Wednesday, October 31, 2007

Common and Special Causes

From 1703 until his death in 1705, Jacob Bernoulli exchanged a number of letters with Gottfried Leibniz. Leibniz wrote to him:

"La nature a sans doute ses habitudes, provenant du retour des causes, mais ce n'est que la plupart du temps. C'est pourquoi, ne peut-on pas objecter qu'une nouvelle expérience puisse s'écarter un tant soit peu de la loi de toutes les précédentes, du fait de la variabilité même des choses ? De nouvelles maladies se répandent souvent sur le genre humain et par conséquent quelque soit le nombre de morts dont vous avez fait l'expérience ce n'est pas pour autant que vous avez établi les limites des choses de la nature au point qu'elle ne puisse en varier dans le futur."

"Nature has established patterns originating in the return of events but only for the most part. Therefore, can't we argue that a new experience could deviate from the law of all the previous ones, even a little bit, because of the very essence of variability of things ? New illnesses often flood the human race, so that no matter how many experiments you have done, you have not thereby established a limit on the nature of events so that in the future they could not vary."

Later, John Maynard Keynes directly refers to Leibniz in his essay on "Probability in relation to the theory of knowledge". According to a Cambridge Journal's article, "Keynes's Treatise on Probability contains some quite unusual concepts, such as non-numerical probabilities and the ‘weights of the arguments’ that support probability judgements. Their controversial interpretation gave rise to a huge literature about ‘what Keynes really did mean’, also because Keynes's later views in macroeconomics ultimately rest on his ideas on uncertainty and expectations formation". But what Keynes really means was just what he once told clearly:

"By uncertain knowledge … I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty ...

The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention … About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know!"

At the same time, during the 1920s, Walter A. Shewhart, statistician and engineer, was commissioned to improve the quality of telephones manufactured by Bell Laboratories.

Shewhart framed the problem in terms of Common and Special-Causes of variation. Though Shewhart may not have been the first to reveal this concept, he is the first who has established an operational mean to distinguish between the two: on May 16, 1924, he wrote an internal memo introducing Statistical Process Control with a Control Chart as a tool for Continuous Process Improvment.

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