Does butterfly affect?

Let us ignore quantum indeterminacy.

The butterfly effect comes from chaos theory. The word "cause" as used in chaos theory means whether the a change to an initial state from $t_a$ to $t_b$ of a system from will change a final state $f_a$ to final state $f_b$. Human intentional control is irrelevant.

In this comment I use chaos theory's definition of "cause".

But can we really say that this impurity “caused” the transition?

Yes.

This seems to depend on the counterfactual world: what would have happened otherwise?

The water wouldn't have transitioned at that point in time. (Assuming there no other perturbation.)

Would the hurricane have happened if not for the butterfly?

Probably not. (Rounds to zero.)

Do you buy the logic - and the conclusion?

No. You are conflating two different uses of the word "cause". One is a vague philosophical definition involving human intention. The other is a technical definition derived from mathematics.

You never defined the word "cause". I think that if you rigorously defined the word "cause" at the beginning of your post then your argument would selfdestruct. Either it would no longer apply to chaos theory or it would no longer apply to your scenarios involving human intentionality.

[Edit: This is overly harsh. See continued discussion.]

Or is this a bit of a straw-man argument, and people don't really think this way about causes?

A straw-man argument is performed with the wrong intentions. I don't think your argument is straw-man. Your intentions are fine. Your words are clear, coherent and falsifiable. Your argument is merely wrong.

[Edit: This is overly harsh. See continued discussion.]

I commented [LW(p) · GW(p)] about this on a related post.

Would the hurricane have happened if not for the butterfly?

You are talking about counterfactuals, and those a difficult problem to solve when there is only one deterministic or probabilistic world and nothing else. A better question is "Does a model where 'a hurricane would not have happened as it had, if not for the butterfly' make useful and accurate predictions about the parts of the world we have not yet observed?" If so, then it's useful to talk about a butterfly causing a hurricane, if not, then it's a bad model. This question is answerable, and as someone with an expertise in "complexity science," whatever it might be, you are probably well qualified to answer it. It seems that your answer is "the impact of butterfly’s wings will typically not rise above the persistent stochastic inputs affecting the Earth, " meaning that the model where a butterfly caused the hurricane is not a useful one. In that clearly defined sense, you have answered the question you posed. 

Instead, we must consider the full statistical ensemble of possible world, and quantify to what extent the butterfly shifts that ensemble.

add some small stochastic noise to it at all times t to generate the statistical ensemble of possibilities

In the typical scenario, the impact of this single perturbation will not rise above the impact of the persistent background noise inherent to any complex real-world system.

I think these quotes illustrate the mind projection fallacy. The "noise" is not an objective thing sitting out there in the real world, it is a feature of your own uncertainty. 

Suppose you have a computational model of the weather. You make the simplifying assumption that water evaporation is a function only of air temperature and humidity. Whereas in reality, the evaporation depends on puddle formation and plant growth and many other factors. Out in the real world, the weather follows its own rules perfectly. Those rules are the equations of the whole universe. "noise" is just what you call a hopefully small effect you don't have the knowledge, compute or inclination to calculate. 

If you have a really shoddy model of the weather, it won't be able to compute much. If you add a butterflys wing flaps to a current weather model, the knowledge of that small effect will be lost due to the mass of other small effects metrologists haven't calculated. Adding or removing a butterfly's wingflap doesn't meaningfully change our predictions given current predictive ability.  However, to a sufficiently advanced future weather predictor, that wingflap could meaningfully change the chance of a tornado. The predictor would need to be tracking every other wingflap globally, and much else besides. 

We are modelling as probabilistic processes that are actually deterministic but hard to calculate.

I'm strikethrough-ing this comment for being less kind than the author/post deserves. But it does make true and useful points, and I don't have the energy to rewrite it to be kinder right now, so I'm not deleting it outright.

The supercooled water example isn't actually an example of chaos. It's an example where the system is in a metastable state, and any perturbation causes it to switch to a more-stable state. Stable states are exactly what chaos isn't.

