If I played bridge very, very fast, dealing out one hand every minute, that means I'd still have to wait 1.1 million years to get any particular hand you might specify ahead of time…and my life expectancy is only on the order of 102 years. Therefore, bridge is impossible. Similarly, if you add up all the nucleotide differences between me and my cousin, the likelihoods of these particular individuals is infinitesimally small…but so what? We're here.
|No more unlikely than other hands|
But that would completely miss the point of what randomness deficiency is. Myers is essentially arguing that since all microstates in a 'gas in a box' are equally unlikely, there isn't anything unusual about ending up in an improbable macrostate (like say, all the gas particles consolidated in one small corner of the box) since that particular microstate is no more unlikely that any of the quadrillions less special microstates.
If I am handed a Rubik's cube in a scrambled state, and I give it 20 turns and find it completely unscrambled, in Myers' world since this unscrambled state is just as likely to be generated as any other cube configuration, most of which are very disordered, we shouldn't be that amazed if the outcome is one of those highly ordered states.
Wait, you may say, don't highly unlikely coincidences happen all the time? Sure they do. If you expand your sample space to the space of all events, then there are myriads of ways to be surprised by coincidences--but then the bits of information needed to describe/prescribe exactly which of these quintillions of ways to be surprised was/will be instantiated approaches the logarithm of all the possible ways. It's a one-in-septillion chance to be surprised in any one way, but you've bought a septillion lottery tickets by being willing to be surprised by any one of them. But there will still be some limit to the number of lottery tickets even if one's 'universe of discourse' is the known physical universe. As one approaches the limit of the Universal Plausibility Bound, one starts to exhaust the universe's capacity for producing accidental coincidences. As the randomness deficiency approaches 450-500 bits, the sequence starts to be inexplicable in terms of chance alone, even with helpful distributions.
See Richard Dawkins below argue that coincidences are meaningless, in a very similar manner to P.Z. Myers, and consider why in a world in which "biology is the study of things that appear to be designed" it is important to be able to dismiss all incredible coincidences. Are all coincidences meaningless, or do we generally need to apply reason to separate meaningless coincidences from meaningful coincidences?