the notion (under some reasonable definition) will be implicit in their complexity-optimal models for representing these correlations.
Comment #32 November 3rd, 2012 at 3:33 pm
Also, what Max_M’s link said.
Comment #33 November 3rd, 2012 at 3:54 pm
Can the armcharians perceive the passage of time?
Is it possible to perceive events in time and not experience the asymmetry of cause-effect relations?
Comment #34 November 3rd, 2012 at 4:38 pm
Wouldn’t they have to think of their observations as the cause for the predictions they’d come up with?
Comment #35 November 3rd, 2012 at 5:00 pm
Armchairians existed. They are known by the name “ancient greek philosophers” and they lived 1500 years before Roger Bacon had the brilliant idea of putting forward the experimental method.
Comment #36 November 3rd, 2012 at 5:57 pm
In my youth I heard repeated claims that dolphines are as intelligent as humans or even much much more so, and to my surprise these clains are still around http://macedoniaonline.eu/content/view/18603/56/ and were even manifested in the “Hitchiker guide to the galaxy”.
So if indeed dolphines are hyperintelligent (I am skeptical, but, you know,,,) then they can serve as the armchairians for the purpose of Scott and Pedro’s thought experiment! In fact we can simply *assume* that dolphines are hyperinteligent for the sake of the thought experiment. (Strictly speaking Dolphines don’t have armchairs, any kind of chairs or even notable arms, but otherwise they fit perfectly.)
So do you think that dolphines understanding of causality compared to their understanding of correlation is much smaller than our understanding of causality compared to our understanding of correlations? (Actually, if dolphines are hypersmart they can give us some useful tips for living underwater re: the previous gloomy post.)
Comment #37 November 3rd, 2012 at 6:05 pm
Alexander Clark #20,
Thx for pointing this. Could you provide a short list of papers?
Comment #38 November 3rd, 2012 at 6:33 pm
There is no a priori reason to make any kind of causal inferences, as Hume noted. Whether we participate or merely observe does not change this. We are born with minds that expect a universe with some degree of statistical correlation between precedents and antecedents, and that is what we end up observing. Would they “develop” the idea on their own? I would say only if they were subject to evolutionary forces, as we were. But if the only observe, and do not participate, they probably would not.
Comment #39 November 3rd, 2012 at 6:46 pm
chorasimilarity #35:
Armchairians existed. They are known by the name “ancient greek philosophers” and they lived 1500 years before Roger Bacon had the brilliant idea of putting forward the experimental method.
But did ancient Greek philosophers actually care about making accurate predictions? From my limited knowledge, my impression is that they didn’t: they were interested in questions like “what is justice?” and “what is the ideal ruler?,” not so much in predicting phenomena around them (with the interesting possible exception of astronomy—where, of course, their causal explanations were fanciful and wrong). If they had cared more about prediction, is it possible that they would have invented the experimental method?
Comment #40 November 3rd, 2012 at 6:51 pm
@zabnolar: In an anthropic vein, Max Tegmark makes the argument that a universe with more or less than 1 unidirectional (temporal) dimension would make prediction difficult:
“With more or less than one time dimension, the partial differential equations of nature would lack the hyperbolicity property that enables observers to make predictions.”
“[I]f observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability, then all such ensemble theories may actually predict that we should find ourselves inhabiting a (3 + 1)-dimensional spacetime with 100% certainty, as illustrated in figure 1 […]”
http://space.mit.edu/home/tegmark/dimensions.pdf
Fascinating result. An anthropic basis for the existence of temporal correlations and a single time dimension.
Comment #41 November 3rd, 2012 at 11:39 pm
Perhaps it’s hypothetically possible that we only perceive order and causality because we ignore observations that contradict our biases. Which would be more likely:
a) We live in a disordered (or even uncomputable) universe, but believe it’s predictable because of our own selective (or manufactured) perceptions.
b) We live in an ordered universe and our perceptions are well-grounded.
Biased entities might believe in order regardless of external events, and can exist in any universe. Reliable observers believing in order are only likely in rarer, low-entropy universes. Pseudo-observers increasingly outnumber reliable ones as entropy increases. Entities in (a) might not be very stable, even though they might firmly believe they are!