A better intuition for something chaos-like: imagine that we take add together a whole bunch of numbers, then check whether the result is odd or even. Changing any single number from odd to even, or vice-versa, causes the end result to flip. Chaos is like that: one small perturbation can cause a large-scale change (like changing the path of a hurricane); there are a wide variety of possible small perturbations, any one of which could cause the large-scale outcome to change back and forth between possible outcomes.

there is no reasonable sense in which we can say that a butterfly’s wings can cause a hurricane... Now, this counterfactual definition of causality, formalized by Judea Pearl using tools information theory, similarly gives problems for the classic interpretation of the butterfly effect... To answer this question carefully, it isn’t enough to look at what the world would look like if we removed the butterfly, but held everything else fixed.

Um... no. Removing the butterfly and holding everything else (specifically all other initial conditions/"random" external inputs) fixed is exactly what Pearl's counterfactual framework says to do here. And that Pearl-style counterfactual does not give any troubles whatsoever interpreting chaos. A small perturbation can indeed cause a macroscopic change, in the exact sense of "cause" formalized by Pearl: the macroscopic change would not have happened without the small perturbation, holding everything else fixed.

There is a perfectly reasonable sense in which small perturbations cause large changes in realistic chaotic systems, and Pearl's counterfactual framework is exactly the "reasonable sense" in question. If this is "unreasonable" in some sense, then this post has not actually made an argument for that or said in what sense it is unreasonable.

(I do not know if weather systems are chaotic enough that a small perturbation could cause a hurricane to not happen at all, but I'm pretty sure they're chaotic enough that a small perturbation could cause a hurricane's path to change significantly, e.g. send it to Florida rather than Mexico or vice-versa.)

(Side-note: in the supercooled water example, the counterfactual analysis would presumably say that any particular impurity did not cause the transition, precisely because there were likely other impurities which would have caused the transition anyway.)

I do think there's probably a way to turn the thing-you're-trying-to-say into a viable argument, but it isn't about chaos. In particular:

it may often be quite difficult to cleanly attribute a real-world outcome to one particular cause.

This is absolutely true. The number-adding analogy shows why: if changing any number would change the outcome, then there isn't really a sense in which one number caused the outcome more than any other. For each number, there is a well-defined counterfactual in which that number caused the outcome.

Counterfactual analysis - i.e. "holding the world fixed and only changing that one past decision"  - is not at all problematic, for butterflies or hurricanes or anything else. The mistake which I think you're trying to point to is in arbitrarily picking one particular cause to focus on, when any other cause is just as relevant.

Thank you for this interesting post. Could you clarify your assertion that the real world is not an idealistic deterministic system? Of course we cannot model it as such, but ignoring quantum effects, the world is deterministic. In that sense it seems to me that we might be unable to never confidently conclude that the butterfly caused the hurricane, but it could still be true. (and yes, in that Buddhist fable, my position has always been that trees do fall down, even if nobody sees it)

Even if this isn’t surprising, as intuitively people won’t attribute a hurricane to a butterfly, I would argue that causally attributing World War I to the assassination of Archduke Ferdinand follows the same fallacy.

If "cause" means that given A, B must necessarily happen , irrespective if other factors , then the butterfly wing and the assassination aren't causes. But there are other was of defining "cause" where they are!

But out in the messy “real world,” abundant with impurities of all kinds, supercooled water would not survive long anyhow — if not this impurity, then another would have seeded the transition a moment late

If "cause" means that given A, B must necessarily happen , and nothing but A could bring about B , then the impurity wasn't the cause. But there are other was of defining "cause" where it was!

Sure, the butterfly is really minor compared to everything else going on, and so only "causes" the hurricane if you unnaturally consider the butterfly as a variable while many more important factors are held fixed.

But, I don't believe the assassination of Franz Ferdinand is in the same category. While there's certainly a danger that hindsight could make certain events look more pivotal than they really were, the very fact that we have a natural seeming chain of apparent causation from the assassination to the war is evidence against it being a "butterfly effect".