Ideas behind their time: formal causal inference?

Alex Tabarrok at Marginal Revolution blogs about how some ideas seem notably behind their time:

We are all familiar with ideas said to be ahead of their time, Babbage’s analytical engine and da Vinci’s helicopter are classic examples. We are also familiar with ideas “of their time,” ideas that were “in the air” and thus were often simultaneously discovered such as the telephone, calculus, evolution, and color photography. What is less commented on is the third possibility, ideas that could have been discovered much earlier but which were not, ideas behind their time.

In comparing ideas behind and ahead of their times, it’s worth considering the processes that identify them as such.

In the case of ideas ahead of their time, we rely on records and other evidence of their genesis (e.g., accounts of the use of flamethrowers at sea by the Byzantines ). Later users and re-discoverers of these ideas are then in a position to marvel at their early genesis. In trying to see whether some idea qualifies as ahead of its time, this early genesis, lack or use or underuse, followed by extensive use and development together serve as evidence for “ahead of its time” status.

On the other hand, in identifying ideas behind their time, it seems that we need different sorts of evidence. Taborrok uses the standard of whether their fruits could have been produced a long time earlier (“A lot of the papers in say experimental social psychology published today could have been written a thousand years ago so psychology is behind its time”). We need evidence that people in a previous time had all the intellectual resources to generate and see the use of the idea. Perhaps this makes identifying ideas behind their time harder or more contentious.

Y(X = x) and P(Y | do(x))

Perhaps formal causal inference — and some kind of corresponding new notation, such as Pearl’s do(x) operator or potential outcomes — is an idea behind its time.¹ Judea Pearl’s account of the history of structural equation modeling seems to suggest just this: exactly what the early developers of path models (Wright, Haavelmo, Simon) needed was new notation that would have allowed them to distinguish what they were doing (making causal claims with their models) from what others were already doing (making statistical claims).²

In fact, in his recent talk at Stanford, Pearl suggested just this — that if the, say, the equality operator = had been replaced with some kind of assignment operator (say, :=), formal causal inference might have developed much earlier. We might be a lot further along in social science and applied evaluation of interventions if this had happened.

This example raises some questions about the criterion for ideas behind their time that “people in a previous time had all the intellectual resources to generate and see the use of the idea” (above). Pearl is a computer scientist by training and credits this background with his approach to causality as a problem of getting the formal language right — or moving between multiple formal languages. So we may owe this recent development to comfort with creating and evaluating the qualities of formal languages for practical purposes — a comfort found among computer scientists. Of course, e.g., philosophers and logicians also have been long comfortable with generating new formalisms. I think of Frege here.

So I’m not sure whether formal causal inference is an idea behind its time (or, if so, how far behind). But I’m glad we have it now.

1. There is a “lively” debate about the relative value of these formalisms. For many of the dense causal models applicable to the social sciences (everything is potentially a confounder), potential outcomes seem like a good fit. But they can become awkward as the causal models get complex, with many exclusion restrictions (i.e. missing edges). [↩]
2. See chapter 5 of Pearl, J. (2009). Causality: Models, Reasoning and Inference. 2nd Ed. Cambridge University Press. [↩]