We know that the Being in Newcomb's paradox has an uncanny ability to figure out what you will do, because such is stipulated in the statement of the paradox.  However, if we really encountered such a Being, there would be no such authoritative stipulation, and we would know only what we could infer by observing what he does.  If he offered two boxes to a large number of individuals and successfully foresaw what every one of them would do, we could reasonably conclude that he had an extraordinary ability to foresee but would be uncertain how he did it.  His superpower need not be a preternatural understanding of how people think.  We might find it just as likely that, for example, he is a clairvoyant who, before arranging the boxes and making his offers, peeked into the future when the individuals will make their choices, thereby learning what those choices will be (even when randomness is involved).  Alternatively, the Being could be a time traveler; that is, he could have traveled forward in time, observed the choices being made, then traveled back to the time from which he had departed and arranged the boxes' contents accordingly.  So the paradox might be a paradox, not of free will, but of time travel.
        If a future time turns out to be different from what a clairvoyant sees, the obvious interpretation is that his clairvoyance is unreliable.  However, if a future time turns out to differ from what a time traveler experienced when he briefly visited that same time, then what are we to think?  The situation becomes more clearly paradoxical if the traveler travels into the past (rather than the future) and while there changes something in a way that is inconsistent with the present from which he departed.  For example, suppose that during his time trip he sneaks into a museum after hours and destroys a unique and irreplaceable antique that was intact when the trip began.  When he returns to the present, the antique is missing from the museum, and the fact of its mysterious overnight destruction is in people's memories and in written records.  How can this be reconciled with the fact that when the time trip began the antique was safely in the museum and there were no memories or records of its having been destroyed?  It seems that the only way to make sense of all this is to suppose that there are parallel universes and that the time traveler did not travel into the past of the same universe from which he departed but instead jumped to a parallel universe where things are similar but not the same.
        Excellent science fiction stories have been written in which time travel to the past alters the present; Ray Bradbury's A Sound of Thunder comes to mind.  However, their excellence does not lie in their conception of time travel, which suffers from the inconsistency cited above.  Consistent time travel stories must present a single course of history.  If a time traveler tries to change a past event from what he knows it to have been, circumstances should always thwart his efforts.  This means that the more ignorant a traveler is of the past, the more naturally he can act while he is there, because he has no preconceptions as to what he cannot do.  I find that the best stories include the irony that a past action undertaken with the intent of changing the present turns out to be an action essential to bringing about the present as it already is known to be; the first Terminator motion picture comes to mind.
        The essential element in the paradoxes mentioned here is that some information flows backward in time.  Coupling this with the usual flow forward in time leads to a cyclic flow of information that can be either inconsistent (as illustrated above) or consistent.  An illustration of the latter is an invention without an inventor, such as the following:  An engineer finds a set of plans of unknown origin.  He determines that they are plans for a time machine, and he uses them to construct such a machine.  His first time trip is to go into the past and leave where he found them the very set of plans he used to build the time machine.  So who invented the time machine; that is, who had the idea?  Not the engineer.
        Cyclic flow of information also is involved in certain mathematical and logical puzzles and proofs, such as whether the sentence, "This sentence is false," is true or false.  Another example is Turing's proof (previously discussed) of the impossibility of designing a computer program that, given a copy of any computer program, can determine whether or not that program will terminate, rather than run forever.  However, I shall pursue the subject no further but next shall turn to a different topic related to free will.
February 1, 2010
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