Labyrinths of Reason (43 page)

Now back to Newcomb’s situation. You can make a good case that the experiment as usually stated is impossible—that is, the prediction is impossible. The reason is essentially the same as above. Endless regress rules out a 100 percent accurate prediction.

Yes, but wouldn’t we be satisfied with a 90 percent prediction? Given the contrary nature of the human mind, small uncertainties about a subject’s or predictor’s mental state may grow exponentially and produce total uncertainty. Predicting the system of predictor and predicted is as impossible as predicting any chaotic phenomenon. Thus there is no casual distinction between 100 percent and 90 percent accuracy. It is like being 90 percent sure of the arrangement of a deck of cards before it was shuffled. Unless the predictor can get a complete lock on the state of the room (it can’t), it may not be able to predict with
any
accuracy at all.

If the paradoxes I have gathered on these pages have one recurring theme, it is the folly of denying ignorance. Just because something is so doesn’t mean that we can know it. There is necessary
ignorance, and it is more significant than mere solipsism would have us believe.

The assumption that anything true is knowable is the grandfather of paradoxes. In its purest form this is the foundation of Buridan sentences and infinity machines. The riddles of Hempel and Goodman trade on the fallacy that the import of any observation is knowable a priori. The victim of the unexpected hanging errs in thinking he can deduce something he cannot; Newcomb’s experiment founders on the impossibility of a predictor knowing his own mind.

The physicist Ludwig Boltzmann conjectured that our astonishment at the order of the world is misplaced: The known universe may be one small random fluctuation in an infinite universe that contains all possible arrangements of atoms. One may be forgiven for wondering if our knowledge is similarly engulfed in a larger whole. Perhaps the real mystery is that everything imaginable is true—somehow, somewhere—and our minds are preoccupied with an infinitesimal part of the whole of existence, whose paths we have worn in our first explorations.

There is no more satisfying resolution to a decision paradox than to show that the situation itself can never arise. Unfortunately, I am forced to conclude that a slightly modified version of the experiment
is
conceivable. To do so, I resort to either of two science-fictional devices.

The Newcomb experiment is being held in the year 3000 A.D., and the predictor has at his disposal two gadgets, a time machine and a matter scanner. In the first case, the predictor hops in the time machine and sets the dial for just after the subject makes his choice. Arriving in the near future, he gets out and learns the decision. Then he gets back in the time machine and returns to the day before the experiment. He makes his prediction on the strength of certain knowledge of the future.

This would give the subject planning to take both boxes pause to consider. You’re the subject, and you notice a video camera in the corner of the room. Just before you decide, the predictor walks in and hands you a videotape.
It’s a tape of you opening the box(es) he brought back from the future
. Not only has the predictor an evidently correct prediction, he has a motion picture of it.

Time travel is such an iffy idea that it may be unwise to set much
store by it. The other futuristic method of prediction, one you might be more comfortable with, is a matter scanner. The scanner duplicates matter exactly. You set up the machine, scan a $1000 bill, and it creates a new bill that is identical in every possible way, down to the quantum states of its atoms. Scanning a person with the machine creates an exact duplicate. Armed with this technology, it is also possible to predict with certainty the result of a Newcomb experiment.

There are logistic subtleties, though. It would not do simply to create a twin of the subject and do a trial run of the experiment with the twin. The minutiae of the experiment would not be the same. It would be a different time of day; the twin might be in a different mood; the experimental proctor might explain something slightly differently. These trifles might not make a difference, but you never know. The subject
could
be contrary. Knowing about the doppelgänger, he might decide to do just the opposite of his “first impulse” to prove his free will. We want to assure ourselves that the prediction can be arbitrarily certain.

To ensure the validity of the prediction, two drastic steps are necessary. You would have to create an exact duplicate of the subject, the boxes, the table, the room, the guards, everything and everyone involved in the experiment. The duplicated region would have to be so large that no outside influence could reach the subject before making the choice. You’d want a hermetically sealed, artificially lighted room. Otherwise, even the angle of the sunlight streaming through the windows might make a difference—and you can’t duplicate the sun.

The other problem is timing. Now you have two subjects in two rooms. You want to fast-forward the duplicate experiment to its conclusion so that you know what the real subject will do before he does it. Otherwise, all this effort goes to waste; there is no prediction.

There are two conceivable solutions. One, you could pack the original subject and surroundings into a gigantic rocket and shoot them away from the earth at near the speed of light. The rocket’s computers steer a course several light-years out into space, turn around, and return at near the speed of light. The rocket acceleration creates 1 g of artificial gravity, so the subject in the sealed room remains ignorant of his journey. By the time the subject returns in the rocket, you know what the duplicate did; thanks to a twin paradox, the real subject has not yet made his choice.

A more practical method is to run the experiment with the duplicate
as the subject. The scanning and duplicating process must take some time. So scan the original subject, watch what choice he makes,
then
create the duplicate. You predict what the duplicate will do.

All right then. It is the year 3000 A.D., and you are the subject in a Newcomb experiment. Just before you decide, you are told—gasp!—that you may be only a duplicate of the real you, created just five minutes ago. How Russellian! You have no reason to doubt this: Matter scanners are as common in 3000 A.D. as microwave ovens are today. You accept that the experiment’s predictor attains 100 percent accuracy by watching an exact double in an identical room.

You might ask how you can possibly know if you are the duplicate or the original. You can’t. The situation
is
exactly as in Russell’s thought experiment about the world being created five minutes ago. Duplicate and original have identical memories, including the memory of walking to the room a few minutes ago so they could scan it and create the duplicate. Both original and duplicate are asked to make the choice of boxes.

The experiment’s sponsors even had to tell the
real
you that he might be a duplicate too. The experiment is designed around you, the duplicate, who makes his choice after the original has been observed. Consequently the sponsors had to tell the original he might be a duplicate in order to tell you that you are. Only after choosing, when you walk out of the room, do you find out whether you are the original or the duplicate.

This nips contrary stratagems in the bud. You can’t outsmart the predictor by doing one thing in the “trial run” and another in the real experiment. You have no way of knowing which is which. This is the case even when you have full knowledge of the prediction method.

Another technical point is what to put in the boxes. Whatever is inside the original room’s boxes will necessarily be in the cloned room’s boxes. Of course, they don’t know what to put in the boxes until after the original room’s experiment is run. The solution is to leave the boxes empty or eliminate them altogether. Instead, you state what you would do, and collect your money when you leave the room, provided you turn out to be the duplicate (the subject of the “real” experiment).

The matter scanner does not change the paradox one whit; it only demonstrates a way the prediction could avoid infinite regress. You can’t dismiss Newcomb’s paradox as depending on infinities, an omniscient deity, ESP, or any other imponderable. Agreed, quantum
uncertainty would probably rule out the matter scanner. It seems unsatisfying, however, for mere physics to stand in the way of a paradox of logic.

If a matter scanner is possible, we would have the paradox in its acutest form. There would be two identical persons in identical rooms; they would, after puzzling over the situation, make their choice halfheartedly or with confidence; and the predictor, watching the first person, would know what the time-delayed doppelgänger would do as surely as he could know the outcome of a rerun football game on television. The subjects taking both boxes would always get $1000; the subjects taking box B would always get $1 million. There is the situation, and it is as inscrutable as ever.

THIS BOOK is only a sampler of the many provocative paradoxes and thought experiments being discussed in the scientific and philosophical literature. Those interested in further reading would do well to start with recent issues of
Analysis, The British Journal for the Philosophy of Science, Mind, Philosophical Studies
, and
Philosophy of Science
.