Along those lines, the Boltzmann Brain paradox suggests it’s all a mirage:
“In an infinite universe, the number of self-aware brains that spontaneously randomly form out of the chaos, complete with false memories of a life like ours, should vastly outnumber the real brains evolved from an inconceivably rare local fluctuation…”
http://en.wikipedia.org/wiki/Boltzmann_brain
Self-awareness might imply a belief in causality. Can a being recognize itself if its memory is just a set of uncorrelated states? …
Comment #42 November 4th, 2012 at 1:38 am
w.r.t “Greek Philosophers”:
The ‘Armchairians’ sound a lot like the prisoners in Plato’s “Allegory of the Cave”, who are:
“…a group of people who have lived chained to the wall of a cave all of their lives, facing a blank wall. The people watch shadows projected on the wall by things passing in front of a fire behind them, and begin to ascribe forms to these shadows. According to Plato, the shadows are as close as the prisoners get to viewing reality.”
Comment #43 November 4th, 2012 at 3:24 am
Scott #35, according to Aristotle, Thales of Miletus, the eldest of them, “reserved [olive] presses ahead of time at a discount only to rent them out at a high price when demand peaked, following his predictions of a particular good harvest. Aristotle explains that Thales’ objective in doing this was not to enrich himself but to prove his fellow Milesians that philosophy could be useful, contrary to what they thought.”[wiki dixit]
He also predicted, according to Diogenes Laertius, a sun eclipse which shortened a war.
I can predict that, in 2000 years from now, there will be similar stories about Turing of Cambridge, his machine and contributions to a local war in this part of the galaxy.
Comment #44 November 4th, 2012 at 5:36 am
Correlation implies causation if there is no unobserved confounding, and the direction is clear. With a sufficiently granular/detailed model of at least Newtonian level things all unobserved confounding goes away. If, in their quest for predictive quality, Armchairians actually get enough granularity in their models, they will end up being causal, or at least one would be able to derive causal information from them.
Comment #45 November 4th, 2012 at 5:40 am
I would go with No.
1. Without acting they do not need “cause” and “effect” terms.
2. The 100% correlation between two events are not enough for two to be cause and effect. (P=1 can still lead to contradictory observation, while cause-effect relation cannot)
3. They can learn data patterns similar to image recognition in human visual system, and that has nothing to do with causation – visual system exist for much longer time than cause -effect terms or any terms expressed in language.
4. So they can learn statistical model of the world if they leave long enough, but since they do not act, they will not develop language to share their model, nor to define terms cause and effect.
5. Since they do not act they will decay, due to acting of external world.
Comment #46 November 4th, 2012 at 10:52 am
You can derive causality from correlations, since it predicts what happens under parameter variation in a simple way.
No guarantee that a species that haven’t evolved to consider actions, reactions and threathening or helpful agents could do this of course. But the principle is simple enough.
@ Arnie:
One of the beauties of eternal inflation, which is damned hard to avoid in an inflationary cosmology such as the current, is that BBs goes away as much less likely. See Susskind and Bousso lately.
Of course, then you meet the premature fiery* end of the universe instead (Bousso 2010), but I think Susskind got rid of it in his tree models even if he doesn’t say so explicitly (2012) and I assume Bousso still disagrees. A universe with only ~ 5 billion years left was hard to stomach! =D
* Which comes out of current hypotheses on what infalling observers may see in black holes, I take it.
Comment #47 November 4th, 2012 at 2:52 pm
Just for pedantry: maybe notion of cause-effect is better described with an assymetrical stuff such as odds ratio, not with statistical correlations.
Comment #48 November 4th, 2012 at 3:21 pm
Landauer’s principle would at least relate their thought to global warming :D. If the number of information bits processed inside the brain of the Armchairian is n, total dissipated energy is nkTln2.
Comment #49 November 4th, 2012 at 4:35 pm
Isn’t the real question here not whether the Armchairians would notice the patterns that we call causes, but whether they would distinguish them as a particularly interesting, special class of correlations?
Or rather, what classes of patterns would they consider interesting, in the absence of an interest in affecting the world?
Comment #50 November 4th, 2012 at 9:05 pm
Armchairian physics is a great topic, and as a specific topic of inquire, it is (for me) fun to speculate whether the Armchairian culture might (sooner or later) discover the Three Laws of Thermodynamics? And if so, by what observational/mathematical path?
