Measures of finetuning are meaningless

Intuitively we may feel that some physical parameters are remarkably fine-tuned for life, but can this feeling ever be made mathematically precise? The fact that a variation in the strength of the strong nuclear force by only a few per cent may disrupt the biological prospects for the Universe appears to offer a surprisingly narrow window of biophilic values, but what determines the measure on the space of parameters? If the strength of the nuclear force could, in principle, vary over an infinite range, then any finite window, however large, would be infinitesimally improbable if a uniform probability distribution is adopted. Even the simple expedient of switching from a uniform to a logarithmic distribution can have a dramatic change on the degree of improbability of the observed values, and hence the fineness of the fine-tuning. There will always be an element of judgement involved in assessing the significance, or degree of surprise, that attaches to any given example.

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