Sunday, October 12, 2008

the economy (or, divine providence)

This Ratio once discovered, and manifestly serving to a wise purpose, we conclude the Ratio itself, or if you will the Form of the Die, to be an Effect of Intelligence and Design.

Abraham De Moivre (1756) The Doctrine of Chances, 3rd ed.


1711: Dr. John Arbuthnot argues for "Divine Providence" on the basis of the statistical significance of the relative difference between the birth rates of boys and girls recorded in the London Bills of Mortality for the previous 82 years.

His reason: a chance process could not have produced this discrepancy.

Bernoulli's response: "if sex is likened to tossing a 35-sided die, with 18 faces labelled "male," and 17 labelled "female," then Arbuthnot's data are entirely consistent with the outcome of chance."

[see S. L. Zabell (1988) "Symmetry and Its Discontents"]

De Moivre makes his remark in response to Bernoulli. The issue, as Hacking ably demonstrates, arises during a metamorphosis of the concepts of chance and probability. The crucial issue was defining the class of phenomena to which the concept of probability properly applies.

Zabell emphasizes the role of symmetry here: Arbuthnot believes the lack of symmetry in birth rates indicates divine design; Bernoulli demonstrates the presence of symmetry; De Moivre questions the source of this symmetry.

But isn't De Moivre's request for a source of "the Die" just a request for a deeper symmetry? The "wise purpose" which a discrepancy in birth rates seems to "serve" indicates the need for a deeper explanation, hence the appeal to "Design." Unlike the discrepancy in birth rates, the outcomes of die rolls do not appear to favor (statistically) any wise purpose. The new asymmetry here is between stereotypical "chance" events, such as die rolls, oblivious to providence, and a seemingly analogous case, conception, which disanalogously manifests providence.

One goal of an effective theory of evolution is to remove this asymmetry, to account for the discrepancy in birth rates and the providential nature of this discrepancy, by appealing to mechanisms of a purely die-like oblivion. In other words, De Moivre's request for an explanation concerning the shape of the die must itself be answered with an account of the random (and manifestly non-providential) process producing that shape: dice within dice.

Whether De Moivre would be satisfied with such a response is irrelevant here. Furthermore, this is not explicitly a question concerning evolution or design. We can see its modern cousin in string theory's anthropic landscape - a desperate attempt to rule out alternate solutions to the physical equations of string theory by positing a multiverse and arbitrarily licensing consideration of only those universes which can provide for human life.

Effectively, assuming string theory, our universe is then the result of the throw of a 10500 sided die. Only one face on this die produces a universe hospitable to human life. Again, as with De Moivre, this asymmetry, this apparent providence demands an explanation which restores symmetry. The preferred move of modern string theorists, rather than positing divine intervention, is simply to posit 10500 dice, each thrown simultaneously (= "the cosmic landscape").

Their solution is every bit as unsatisfying and anti-scientific as De Moivre's, however. For De Moivre's solution is unsatisfying not because of its appeal to God, but because the appeal to God indicates the end of scientific inquiry: and you cannot provide me a suitable explanation. Likewise with the multiverse, for, by its very nature, the other "universes" of the multiverse are beyond empirical inquiry, and the positing of this monster licenses string theorists to declare victory for their theory, ending inquiry by appealing to that the properties of which cannot be investigated via the experimental method.

In the case of the economy, the situation is far worse. For the die throws which govern the economy (unlike those which govern the fundamental physical constants) are subject to intervention. We are dissatisfied with the result of rolling this 6-sided die, so we replace it with a 35-sided one, suitably labeled. Providence attributed to the hand of God in the case of birth rates is now attributed to the hand of Man.

But surely the problem here is one of calculation: it took careful analysis of 82 years of records to determine the operation of a single 35-sided die. If there is any analog in the economy, surely many different dice are being thrown at asynchronous intervals. But how can the underlying form of these die be discovered if, rather than observing and analyzing this complex phenomenon, we insist upon participating, toss our own homemade dice upon the table, or taking the die of our neighbor and shaving one of its sides?

But wait, you say: participation is demanded, how else can we avoid catastrophe? Here, perhaps, it is the trust to divine providence itself which is the scientific response, and not the egocentric hubris of the modern man.

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