Here are some reasons why the Armchairian Culture might discover the Three Laws comparably fast to our own culture, and perhaps even understand the Three Laws more deeply than we do.
We will presume that the Armchairians enthusiastically contemplate all of the chemistry and physics that they see in their 17th-century kitchens, fields, and blacksmith shops … or when sailing, mountain-climbing, or sky-gazing … and we assume further that the Armchairians are outstanding geometers and algebraists. The Armchairians therefore have all they require to deduce:
• The Zeroth Law By observing that dynamical systems in contact equilibriate to the same temperature (observed in cooking).
• Matter is Atomic By contemplating the effects of oil-on-water (for example).
• The First Law By observing conservation of mass, light, momentum, and charge (subtly from lightning).
• Hamiltonian Dynamics The natural microscopic foundation for the First Law, and the natural macroscopic foundation for planetary motion.
• The Second Law Predicted from Hamiltonian dynamics viewed a symplectomorphic flow, affirmed by the observed subtleties of entropic flow in living ecosystems.
• The Third Law As explained by Lindbladian equilibriation; as theoretically deduced as the unique, mathematically natural, non-classical generalization of classical Hamiltonian dynamics; as observationally required by the observed absence of ultraviolet radiation from hot ovens and campfires!
By the above research path, the Armchairians might plausibly evolve a better appreciation of quantum dynamics (in some respects) than we Experimentarians possess … particularly in regard to quantum localization phenomena!
In regard to the entropic arrow of time, and/or quantum localization dynamics, and/or the Third Law, there is a considerable modern literature, some of which I have referenced on GLL in the context of the Kalai-Harrow Debate.
It is fair to say (perhaps) that our own culture’s understanding of quantum thermodynamics is (surprisingly) not notably advanced beyond what Armchairian culture might plausibly have achieved! 🙂
Comment #51 November 4th, 2012 at 9:40 pm
Comment #52 November 5th, 2012 at 5:36 am
A celebrated Armchairian manifesto, by the redoubtable thermodynamicist Clifford Truesdell, appears in the introduction to his textbook The Non-Linear Field Theories of Mechanics:
Caveat This is the same Clifford Truesdell who authored (serious) articles with titles like “The computer: ruin of science and threat to mankind” (1984)! 🙂
Comment #53 November 5th, 2012 at 7:48 am
It all depends on which kind of complexity theory they would believe in. If they were votaries of average-case analysis, they would be satisfied with correlation; the more pragmatic typical-case types would cherish the notion of causality. As for the worst-case fanatics, the less said the better: they wouldn’t bother with predictions until they prove NP = P.
Comment #54 November 5th, 2012 at 4:19 pm
I’m going to go with option 3:
‘It depends entirely on what we mean by “developing the notion of cause and effect”‘
One simple way of mathematizing “cause and effect” is to factor a joint distribution in terms of conditional probabilities.
There are some apparently natural mathematical definitions which can allow one to derive unique factorizations of a joint distribution into tables of conditional probabilities.
One example (of many):
http://en.wikipedia.org/wiki/Bayesian_information_criterion
Thus if the Armchairians can do something like the mathematical reasoning we are familiar with, they could reasonably be expected to have the capability of reasoning about something formal that equates pretty well with our notion of cause and effect. This is no different from our ability to reason about a mathematical model of the universe which lacks cause and effect (presumably mostly not very interesting models to us, but we can nonetheless reason about them).
On the other hand, would an Armcharian venture to make an absolute statement about cause and effect? In fact, should even those of us capable of interventionist experiments make such a statement? I would argue no. It is always possible (although vanishingly improbable), that in a finite numbers of samples of an experiment we have seen a series of outcomes that would lead us to an incorrect conclusion (unless you are assuming a deterministic universe and a sufficiently rich experimental model to capture this determinism).
The reason interventionist experiments seem the natural gold standard for causation is that they exactly sample from the distribution of interest. Mathematically: P(outcome | intervention leading to an event A) rather than P(outcome | A). The former is the distribution of interest precisely because we have the *option* of sampling from it in the future, and depending on the nature of the intervention there can be subtle differences between the two (we rarely have an intervention that we can be confident will produce exactly and only A). To Armchairians this would likely be of much more theoretical interest, since they do not have a natural reason to care about potential distinctions between A and some intervention leading to A.
