Calculatiing Schwarzenegger’s Letter Statistics

Politics can be about principled differences fought out verbally in public. Politics can represent our noblest aspirations for creating a free and orderly society. Sometimes, politics can also resemble middle-schoolers calling names in the school yard. Perhaps it is not surprising that such behavior can be found in California, that seems to lead the country in so many regards.

San Francisco assemblyman Tom Ammiano in an emotional outburst disagreed with California Governor Arnold Schwarzenegger shouting, “You lie,” as Schwarzenegger began to speak at a Left-of-center group. Ammiano further suggested that the governor, “kiss my gay ass?” The incident certainly did not resemble the civility of the Lincoln-Douglas debates.

Apparently, the Governor’s office is not above subtle slights of its own. The Governor vetoed Ammiano’s bill for financing for the Port of San Francisco. The curt letter explaining the veto apparently contained a hidden message. If you carefully examine the letter reproduced below,

you might notice that the first letters of the lines in the body of the text spell out “I f— you.”This is so silly, that one might believe that the whole story is apocryphal, but is was reported, presumably seriously by the San Francisco Chronicle. No one believes that the hidden message is the “weird coincidence” press secretary Aaron McLear argued it was, but there is a interesting statistical question as to how likely is it that message would have appeared randomly.If Pw(i) is the probability that a word in the English language begins with the letter i, and Pw(f) is that a word begins with f, etc., then the probability of this curious sequence is

Pw= Pw(i) Pw(f) Pw(u) Pw(c) Pw(k) Pw(y) Pw(o) Pw(u).

Unfortunately, those probabilities about word beginnings were not easily found. A less direct means to estimate the likelihood of the letter sequence is to use the probabilities of the letters occurring in the English language. These values can be obtained from Wikipedia. The probability of this “weird coincidence” would then be:

P= P(i) P(f) P(u) P(c) P(k) P(y) P(o) P(u)

or

P= (0.0697) (0.0223) ( 0.0276) ( 0.0278) ( 0.0077) (0.0197) ( 0.0751) (0.0276)

or

P= 3.74971 x 10^(-13)

or one chance in 2.7 trillion.

We thank the Governor Schwarzenegger and Assemblyman Ammiano for the entertainment and an opportunity to make an interesting calculation.