By modern standards the criminal code of Ypiaria [pronounced, of course, "E-P-aria"] allowed its police force excessive powers of arrest and interrogation. Random detention and questioning were accepted weapons in the fight against serious crime. This is not to say the police had an entirely free hand, however. On the contrary, there were strict constraints on the questions the police could address to anyone detained in this way. One question only could be asked, to be chosen at random from a list of three: (1) Are you a murderer? (2) Are you a thief? (3) Have you committed adultery? Detainees who answered "yes" to the chosen question were punished accordingly, while those who answered "no" were immediately released. (Lying seems to have been frowned on, but no doubt was not unknown.)
To ensure that these guidelines were strictly adhered to, records were required to be kept of every such interrogation. Some of these records have survived, and therein lies our present concern. The records came to be analyzed by the psychologist Alexander Graham Doppelganger, known for his work on long distance communication. Doppelganger realized that among the many millions of cases in the surviving records there were likely to be some in which the Ypiarian police had interrogated both members of a pir of twins. He was interested in whether in such cases any correlation could be observed between the answers given by each twin.
As we now know, Doppelganger's interest was richly rewarded. He uncovered the two striking and seemingly incompatible correlations now known collectively as Doppelganger's Twin Paradox. He found that
(8.1) When each member of a pair of twins was asked the same question, both always gave the same answer;
and that
(8.2) When each member of a pair of twins was asked a different question, they gave the same answer on close to 25 percent of such occasions.
It may not be immediately apparent that these results are in any way incompatible. But Doppelganger reasoned as follows: 8.1 means that whatever it is that disposes Ypiarians to answer Y or N to each of the three possible questions 1, 2, and 3, it is a disposition that twins always have in common. For example, if YYN signifies the property of being disposed to answer Y to questions 1 and 2 and N to question 3, then correlation 8.1 implies that if one twin is YYN then so is his or her sibling. Similarly for the seven other possible such states: in all, for the eight possible permutations of two possible answers to three possible questions. (The possibilities are the two homogeneous states YYY and NNN, and the six inhomogeneous states YYN, YNY, NYY, YNN, NYN, and NNY.)
Turning now to 8.2, Doppelganger saw that there were six ways to pose a different question to each pair of twins: the possibilities we may represent by 1:2, 2:1, 1:3, 3:1, 2:3, and 3:2. (1:3 signifies that the first twin is asked question 1 and the second twin question 3, for example.) How many of these possibilities would produce the same answer from both twins? Clearly it depends on the twins' shared dispositions. If both twins are YYN, for example, then 1:2 and 2:1 will produce the same response (in this case, Y) and the other four possibilities will produce different responses. So if YYN twins were questioned at random, we should expect the same response from each in about 33 percent of all cases. And for homogeneous states, of course, all six posible question pairs produce the same result: YYY twins will always answer Y and NNN twins will always answer N.
[Note--I think Price actually gets the probability wrong here. If both twins are YYN, for example, then if they are questioned at random, the probability both will give the same answer would be P(first twin answers Y)*P(second twin answers Y) + P(first twin answers N)*P(second twin answers N) = (2/3)*(2/3) + (1/3)*(1/3) = 5/9, not 1/3 as Price claims. But this doesn't change the overall argument.]
Hence, Doppelganger realized, we should expect a certain minimum correlation in these different question cases. We cannot tell how many pairs of Ypiarian twins were in each of the eight possible states, but we can say that whatever their distribution, confessions should correlate with confessions and denials with denials in at least 33 percent of the different question interrogations. For the figure should be 33 percent if all the twins are in inhomogeneous states, and higher if some are in homogeneous states. And yet, as 8.2 describes, the records show a much lower figure.
Doppelganger initially suspected that this difference might be a mere statistical fluctuation. As newly examined cases continued to confirm the same pattern, however, he realized that the chances of such a variation were infinitesimal. His next thought was therefore that the Ypiarian twins must generally have known what question the other was being asked, and determined their answer partly on this basis. He saw that it would be easy to explain 8.2 if the nature of one's twin?'s question could influence one's own answer. Indeed, it would be easy to make a total anticorrelation in the different question cases be compatible with 8.1--with total correlation in the same question cases.
Doppelganger investigated this possibility with some care. He found, however, that twins were always interrogated separately and in isolation. As required, their chosen questions were selected at random, and only after they had been separated from one another. There therefore seemed no way in which twins could conspire to produce the results described in 8.1 and 8.2. Moreover, there seemed a compelling physical reason to discount the view that the question asked of one twin might influence the answers given by another. This was that the separation of such interrogations was usually spacelike in the sense of special relativity; in other words, neither interrogation occurred in either the past or the future light cone of the other. (It is not that the Ypiarian police force was given to space travel, but that light traveled more slowly in those days. The speed of a modern carrier pigeon is the best current estimate.) Hence according to the principle of the relativity of simultaneity, there was no determinate sense in which one interrogation took place before the other.
."
