# Causal inference developed by Pearl

• A
• Demystifier
Exercising will make you...fit". "Having a social life will make you...happy".There is no logical connection between the two.Something else caused them both.
Ackbach said:
I strongly disagree with this. Science has long been concerned with causation - I would say primarily concerned with causation. It's the most important question! Mill's Methods show how an experiment demonstrates causality, but as I have just said in this thread, the New Causal Revolution has demonstrated how you can get causality from an observational study, given the right conditions. This opens up many new possibilities.

The field of statistics, for a long time, distanced itself from causality because it didn't have the vocabulary and tools necessary to deal with it, other than in experiments. But again, the New Causal Revolution has changed all that.
Please see my reply sbove to Demystifier. That is what I meant. But , yes, @Bergmann , I was not saying Pearl does not provide a clear setup; I am not familiar with it. I meant now science must sbsorb it and work with it. I will read it when I get a chance. I am not saying that the concept is not relevant to science, only that at this point it is at its infancy and hasn't been yet absorbed. Thats all.

• jbergman, Dale and Ackbach
Ackbach said:
Science has long been concerned with causation - I would say primarily concerned with causation.
I think that the truth is probably somewhere between your position and @WWGD's position.

Science students tend to dramatically overly apply causation and causality. It is something that has to be corrected frequently.

For example, Newton's 3rd law can be written ##\vec F_{ij}=-\vec F_{ji}##. It is common for students to believe that the force on the left is an "action" which causes the "reaction" force on the right. They can then become confused on how to apply Newton's 3rd when the cause and effect is not clear. Since causes precede effects and since the forces in Newton's 3rd law are simultaneous they generally should not be thought of in terms of cause and effect. Even worse is if they do find a pair of causally related forces (one preceding the other) and try to apply Newton's 3rd law across time.

Another example is Maxwell's equations. $$\nabla \cdot \vec E = \rho$$$$\nabla \cdot \vec B = 0$$$$\nabla \times \vec E = -\partial_t \vec B$$$$\nabla \times \vec B = \vec J + \partial_t \vec E$$ Not just students, but also more experienced scientists will describe the left hand side as effects and the right hand side as causes. They will even describe light as "changing E fields causing changing B fields causing changing E fields and repeating" while referring to these equations. This has the same problem as above: causes precede effects but the things in Maxwell's equations happen at the same time.

There is a causal formulation of electromagnetism called Jefimenko's equations (or rather the retarded potentials): $$\phi(\vec r,t)=\int\frac{\rho(\vec r',t_r)}{|\vec r-\vec r'|} d^3\vec r'$$$$\vec A(\vec r,t)=\int \frac{\vec J(\vec r',t_r)}{|\vec r-\vec r'|} d^3\vec r'$$$$t_r=t-\frac{\vec r-\vec r'}{c}$$In this formula causes on the right side of the equations precede effects on the left side. This does express a true causaul relationship, but such equations are actually rather uncommon so I wouldn't say that science is primarily concerned with causation. It is certainly a topic of some concern, but not so ubiquitously as you imply. Even when causal relations do exist, they are often not the most convenient or useful approach to a phenomenon.

• Ackbach
WWGD said:
Please see my reply sbove to Demystifier. That is what I meant. But , yes, @Bergmann , I was not saying Pearl does not provide a clear setup; I am not familiar with it. I meant now science must sbsorb it and work with it. I will read it when I get a chance. I am not saying that the concept is not relevant to science, only that at this point it is at its infancy and hasn't been yet absorbed. Thats all.
Yes, I agree. The New Causal Revolution needs to make significant inroads on traditional statistics and science education, and it hasn't, yet.
Dale said:
I think that the truth is probably somewhere between your position and @WWGD's position.

Science students tend to dramatically overly apply causation and causality. It is something that has to be corrected frequently.