Comment #55 November 5th, 2012 at 5:24 pm
Continuing John’s comments on Truesdell, his most entertaining work by far is “An Idiot’s Fugitive Essays on Science: Methods, Criticism, Training, Circumstances”.
Check it out.
Comment #56 November 5th, 2012 at 8:44 pm
The psychology of Simpson’s paradox implies that humans have a basic (whether innate or just learned very early is moot) predilection to analyze events in terms of causality. Perhaps the Armchairians would see no paradox!
Comment #57 November 6th, 2012 at 4:44 am
E #54. If cause is unobservable, but you have two consequences slightly separated in time, the only way to distinguish mere correlation from causation is to perturb (i.e. perform controllable experiment) earlier consequence, and see whether it effects the later one.
Moreover, the only effect can be derived, for which external world performs experiment for you, and performs it frequently enough to compute statistics. So, it is very hard to imagine what would lead to the prediction of computer design with its operations (given that core of it is from quantum mechanics – band structure of solid state bodies ). It took many controlled experiments based on the results of previous experiments in refining, and cleaning conditions, that it has very small probability of being performed by the nature in natural conditions.
Comment #58 November 6th, 2012 at 11:08 am
It seems to me that simply making inferences of any kind forces the Armcharians to follow a model of cause and effect. You start with some set of axioms, theorems, data, conclusions, and rules of inference. If you observe more data, you apply your axioms, theorems, and rules to produce more conclusions. Voila… cause and effect.
Comment #59 November 6th, 2012 at 10:04 pm
Pearl was inspired by engineering, the non-armchairian faith.
Comment #60 November 7th, 2012 at 7:51 am
Sorry, odds ratio is also symmetric. Maybe something like
P(A OR NOT B) ? Also not quite good. Any other asymmetrical measures?
Comment #61 November 7th, 2012 at 5:44 pm
Michael Vassar: are you disputing to my claim about Pearl? In any event, what do you mean by “inspired” and what leads you this belief?
Pearl certainly was an engineer who studied decision theory, so he was even more contaminated by causal thinking than most humans. I probably should not have said Pearl claimed to be an armchairian, just that he claimed to have at some point disbelieved in causality and derived a belief in causality from non-causality (a claim that I misunderstood, see end). If he developed bayes nets without seeking causality, it is easy to imagine armchairians doing the same thing.
In the 1982 paper about tree bayes nets, Pearl does not mention causality. In 1984 or 1985, he says “This paper takes the position that human obsession with causation is computationally motivated. Causal models are only attractive because they provide effective data-structures for representing empirical knowledge…” which seems to be the assertion that armchairians would introduce such models. I don’t put much stake in an argument from authority: what does he know of armchairians? If he developed the 1982 paper with no thought of causality, I think that is strong evidence. But the lack of mention of causality in the paper is only weak evidence of his thoughts.
In the 1985 paper of full-fledged DAG bayes nets, he is more enthusiastic about causality, but is still nervous about its reality.
Actually, I misremembered the passage that lead me to describe past-Pearl as an armchairian. He does not claim to have ever disbelieved in causality or avoided talking about it (though he does seem to avoid it in the 1982 paper). From the preface of Causality, the passage is: “Ten years ago [in 1988] I was working in the empiricist position…[I held] that] causality simply provides useful ways of abbreviating and organizing intricate patterns of probabilistic relationships…I now take causal relationships to be the fundamental building blocks…” He is talking about a later transition. If he could make that transition, maybe armchairians could, but it is pretty weak evidence. But I don’t think the armchairians need to make that transition to count for Scott’s purposes.
Comment #62 April 12th, 2013 at 6:31 am
If the sole goal of the Armchairians is to observe the world around them, then they will surely report on the cyclical nature of many events. Some examples would be the housing/proerty cycle or stock market cycle. Both exhibit classic human traits of greed, as in a rapidly increasing stock market or of property prices to unsustainable levels coupled with so called experts telling everyone it is different this time. This is followed by a rapid decline in stock or property prices excellerated by fear.
The Armchairians would have noted this recurring cycle of events and our apparent inability to learn from history.