July 2012
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Bayesian Anthropic Law

This one has been on my plate for a long time. There is a popular argument for the existence of God/Creator known as the “Fine-Tuning Argument”. When looking at the universe, we notice that it has a specific construction which supports carbon-based life-forms such as ourselves. For example, physicist Paul Davies [1993. The Accidental Universe, Cambridge University Press, p70-71] claims “the strong nuclear force were 2% stronger than it is (i.e., if the coupling constant representing its strength were 2% larger), while the other constants were left unchanged, diprotons would be stable and hydrogen would fuse into them instead of deuterium and helium.” [Wikipedia]. People of a religious persuasion like to claim that this precise tuning of the fundamental constants could only have been accomplished via a divine and benevolent being.

Without a soliloquy about puddles waking up to believe that the world fits their contours perfectly [1998. Douglas Adams. Anthropic Principle which answer with “Because otherwise we wouldn’t be here to ask.” These responses are just as empty and void of predictive value as “God did it.”. Martin Gardner [1986, WAP, SAP, PAP, & FAP] seems to be of the same opinion:

What should one make of this quartet of WAP, SAP, PAP, and FAP? In my not so humble opinion I think the last principle is best called CRAP, the Completely Ridiculous Anthropic Principle.

Even I, in my devout atheism, find myself naively thinking that “observed fitness” is a positive mark on the designer’s side of the ledger of weighted evidence. Apparently, with some Bayesian Logic, the exact opposite can be proved [1997. Ikeda and Jefferys. The Anthropic Principle Does Not Support Supernaturalism]. Their logic proceeds:

L = Our universe exists and contains life. P(L) = 1.
F = Our universe is 'life friendly'. That is, the conditions in or universe (such a physical laws, etc.) permit or are compatible with life existing naturalistically.
N = The universe is governed solely by Naturalistic law.

P(F|N&L) = 1 by the weak anthropic principle.

P(natural law given life and observed fit)
    = P(N | F & L)
    = P(F | N & L) * P(N|L) / P(F|L)
    = P(N | L) / P(F|L)
    >= P(N|L) = P(natural law given life)  

Which really just goes to show how bad I am at calculating my probabilities and ascribing evidence. The observation of fit should, logically, lead me to believe more in a completely naturalistic universe.

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