Hm, I think I'm inclined to agree with the excerpt from the book, that correlation is necessary (just not sufficient) for causation. I'm prepared to be wrong, but at very least, that's not at all a satisfying counter-example:
> The correlation between pressing on the gas and the speed of the car is zero but they’re obviously causally related, it’s that the agent is optimizing speed!
Why are they 'obviously causally related'? Pushing the accelerator causes something, but only indirectly and not always a change in speed, as stated in other passages.
If I cycle home I'll probably want to have a shower, but pedalling doesn't cause me to get wet?
The reason it is causally related is that if you were to not push the pedal at any of those instances, the car would move slower than if you were to push it faster.
There's also a causal effect from biking to showering, although there are a few other things in the causal path such as getting sweaty. If you walked home instead of biking, you might avoid the shower. So biking does cause you take a shower.
> if you were to not push the pedal at any of those instance
That's the key to it IMHO. There has to be isolation for identifying causal relationships. Science is the work to be sure you're measuring the thinnest partial derivative.
I'd generalize it to "All else being equal"
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On another note, I believe there are classes in causality, arranged in a hierarchy. If you're studying the 'physical' class (level 0), you'll end up with causators in the same level or higher ('system' class, level 1).
In our case the 'all things being equal' has to take account of an instance of a higher class (the human 'system' regulating the fuel input with the pedal)
The level 2 would be system of systems; for example processes like the Darwinian evolution.
It's precisely this 'at any of those instances' and 'path' of causations that aren't sitting comfortably with me; primarily the first, but when it interacts with the latter and things are related by physics and derivatives w.r.t. time say, it's not any of more a causal factor than any other input?
If all we mean by 'x causes y' is that 'y is a function of (perhaps among other things) x', then.. fine?
I made up these phrases to give a simple explanation instead of causal inference terms, and they are probably not good terms, so sorry for the confusion.
If I describe it in more standard vocabulary, 'at any of those instances' refer to doing interventions (such as randomized controlled trials).
As far as I'm inclined to agree, that causation can't be easily defined, I believe that your cycling argument is incorrect. Not only because of what the @dentalperson wrote below (they are completely right that there is a crucial difference), but also because it doesn't follow the human intuition on causation.
I understand the sentiment though. Causation should imply correlation at least on a "direct" level. Pressing the gas pedal correlates with the higher speed of the engine, not the vehicle speed. I believe the problem lies in our ability to detect the correlation. Sometimes, the correlation may go undetected (as in the case, when we ignore the engine speed in the vehicle example). I would be very happy to hear a stronger argument against "causation -> correlation" :)
> I believe that your cycling argument is incorrect. Not only because of what the @dentalperson wrote below (they are completely right that there is a crucial difference), but also because it doesn't follow the human intuition on causation.
Well, I was looking for an example that didn't, because my position was 'why is that obviously causal', so I wanted something that seemed silly to suggest was causal, but is IMO equivalent. To clarify it a bit:
Pedalling causes my core temperature to increase; which causes my body to regulate it by sweating; which causes me to desire a shower; which (may) cause me to decide to have a show; which will cause me to get wet.
If we assume I always decide to have a shower when I desire one, then there's a complete chain of causal events, but it seems silly to say 'pedalling causes me to get wet'.
But it's not just the chain that I find troubling; even in shorter examples other 'inputs' (like the decision here if we remove that assumption) make it seem unfair to call it causation to me.
Maybe it's all just semantic, hinging entirely on how you define 'causation', and doesn't matter at all.
I am not convinced. Pressing the gas makes the car to go faster independently of whether it is on the hill or not. That's the causation and a correlation.
If you compare some observable at one point with the parameter value in another it is not the new Kahneman book who does stupid mistakes.
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[ 4.0 ms ] story [ 31.4 ms ] thread> The correlation between pressing on the gas and the speed of the car is zero but they’re obviously causally related, it’s that the agent is optimizing speed!
Why are they 'obviously causally related'? Pushing the accelerator causes something, but only indirectly and not always a change in speed, as stated in other passages.
If I cycle home I'll probably want to have a shower, but pedalling doesn't cause me to get wet?
There's also a causal effect from biking to showering, although there are a few other things in the causal path such as getting sweaty. If you walked home instead of biking, you might avoid the shower. So biking does cause you take a shower.
That's the key to it IMHO. There has to be isolation for identifying causal relationships. Science is the work to be sure you're measuring the thinnest partial derivative.
I'd generalize it to "All else being equal"
----
On another note, I believe there are classes in causality, arranged in a hierarchy. If you're studying the 'physical' class (level 0), you'll end up with causators in the same level or higher ('system' class, level 1).
In our case the 'all things being equal' has to take account of an instance of a higher class (the human 'system' regulating the fuel input with the pedal)
The level 2 would be system of systems; for example processes like the Darwinian evolution.
If all we mean by 'x causes y' is that 'y is a function of (perhaps among other things) x', then.. fine?
'causal path' refers to a path in a directed acyclic graph that models the causality. https://cran.r-project.org/web/packages/ggdag/vignettes/intr... has some examples.
I understand the sentiment though. Causation should imply correlation at least on a "direct" level. Pressing the gas pedal correlates with the higher speed of the engine, not the vehicle speed. I believe the problem lies in our ability to detect the correlation. Sometimes, the correlation may go undetected (as in the case, when we ignore the engine speed in the vehicle example). I would be very happy to hear a stronger argument against "causation -> correlation" :)
Well, I was looking for an example that didn't, because my position was 'why is that obviously causal', so I wanted something that seemed silly to suggest was causal, but is IMO equivalent. To clarify it a bit:
Pedalling causes my core temperature to increase; which causes my body to regulate it by sweating; which causes me to desire a shower; which (may) cause me to decide to have a show; which will cause me to get wet.
If we assume I always decide to have a shower when I desire one, then there's a complete chain of causal events, but it seems silly to say 'pedalling causes me to get wet'.
But it's not just the chain that I find troubling; even in shorter examples other 'inputs' (like the decision here if we remove that assumption) make it seem unfair to call it causation to me.
Maybe it's all just semantic, hinging entirely on how you define 'causation', and doesn't matter at all.