P.Z. Myers and the Bridge Hands Fallacy

In P.Z. Myers' universe all improbable outcomes are equally meaningless.  He states:

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

If I were to flip a coin 100 times, and the resulting pattern of coin flips exhibited inordinately high randomness deficiency, I could argue that the resulting pattern was no more special than a bit sequence with Kolmogorov complexity K(x) > 92 bits.  Using Myers' logic, that is.

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? 

Coincidences

I've been thinking about how coincidences are evaluated in forensics.  How does one separate the pure coincidences from the can't-be-coincidences?

Supposedly, a detective does not believe in coincidence.

Let's say George has some mysterious charges on his bill.   Let's say that something comes to light that the exact digits of his credit card number appeared in a text from a Hans whom George doesn't know, but say George's daughter knows Hans.  There might be enough digits in that number to warrant thinking that it is not a coincidence -- that is, that those doesn't represent something else: a book-of-the-month club user registration, a hotel confirmation number, etc.  A long enough number is supposed to use up probabilitic resources.  After all, it should be the case that a random sequence of digits probably NOT be valid credit card number.  There could be a preponderance of evidence that Hans

To make this more interesting, let's say that these mysterious charges occurred shortly after George died under mysterious circumstances and his credit card went missing.  There is the proximity to George: two degrees of separation.  There is the time proximity: near the time of George's death.

To a detective, this forms a pattern, a specification.  Now the small probability is much larger than the Universal Plausibility Bound, but it is still compelling in many cases, once motive and alibi are dealt with.

The quality Dembski would call tractability, gets into the degrees of separation along with the specificational resources.  What are the chances that someone would have the credit card number and also that this person be only two degrees of separation from the credit card owner, close to the time the card went missing?   Too coincidental?   How to put some firm numbers behind that assessment?  I suspect that departments of justice deal with tractability all the time, and somehow it is not pseudoscience  despite the problem resisting really precise calculations in a lot of cases.