For example, Newton's 3rd law can be written ##\vec F_{ij}=-\vec F_{ji}##. It is common for students to believe that the force on the left is an "action" which causes the "reaction" force on the right. They can then become confused on how to apply Newton's 3rd when the cause and effect is not clear. Since causes precede effects and since the forces in Newton's 3rd law are simultaneous they generally should not be thought of in terms of cause and effect. Even worse is if they do find a pair of causally related forces (one preceding the other) and try to apply Newton's 3rd law across time.

Another example is Maxwell's equations. $$\nabla \cdot \vec E = \rho$$$$\nabla \cdot \vec B = 0$$$$\nabla \times \vec E = -\partial_t \vec B$$$$\nabla \times \vec B = \vec J + \partial_t \vec E$$ Not just students, but also more experienced scientists will describe the left hand side as effects and the right hand side as causes. They will even describe light as "changing E fields causing changing B fields causing changing E fields and repeating" while referring to these equations. This has the same problem as above: causes precede effects but the things in Maxwell's equations happen at the same time.

There is a causal formulation of electromagnetism called Jefimenko's equations (or rather the retarded potentials): $$\phi(\vec r,t)=\int\frac{\rho(\vec r',t_r)}{|\vec r-\vec r'|} d^3\vec r'$$$$\vec A(\vec r,t)=\int \frac{\vec J(\vec r',t_r)}{|\vec r-\vec r'|} d^3\vec r'$$$$t_r=t-\frac{\vec r-\vec r'}{c}$$In this formula causes on the right side of the equations precede effects on the left side. This does express a true causaul relationship, but such equations are actually rather uncommon so I wouldn't say that science is primarily concerned with causation. It is certainly a topic of some concern, but not so ubiquitously as you imply. Even when causal relations do exist, they are often not the most convenient or useful approach to a phenomenon.
Perhaps. But I can't help thinking that most scientists want to know why something is happening. They see a phenomenon and want to explain it - that is, they want to explain why. That's causal language.

• WWGD
Ackbach said:
Perhaps. But I can't help thinking that most scientists want to know why something is happening. They see a phenomenon and want to explain it - that is, they want to explain why. That's causal language.
Yes, but that is much trickier than many realize. When forces are in balance, it is often true that they coexist and neither can be said to cause the other. They are just in balance and may remain stable that way for a long time.

Ackbach said:
Perhaps. But I can't help thinking that most scientists want to know why something is happening. They see a phenomenon and want to explain it - that is, they want to explain why. That's causal language.
Not always. "Why" is broader than causality.

Scientifically "why" can also refer to implication. E.g. you might ask "Why does a fast moving clock tick slower than coordinate time in a given reference frame?" The answer could reasonably be Einstein's two postulates, but the two postulates are not causes that precede effects, they are logical principles from which physical phenomena can be deduced. So it is not a causal relationship that is sought with this "why" question.

"Why" can also signal a request for an explanation in terms of a different theory. Especially when asking about why some classical behavior occurs in terms of some underlying quantum mechanical phenomena. Or when asking about some Newtonian gravitational behavior in terms of general relativity. A more general theory does not precede an approximate theory in any meaningful sense, and in fact historically usually the approximate theory precedes the general theory. So again, it is not a causal relationship that is sought with this "why" question.

Non scientifically "why" can also refer to motivation. In psychology motivations could be considered causes of behaviors, but in physics we try to avoid motivation-based why questions.

So "explain", "why" and even "want to explain why" are not always causal language. The non-causal "why" questions in physics are very important, and perhaps even dominant. In particular, theoretical physics is almost always focused on the non-causal meanings of "why". Which is why (implication) I think that your "primarily" assertion is overly broad.

Not that you are wrong that causality is important nor are you wrong that finally having a framework for causality is very cool, but I think you are overstating your case. This causal inference stuff is interesting enough on its own that it is not necessary to overstate and oversell it.

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• Demystifier, pbuk, FactChecker and 1 other person
I was surprised recently, finding out the extensive role that Category Theory plays in the causation layout.