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|Hume argued convincingly that the WHY is not merely second to the HOW, but that the WHY is totally superfluous as it is subsumed by the HOW.|
On page 156 of Hume's "Treatise of Human Nature", we find the
paragraph that shook up causation so thoroughly that it
has not recovered to this day.
I always get a kick reading it:
"Thus we remember to have seen that species of object we call *FLAME*, and to have felt that species of sensation we call *HEAT*. We likewise call to mind their constant conjunction in all past instances. Without any farther ceremony, we call the one *CAUSE* and the other *EFFECT*, and infer the existence of the one from that of the other."
Thus, causal connections according to Hume are product of observations. Causation is a learnable habit of the mind, almost as fictional as optical illusions and as transitory as Pavlov's conditioning. It is hard to believe that Hume was not aware of the difficulties inherent in his proposed recipe. He knew quite well that the rooster crow STANDS in constant conjunction to the sunrise, yet it does not CAUSE the sun to rise. He knew that the barometer reading STANDS in constant conjunction to the rain, but does not CAUSE the rain.
Now, taking Hume's dictum that all knowledge comes from experience, that experience is encoded in the mind as correlation, and our observation that correlation does not imply causation, we are led into our first riddle of causation: How do people EVER acquire knowledge 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"?|
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.
"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."
"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.
||Francis Galton, inventor of fingerprinting and cousin of Charles Darwin, quite understandably set out to prove that talent and virtue run in families.|
|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.|
|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.|
|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:|
"I felt like
a buccaneer of Drake's days -...
I interpreted that
sentence of Galton to mean that there was a category
broader than causation, namely correlation, of which
causation was only the limit, and that this new
conception of correlation brought psychology,
anthropology, medicine, and sociology in large parts
into the field of mathematical treatment."
Now, Pearson has been described as a person "with the kind of drive and determination that took Hannibal over the Alps and Marco Polo to China." When Pearson felt like a buccaneer, you can be sure he gets his bounty.
|1911 saw the publication of the third edition of his book "The Grammar of Science". It contained a new chapter titled "Contingency and correlation - the insufficiency of causation," and this is what Pearson says in that chapter: "Beyond such discarded fundamentals as 'matter' and 'force' lies still another fetish amidst the inscrutable arcana of modern science, namely, the category of cause and effect."|
|Thus, Pearson categorically denies the need for an independent concept of causal relation beyond correlation. He held this view throughout his life and, accordingly, did not mention causation in ANY of his technical papers. His crusade against animistic concepts such as "will" and "force" was so fierce and his rejection of determinism so absolute that he EXTERMINATED causation from statistics before it had a chance to take root.|
It took another 25 years and
another strong-willed person, Sir Ronald Fisher, for
statisticians to formulate the randomized experiment - the
only scientifically proven method of testing causal
relations from data, and which is, to this day, the one and only causal concept
permitted in mainstream statistics.
And that is roughly where things stand today... If we count the number of doctoral theses, research papers, or textbooks pages written on causation, we get the impression that Pearson still rules statistics. The "Encyclopedia of Statistical Science" devotes 12 pages to correlation but only 2 pages to causation, and spends one of those pages demonstrating that "correlation does not imply causation."
Let us hear what modern statisticians say about causality
|Philip Dawid , the current editor of Biometrika-the journal founded by Pearson - admits: "causal inference is one of the most important, most subtle, and most neglected of all the problems of statistics". Terry Speed, former president of the Biometric Society (whom you might remember as an expert witness at the O.J. Simpson murder trial), declares: "considerations of causality should be treated as they have always been treated in statistics: preferably not at all, (but if necessary, then with very great care.)" Sir David Cox and Nanny Wermuth, in a book published just a few months ago, apologize as follows: "We did not in this book use the words CAUSAL or CAUSALITY.... Our reason for caution is that it is rare that firm conclusions about causality can be drawn from one study."|
Can this state of affairs be the work of just one person? even a buccaneer like Pearson? I doubt it.
But how else can we explain why statistics, the field that has given the world such powerful concepts as the testing of hypothesis and the design of experiment would give up so early on causation?
One obvious explanation is, of course, that causation is much harder to measure than correlation. Correlations can be estimated directly in a single uncontrolled study, while causal conclusions require controlled experiments.
But this is too simplistic; statisticians are not easily deterred by difficulties and children manage to learn cause effect relations WITHOUT running controlled experiments. The answer, I believe lies deeper, and it has to do with the official language of statistics, namely the language of probability. This may come as a surprise to some of you but the word "CAUSE" is not in the vocabulary of probability theory; we cannot express in the language of probabilities the sentence, "MUD DOES NOT CAUSE RAIN" - all we can say is that the two are mutually correlated, or dependent - meaning if we find one, we can expect the other. Naturally, if we lack a language to express a certain concept explicitly, we can't expect to develop scientific activity around that concept. Scientific development requires that knowledge be transferred reliably from one study to another and, as Galileo has shown 350 years ago, such transference requires the precision and computational benefits of a formal language.
I will soon come back to discuss the importance of language and notation, but first, I wish to conclude this historical survey with a tale from another field in which causation has had its share of difficulty. This time it is computer science - the science of symbols - a field that is relatively new, yet it has placed a tremendous emphasis on language and notation and, therefore, may offer a useful perspective on the problem.
When researchers began to encode causal relationships using computers, the two riddles of causation were awakened with renewed vigor.
|Put yourself in the shoes of this robot who is trying to make sense of what is going on in a kitchen or a laboratory. Conceptually, the robot's problems are the same as those faced by an economist seeking to model the National debt or an epidemiologist attempting to understand the spread of a disease. Our robot, economist, and epidemiologist all need to track down cause-effect relations from the environment, using limited actions and noisy observations. This puts them right at Hume's first riddle of causation: HOW?|
|The second riddle of causation also plays a role in the robot's world. Assume we wish to take a shortcut and teach our robot all we know about cause and effect in this room. How should the robot organize and make use of this information? Thus, the two philosophical riddles of causation are now translated into concrete and practical questions:|
|How should a robot acquire causal information through interaction with its environment? How should a robot process causal information received from its creator-programmer? Again, the second riddle is not as trivial as it might seem. Lord Russell's warning that causal relations and physical equations are incompatible now surfaces as an apparent flaw in logic.|
|For example, when given the information, "If the grass is wet, then it rained" and "If we break this bottle, the grass will get wet," the computer will conclude "If we break this bottle, then it rained." The swiftness and specificity with which such programming bugs surface, have made Artificial-Intelligence programs an ideal laboratory for studying the fine print of causation.|
Continue with Part 2