"Mathematics has not developed the asymmetric language required to capture our understanding that if x causes y that does not mean that y causes x. It sounds like a terrible thing to say against science, I know. If I were to say it to my mother, she’d slap me."

His home page [1] links to several presentations (e.g. [2]) where he lays out the key ideas. [0] "Causality: Models, Reasoning and Inference", Pearl

[1] http://bayes.cs.ucla.edu/jp_home.html

[2] http://bayes.cs.ucla.edu/IJCAI99/ijcai-99.pdf

In a simplified closed system, where all you have are barometers and storms, maybe there is no difference between implication and causation; all you know is these variables are correlated. Perhaps once you take every atom in the universe into account, the two start to look the same.

Implication it is a very mathematical thing. It is like you know, that y=f(x), and then you write x=g(x), where g is inverse of f. It works both ways, there are no cause, no effect, just link between two variables. If you use math to reason about causal links in reality, you need to use some implicit knowledge which is not represented in formula. It doesn't means that math is bad. Geometry likes euclidian space while we know from Einstein that our space is not euclidian one -- it doesn't mean that geometry is bad. Euclidian geometry just solves some specific problems and doesn't solve others.

Causal link reflects ability to change dependant variable by changing independant one. It is not something like "fundamental property of the Universe", it is our subjective way to structure information about the reality. It seems to me, that physicists believe the other way, that causation is the inherent property of reality. Maybe they are right in their field, but it doesn't work in everyday life. Causal link is an abstraction that helps us to know what we can do to change outcomes.

In this sense there are no causal link between barometer readings and a storm: if you change barometer readings to reflect a fine weather the storm will come anyway. Maybe there is causal link between atmosphetic pressure and a storm? I do not know it, because I see no way to change atmospheric pressure and I'm not educated well enough to understand scientific weather models. Though it is relatively safe for me to believe that low atmospheric pressure causes storm: causational link or correlational one -- it will not change my behaviour, because I cannot change atmospheric pressure. If I'll find a way, than it would be cruicial to figure out the kind of the link, because I'll be able to break something if I'm wrong. But I said that it is relatively safe, because if I suppose that link is causational, I would use that link differently while reasoning about the weather, it will change my other beliefs and probably it will change my behaviour somehow.

So, the main idea is: causation is just our way to structure reality. We are free to choose which links are causal, it is all up to us. If we think it will help us to reason about reality, then we should speak about casuality. And the most important difference between causation and correlation is the ability to change dependant variable by changing independant. If we can change dependant variable that way, than we should mark link as causational. If we cannot, that we should think about that link as about correlational. Implication just do not draw this difference.

People needed thousands of years to put together a few causal concepts about the world. AI would need its playtime too. It's not like a single person can come up with a causal model of the world by himself/herself. Just keep in mind that when comparing human intelligence with AI, so as not to ask of AI what no human can do.

Use your common sense though. Do you think we would have built the modern world (e.g. electricity) by passive observation of the world, or does really getting to the truth require controlled experiments?

In a difference equation x(t+1) = f(x(t),u(t)), u causes changes to x and not the other way around

It may simply be a predictor of x, as in the 'barometer readings may precede and imply a storm but not cause one' example given by others above.

For differential or non-differential equations, they're still just describing how something is and not the causality behind it. It's always possible that the equation is merely a result of hidden variables and there is no casual relationship between any two points of the solution in any meaningful sense.

It gets even murkier when you think of statements like "Hitler coming into power caused world war 2". There are so many things going on in that system that it couldn't possibly be true (e.g. if you change Hitler out for another person maybe world war 2 still happens), but works as a plausible line of causal reasoning for a lot of people.

For all practical purposes, you can write causality like

p(x|y) = 1 and time(y) < time(x)

I.e. causality is just when one event always happens after another event. Any additional requirements for causality are basically philosophy.

But typical ML systems don't construct networks of causal relations, is basically what he's getting at from my reading of it

> p(x|y) = 1 and time(y) < time(x)

This isn't true at all. For a counterexample, x and y may both have a common cause.

Pearl's work is on this and extends the language to talk about p(y | do(x)), meaning that you talk about what happens to y when you take some hypothetical intervention to change x. Causation framed in terms of intervention talks about "what if it had been this instead of that?" and is probably the most common model of causation.

For more info look up the rubin causal model, the potential outcomes framework, and pearls's "do" notation.

p(x|y) = 1, p(x|!y) = 0, and time(y) < time(x)

That rules out the rooster counter-example. If y is a boolean, I guess the only thing you can "do" to it is negate it.

But it at least rules out x causing y, which is something.

This is in fact the case with the barometer falling before a storm. Both the falling barometer and the subsequent rain and wind of a storm are consequences of an uneven distribution of heat and moisture in the atmosphere approaching equilibrium under the constraints of Earth's gravity and Coriolis force.

Is the rooster causing the dawn?

These two scenarios have the potential to exhibit different behavior -- probabilistic models without a notion of intervention or counterfactuals will only capture the former. But just like this 'selection' operator you c an define an analogous operator for -- selecting on those that you interved on -- then you are in the realms of causality.

Also:

> But I’m asking about the future—what next? Can you have a robot scientist that would plan an experiment and find new answers to pending scientific questions? That’s the next step.

Nearly 10 years ago [1], a robot called Adam both made and tested hypotheses about yeast. Certainly not a general AI, or even an award-winning massive breakthrough, but it's a good step in a direction that he doesn't think exists yet.

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[0] https://en.wikipedia.org/wiki/Association_rule_learning

[1] http://www.sciencemag.org/news/2009/04/robotic-scientists-ma...