The Bible Codes and the Clinton Sex Scandals excerpted from Once Upon a Number - The Hidden Mathematical Logic of Stories,
(p. 57, Basic Books, Nov. 1998) by John Allen Paulos

The brouhaha involving the codes to be found in various holy books brings to mind a lesser-known recent discovery that has been suppressed by President Clinton's lawyers. Encoded within the U.S. Constitution is a prophecy of the Lewinsky sex scandal! Placed there presumably by the Founding Fathers, the ten letters in the words "Bill" and "Monica" appear sequentially at regular intervals within the revered historical document. Remarkably similar to the codes discussed in Michael Drosnin's bestselling The Bible Code, the details are instructive: the interval between the successive letters in Bill/Monica is 76; that is, at a particular position within the Constitution, there is a b, followed after 76 letters by an i, followed after another 76 letters by an l, and so on until the a of Monica is reached 76 letters after the c. (These are the ELS, equidistant letter sequences, that have attracted so much attention.)

Having the discovery of this seemingly prescient sequence of letters brought to our attention, it is only natural to wonder about the probability of its occurrence. If we assume as a first approximation that the letters of the Constitution are randomly distributed, the probability of observing the ten letters in Bill/Monica in any given set of ten equidistant letter positions within the Constitution is easily computed. All that is required is to multiply the probabilities of occurrence of each of the 10 letters in the sequence. (If, for example, in any given position the probability of a b is .014, the probability of an i is .065, and the probability of an l is .011, then the probability that the four letters in "Bill" appear in any four given positions is simply .014 x . 065 x .011 x .011.) Thus the product of ten small numbers - let's call it P - is a truly infinitesimal probability.

Because this likelihood is so minuscule we might think that the occurrence of a Bill/Monica sequence at some particular set of positions within the Constitution is an extraordinary event, but we must be careful about our understanding of this extreme improbability. The meaning is this: If we were to choose one text from the collection of all texts which have the same number of letters of each kind as the U.S. Constitution, and if we were to designate an ordered list of ten particular letter positions and then check to see if the letters in Bill/Monica were in these designated positions, the probability is P that they would be.

This procedure does not reflect, however, the way the Bill/Monica sequence in the Constitution was discovered. In our probability calculation we assumed that the letter sequence and positions were specified beforehand and the text selected and observed afterward. In the actual discovery of the Constitution code, however, the observation came first. That is, the Bill/Monica sequence of letters was found in the document by, we can imagine, a computer-savvy scholar in some think tank on the Potomac. Once the sequence was found, the question of the likelihood of its occurrence became moot.

Another equally salient point is that the Bill/Monica ELS need not occur in some particular place in the Constitution. We're not especially concerned that the sequence begin at, say, the 14,968th letter; rather we look for this pattern beginning anywhere in the Constitution. That is, we look at all the many different letter positions in which the 76-letter equidistant pattern can begin (assume there are X such letter positions within the Constitution) to see if we can find at least one instance of it. The probability of observing the Bill/Monica pattern for this procedure is considerably larger, roughly equal to P x X.

Now suppose that we do not search merely for an interval of 76 between the letters in Bill and Monica, but rather search for the pattern at all possible intervals between, say, 1 and 1000 and beginning anywhere in the Constitution. With this procedure the numbers change again. The probability that we observe the pattern Bill/Monica is approximately equal to P x X x 1,000, and this number is not so amazingly small.

And we can again increase the probability of finding such a sequence by further expanding the number of ways in which it might occur. We might allow backward searches, or look along diagonal lines in the text, or, as is the more common case with the bible codes, permit distinct ELS's for "Bill" and "Monica" to be nearby, but separated in the text, or search for alternative names for the President or for his paramour (or paramours - Paula, Gennifer, Kathleen, etcetera), or loosen the constraints in indefinitely many other ways.

Now if our search for these sequences isn't conducted openly and if the cases in which nothing appropriate is found are discarded (nearby ELS's for "zucchini" and "squash," for example), and if we go public only with the interesting sequences we do find and compute probabilities in a simplistic way, then it is clear that these sequences do not mean what they may seem to mean on the surface. Performing a procedure one way and computing a probability associated with a different procedure is, to put it mildly, just not kosher.

Almost all of the many biblical codes, whether from Jewish, Christian, Islamic, or modern sources, whether utilizing Cabala or Monica, have defects vaguely similar to those of the Constitutional codes**. The statistical paper mentioned in the introduction to this book may illustrate a different more subtle defect having to do with unintentional biases in the choice of sought-after sequences, vaguely-defined procedures, the variety and contingencies of ancient Hebrew spelling, or Ramsey's theorem (to be discussed in a later chapter), a deep mathematical result about the inevitability of order in any sufficiently long sequence of symbols. This, in fact, was the reason for the paper's publication, not a belief in coded prophecies. Common sense underscores the inanity of basing any political, spiritual, or sexual judgments on these contextless numerological oddities.

** As far as I know, the Bill/Monica equidistant letter sequence does not appear in the U.S. Constitution although researchers Brendan McKay and David Thomas have located surprising sequences virtually everywhere they searched - in Genesis (which contains more than two dozen ELS's for Hitler and Stalin), Shakespeare, Tolstoy, Melville's Moby Dick (which contains an ELS for "Oceans hold joy"), a U.S. Supreme Court ruling on creationism, and Chicago Tribune editorials. Thomas has even found that the following verse from the King James Version of Genesis contains a short, topical ELS for Roswell, which is capitalized, and, beginning with the u of "thou," one for UFO as well. And hast not suffered me to kiss my sons and my daughteRs? ThOu haSt noW donE fooLishLy in so doing.

The likelihood of each of these specific ELS's is minuscule, from which nothing can be inferred except that it is quite easy to misconstrue tiny probabilities.