Cracking the Code Math for a Veto Message

By Carl Bialik

My print column this week analyzes the math behind a coded message in a veto by California Gov. Arnold Schwarzenegger. The governor said it was a “total coincidence” that the first letter of each line in his veto message spelled out a common obscenity. Mathematicians who crunched the numbers say the expression was highly unlikely to emerge by chance, though their estimates, as published in the press and on blogs, differ widely.

Steven Piantadosi, a graduate student in cognitive sciences at the Massachusetts Institute of Technology, arrived at a probability of slightly less than one in one trillion, as he noted on his blog. A 1960s-era compilation of American English texts known as the Brown corpus, analyzed by Linguistic Data Consortium researcher David Graff, yielded almost exactly the same calculation. Dave Thomas, a staff scientist at New Mexico Tech, used works from the Project Gutenberg database of copyright-free electronic books, and came up with one in 500 billion. Mathematician Edward Lewand of Goucher College told NPR he came up with about one in 180 billion. “I think it is very unlikely that this acrostic was just a coincidence,” Lewand said.

Schwarzenegger isn’t Jane Austen nor William Shakespeare, two of the sources for the letter-frequency numbers behind Thomas’s calculation. It’s possible that he’s more prone to use words that begin with the letters that made up the coded message. For instance, “K” is the least likely letter in the message to start a word. But the “K” in the veto message comes from a statement that the state legislature “kicks the can down the alley.” Some blogs have suggested that this phrase was included merely to make the encoded veto message work. But the phrase, meaning delaying tough decisions, improbably has become a standard one in California politics in the last year.

Also, as Thomas and others note, these probabilities are for the message to appear in any given seven lines. Schwarzenegger has vetoed about 1,700 bills, and often attaches messages to his rejections. However, these brief missives don’t add up to enough text to explain the improbable profanity. Using the text of the letters from the California government’s Web site, Graff could find no message formed by the beginning of each line that was any edgier than “espy tit,” in a veto of a bill that would have designated 211 as a social-services phone number.

If one broadens the criteria for such codes, they become easier to find. In my brief email to Brendan McKay, a computer scientist at Australian National University in Canberra, about the veto message, he found the word “measures,” by counting backwards four letters at a time from a certain spot in the email. He also found “events,” by counting backwards five letters at a time from elsewhere in the message. “The chance of this happening accidentally (even allowing for all possible starting points and all possible skip amounts forwards or backwards) is about one in a billion,” McKay said. “But I don’t believe you did it on purpose.” That’s partly because he didn’t look specifically for those words; “I fed a whole dictionary [into his computer program] and then spun a story around two of the many words that appeared,” McKay said.

Reflecting on the difficulties of calculating the probability that the veto message arose by chance, Williams College mathematician Edward Burger said, “That’s the annoying thing about coincidences. We should definitely expect them. But the annoying thing is we just don’t know the actual probability that one of these things will happen.”

Further reading: Read more about a one in 10 billion trillion long shot that cost an English journalist a job, a one in 300,000 trillion trillion long shot that riled some Pakistanis and other Numbers Guy writings on coincidences and unlikely events.

Thanks to Jason Fry for the idea.