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> there needs to be some causal connection between the two Umm.. No, there doesn't... This idea features in the earlist 20th C. writings on statistics, but it'

> there needs to be some causal connection between the two Umm.. No, there doesn't... This idea features in the earlist 20th C. writings on statistics, but it's pseudoscience. If one carves up the whole history of the entire universe into all possible events, then there's likely to be a (near) infinite number of pairs of events which "perfectly" co-vary without any causal connection whatsoever. Indeed, one could find two galaxies that are necessarily causally isolated and find correlated events. This is, in part, because the properties of two casually independent systems can have indistinguishable distributions -- just by the nature of what a distribution is. It's this sort of thinking that I was aiming to rule out: really they have nothing to do with each other. It's early 20th C. frequentist pseudoscience that has given birth to this supposed connection, and it should be thrown out all together. Causation is a property of natural systems. Correlation is a property of two distributions. These have nothing to do with each other. If you want to "test" for causation, you need to have a causal theory and a causal analysis in which "correlation" shouldn't feature. If you induce correlation by causal intervention, i'd prefer we gave that a different name ("induced correlation") which is relevant to causation -- and it's mostly this confusion which those early eugenticists that created statistics were talking about.

Izkata 2y ago
Examples: https://www.tylervigen.com/spurious-correlations https://www.tylervigen.com/spurious-correlations
kqr 2y ago
> If one carves up the whole history of the entire universe into all possible events, then there's likely to be a (near) infinite number of pairs of events which "perfectly" co-vary without any causal connection whatsoever. But if they are not linked by a stable causal connection, wouldn't they eventually diverge, if we observe long enough?
- godelski 2y ago
  There's subtleties in what you two are saying that I think are leading to miscommunication. I think it is better to think about this through mutual information rather than "correlation"[0], adding DAGs (directed acrylic graphs) also helps but are hard to draw here. If causation exists between A and B, the two must also have mutual information. This is more akin to the vernacular form of "correlation" which is how I believe you are using it. But statisticians are annoying and restrict "correlation" to be linear. In that case, no, causation does not necessitate nor imply linear correlation (/association). For mjburgess's universe example, I think it may depend on a matter of interpretation as to what is being considered causal here. A trivial rejection is that causation is through physics (they both follow the same physics) so that's probably not what was meant. I also don't really like the example because there's a lot of potential complexity that can lead to confusion[1], but let's think about the DAG. Certainly tracing causality back both galaxies converge to a single node (at worst, the Big Bang), right? They all follow physics. So both have mutual information to that node. *BUT* this does not mean that there is an arrow pointing from one branch to the other branch. Meaning that they do not influence one another and are thus not causally related (despite having shared causal "history", if you will). Maybe let's think of a different bland example. Suppose we have a function f(x) which outputs a truly random discrete outputs that are either 0 or 1 (no bias). Now we consider all possible inputs. Does there exist an f(a) = f(b) where a ≠ b? I think with this example we can see believe this is true but you can prove it if you wish. We can even believe that there is a stronger condition of a having no mutual information between a and b. In the same way here, if we tracked the "origin" of f(a) and f(b) we would have to come through f (f "causes" f(a) and f(b)), but a and b do not need to be constructed in any way that relates to one another. We can even complexity this example further by considering a different arbitrary function g which has a discrete output of [-1,0,1], or some other arbitrary (even same) output, and follow the same process. When doing that, we see no "choke point" and we could even pull a and b from two unrelated sets. So everything is entirely disjoint. Try other variations to add more clarity. [0] I also corrected mjburgess through this too because a subtle misunderstanding led to a stronger statement which was erroneous https://news.ycombinator.com/item?id=41228512 https://news.ycombinator.com/item?id=41228512 [1] Not only the physics part but we now have to also consider light cones and what physicists mean by causation
- mjburgess 2y ago
  > But if they are not linked by a stable causal connection, wouldn't they eventually diverge, if we observe long enough? I'm not sure why you would think so. All that's required is that the process they are following to generate observables is deterministic or law-like random . Consider a possible universe where everything is deterministic, and at t=0 N=infinity objects created each with some very large number of measurable properties. Some never change, so property p=1,1,1,1,1,1,1, etc. forever. Some change periodicially, p=1,0,1,0,1... etc. Now I dont really see why there wouldn't be an infinite number of correlated such properties of objects with no casual relationship whatsoever. Maybe you want to claim that the actual universe is chaotic over long time horizons, with finite objects, finite properties, etc. and as t->inf the probability of finding properties which "repeat together" goes to zero. ... like, Maybe, but that's a radical claim. I'd say its much more likely that, eg., some electron orbiting some atom somewhere vs. some molecule spinning, etc. will always be correlated. Just because there's so many ways of measuring stuff, and so much stuff, that some measures will by chance always correlate. Maybe, maybe not. The point is that the world does not conspire to correlate our measures when causation is taking place. We can observe any sort of correlation (including 0) over any sort of time horzion and still there be no causation. In practice, this is very common. It's quite common to find some measurable aspects of some systems, over horizons we measure them, to "come together in a pattern" and yet have nothing to do with each other. I regard this as the default, rather than vice versa. At least every scientist should regard it as the default.. and yet, much pseudoscience is based on a null hypothesis of no pattern at all.

