SLIDE 24: THE FIRST RIDDLE OF CAUSATION

We saw in the rooster example that regularity of succession is not sufficient; what WOULD be sufficient? What patterns of experience would justify calling a connection "causal"? Moreover: What patterns of experience CONVINCES people that a connection is "causal"?

SLIDE 25: THE SECOND RIDDLE OF CAUSATION

If the first riddle concerns the LEARNING of causal-connection, the second concerns its usage: What DIFFERENCE does it make if I told you that a certain connection is or is not causal:?

Continuing our example, what difference does it make if I told you that the rooster does cause the sun to rise? This may sound trivial. The obvious answer is that knowing what causes what makes a big difference in how we act. If the rooster's crow causes the sun to rise we could make the night shorter by waking up our rooster earlier and make him crow - say by telling him the latest rooster joke.

But this riddle is NOT as trivial as it seems. If causal information has an empirical meaning beyond regularity of succession, then that information should show up in the laws of physics. But it does not! The philosopher Bertrand Russell made this argument in 1913:

SLIDE 26: PURGING CAUSALITY FROM PHYSICS?

"All philosophers, "says Russell," imagine that causation is one of the fundamental axioms of science, yet oddly enough, in advanced sciences, the word 'cause' never occurs ... The law of causality, I believe, is a relic of bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm ..."

Another philosopher, Patrick Suppes, on the other hand, arguing for the importance of causality, noted that: "There is scarcely an issue of *PHYSICAL REVIEW* that does not contain at least one article using either `cause' or `causality' in its title."

What we conclude from this exchange is that physicists talk, write, and think one way and formulate physics in another. Such bi-lingual activity would be forgiven if causality was used merely as a convenient communication device - a shorthand for expressing complex patterns of physical relationships that would otherwise take many equations to write. After all! Science is full of abbreviations: We use, "multiply x by 5", instead of "add x to itself 5 times"; we say: "density" instead of "the ratio of weight to volume". Why pick on causality?

"Because causality is different," Lord Russell would argue, "It could not possibly be an abbreviation, because the laws of physics are all symmetrical, going both ways, while causal relations are uni-directional, going from cause to effect." Take for instance Newton's law f = ma The rules of algebra permit us to write this law in a wild variety of syntactic forms, all meaning the same thing - that if we know any two of the three quantities, the third is determined. Yet, in ordinary discourse we say that force causes acceleration - not that acceleration causes force, and we feel very strongly about this distinction. Likewise, we say that the ratio f/a helps us DETERMINE the mass, not that it CAUSES the mass. Such distinctions are not supported by the equations of physics, and this leads us to ask whether the whole causal vocabulary is purely metaphysical. "surviving, like the monarchy...etc."

Fortunately, very few physicists paid attention to Russell's enigma. They continued to write equations in the office and talk cause-effect in the CAFETERIA, with astonishing success, they smashed the atom, invented the transistor, and the laser. The same is true for engineering. But in another arena the tension could not go unnoticed, because in that arena the demand for distinguishing causal from other relationships was very explicit. This arena is statistics.

The story begins with the discovery of correlation, about one hundred years ago.
SLIDE 27: FRANCIS GALTON (PORTRAIT)

Francis Galton, inventor of fingerprinting and cousin of Charles Darwin, quite understandably set out to prove that talent and virtue run in families.

SLIDE 28: TITLE PAGE "NATURAL INHERITANCE"

These investigations, drove Galton to consider various ways of measuring how properties of one class of individuals or objects are related to those of another class.

SLIDE 29: GALTON'S PLOT OF CORRELATED DATA (1888)

In 1888, he measured the length of a person's forearm and the size of that person's head and asked to what degree can one of these quantities predict the other. He stumbled upon the following discovery: If you plot one quantity against the other and scale the two axes properly, then the slope of the best-fit line has some nice mathematical properties: The slope is 1 only when one quantity can predict the other precisely; it is zero whenever the prediction is no better than a random guess and, most remarkably, the slope is the same no matter if you plot X against Y or Y against X. "It is easy to see," said Galton, "that co- relation must be the consequence of the variations of the two organs being partly due to common causes." Here we have, for the first time, an objective measure of how two variables are "related" to each other, based strictly on the data, clear of human judgment or opinion.

SLIDE 30: KARL PEARSON (PORTRAIT, 1890)

Galton's discovery dazzled one of his students, Karl Pearson, now considered the founder of modern statistics. Pearson was 30 years old at the time, an accomplished physicist and philosopher about to turn lawyer, and this is how he describes, 45 years later, his initial reaction to Galton's discovery: