Tuesday, January 17, 2012

The Effect of Infinite Probabilistic Resources on ID and Science (Part 1)

Copied from Uncommon Descent:


One common critique of intelligent design is that since it is based on probabilities, then with enough probabilistic resources it is possible to make random events appear designed. For instance, suppose that we live in a universe with infinite time, space and matter. Now suppose we’ve found an artifact that to the best of our knowledge (assuming finite probabilistic resources) passes the explanatory filter and exhibits CSI. However, one of the terms in the CSI calculation is probabilistic resources available. If the resources are indeed infinite, then the calculation will never give a positive result for design. Consequently, if the infinite universe critique holds, then not only does it undermine ID, but every huckster, conman, and scam artist will have a field day.
Say I had a bet with you that I’m flipping a coin and whenever it came up heads I’d pay you $100 and whenever it came up tails you’d pay me $1. Seems like a safe bet, right? Now, say that I flipped 100 tails in a row and you now owe me $100. Would you be suspicious? I might say 100 tails is just a likely, probabilistically speaking, as 50 tails followed by 50 heads, or alternating tails and heads, or any other permutation of 100 flips, which would be mathematically correct. To counter me, you bring in the explanatory filter and say, “Yes, 100 tails is equally probable, but it also exhibits CSI because there is a pattern it conforms to.” In a finite universe, this counter would also be mathematically valid. I’d be forced to admit foul play. But, if we lived in an infinite universe then even events seeming to exhibit CSI will turn up, and I could claim there is no rational reason to suspect foul play. I could keep this up for 1,000 or 1,000,000 or 1,000,000,000,000 tails in a row, and you’d still have no rational reason to call foul play (though you may have rational reason to question my sanity).
Not only do many incredible events become reality, but we begin to lose a grip on reality itself. For instance, it is much more likely, from an a priori probability, that we are merely boltzmann brains [2] instantiated with a momentary existence, only to disappear the next instant. Furthermore, it is much more likely that our view of reality itself is an illusion and the objective world is merely a random configuration that just happens to give us a coherent perception. As a result, in an infinite universe, our best guess is that we are hallucinating, instantaneous brains floating in space, or perhaps worse.
A more optimistic person might say, “Yes, but such a pessimistic situation only exists if we make assumptions about the a priori probability, such as it is a uniform or nearly uniform distribution. There are many other distributions that lead to a coherent universe where we are persistent beings that have a grasp on objective reality. Why make the pessimistic assumption instead of the optimistic assumption?”
Of course, this is good advice, whenever we have such a choice of alternatives. Unfortunately, this advice ignores the mathematical structure of the problem. The proportion of coherent distributions to incoherent distributions drops off exponentially, and as an exponential equation approaches infinity it becomes an almost binary drop off. This means that as probabilistic resources approach infinity, the number of coherent distributions approaches zero. Nor does the situation get any better if we talk about probability distributions over probability distributions, the problem remains unchanged or even gets exponentially worse with every additional layer.
The end result is that with an infinite number of probabilistic resources the case for ID may be discredited, but then so is every other scientific theory.
However, perhaps there is a rational way to preserve science even if there are infinite probabilistic resources. If so, what effect does this have on ID? Maybe ID even has a hand in saving science? More to follow…
[1] http://en.wikipedia.org/wiki/Law_of_large_numbers
[2] http://en.wikipedia.org/wiki/Boltzmann_brain

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