Izkata 2y ago

Examples: https://www.tylervigen.com/spurious-correlations https://www.tylervigen.com/spurious-correlations

kqr 2y ago

> If one carves up the whole history of the entire universe into all possible events, then there's likely to be a (near) infinite number of pairs of events which "perfectly" co-vary without any causal connection whatsoever. But if they are not linked by a stable causal connection, wouldn't they eventually diverge, if we observe long enough?

godelski 2y ago
There's subtleties in what you two are saying that I think are leading to miscommunication. I think it is better to think about this through mutual information rather than "correlation"[0], adding DAGs (directed acrylic graphs) also helps but are hard to draw here. If causation exists between A and B, the two must also have mutual information. This is more akin to the vernacular form of "correlation" which is how I believe you are using it. But statisticians are annoying and restrict "correlation" to be linear. In that case, no, causation does not necessitate nor imply linear correlation (/association). For mjburgess's universe example, I think it may depend on a matter of interpretation as to what is being considered causal here. A trivial rejection is that causation is through physics (they both follow the same physics) so that's probably not what was meant. I also don't really like the example because there's a lot of potential complexity that can lead to confusion[1], but let's think about the DAG. Certainly tracing causality back both galaxies converge to a single node (at worst, the Big Bang), right? They all follow physics. So both have mutual information to that node. *BUT* this does not mean that there is an arrow pointing from one branch to the other branch. Meaning that they do not influence one another and are thus not causally related (despite having shared causal "history", if you will). Maybe let's think of a different bland example. Suppose we have a function f(x) which outputs a truly random discrete outputs that are either 0 or 1 (no bias). Now we consider all possible inputs. Does there exist an f(a) = f(b) where a ≠ b? I think with this example we can see believe this is true but you can prove it if you wish. We can even believe that there is a stronger condition of a having no mutual information between a and b. In the same way here, if we tracked the "origin" of f(a) and f(b) we would have to come through f (f "causes" f(a) and f(b)), but a and b do not need to be constructed in any way that relates to one another. We can even complexity this example further by considering a different arbitrary function g which has a discrete output of [-1,0,1], or some other arbitrary (even same) output, and follow the same process. When doing that, we see no "choke point" and we could even pull a and b from two unrelated sets. So everything is entirely disjoint. Try other variations to add more clarity. [0] I also corrected mjburgess through this too because a subtle misunderstanding led to a stronger statement which was erroneous https://news.ycombinator.com/item?id=41228512 https://news.ycombinator.com/item?id=41228512 [1] Not only the physics part but we now have to also consider light cones and what physicists mean by causation
mjburgess 2y ago
> But if they are not linked by a stable causal connection, wouldn't they eventually diverge, if we observe long enough? I'm not sure why you would think so. All that's required is that the process they are following to generate observables is deterministic or law-like random . Consider a possible universe where everything is deterministic, and at t=0 N=infinity objects created each with some very large number of measurable properties. Some never change, so property p=1,1,1,1,1,1,1, etc. forever. Some change periodicially, p=1,0,1,0,1... etc. Now I dont really see why there wouldn't be an infinite number of correlated such properties of objects with no casual relationship whatsoever. Maybe you want to claim that the actual universe is chaotic over long time horizons, with finite objects, finite properties, etc. and as t->inf the probability of finding properties which "repeat together" goes to zero. ... like, Maybe, but that's a radical claim. I'd say its much more likely that, eg., some electron orbiting some atom somewhere vs. some molecule spinning, etc. will always be correlated. Just because there's so many ways of measuring stuff, and so much stuff, that some measures will by chance always correlate. Maybe, maybe not. The point is that the world does not conspire to correlate our measures when causation is taking place. We can observe any sort of correlation (including 0) over any sort of time horzion and still there be no causation. In practice, this is very common. It's quite common to find some measurable aspects of some systems, over horizons we measure them, to "come together in a pattern" and yet have nothing to do with each other. I regard this as the default, rather than vice versa. At least every scientist should regard it as the default.. and yet, much pseudoscience is based on a null hypothesis of no pattern at all.