Having already used the awesome power of math to shoot down Balloon Boy, tonight, I'll take a crack at the Governator himself, Arnold Schwarzenegger.
You've already seen his secret message to Assemblyman Tom Ammiano. Ahnold's office claims the big "fuck you" formed by the first column of letters in his veto message was "a strange coincidence." and that "When you do so many vetoes, that’s bound to happen."
The question before us: is something like this "bound to happen"? How likely is it that those 7 letters and that one space would appear in that particular arrangement just by chance?
To answer that question, we need a rough and ready estimate of the probabilities involved. (It's about 1 in 282 billion, if you want to skip the math. But who would want to do that?)
Let's assume that all 8 letter acrostics are equally likely. That's obviously wrong, since way more words start with 's' and 't' than with 'z' or 'x'. But we're estimating here and this simplifying assumption won't throw us too far off.
With that assumption, we can easily estimate the odds of "fuck you" appearing by chance. Each line of the veto message could begin with any of 27 characters: one of the 26 English letters or a space, which means the total possible combinations is just 27^8. Written out that's 282,429,536,481.
So the odds of "fuck you" appearing randomly are roughly 1 in 282 billion. It's not looking good for the Governator.
Not so fast!
In calculating these odds, we've over looked one big gotcha.
We're really good at spotting patterns in random data. It's not just "fuck you" that would have caught our attention. If the veto message had formed the acrostic "love you", "call you" and even "hot dogs", we still might have taken notice.
To correct for this, we need an estimate of how many recognizable 8 letter words and phrases there are. That takes a bit more work.
Let's start with a list of the 1,000 most common English words. Searching Scrabble sites, I found such a list, sampled it at random and counted words of different lengths.
Estimating from that sample, I got 50 1 letter words, 250 each for 2, 3 and 4 letter words, 100 with 5 letters, 50 with 6 and 25 each with 7 and 8 letters. (Again, we're just estimating here. So having twice as many 1 letter words as there are letters doesn't hurt. In fact, that will shift the odds in Arnold's favor.)
Multiplying out and adding up all the combinations gives roughly 800,000 8 letter phrases which could have shown up in the veto message. But most of those would have been nonsense and unlikely to attract attention. "Doghaste" or "as sixth" any one?
Let's say only 1% of possible combinations would catch someone's eye and be noteworthy enough to make the news. That makes our corrected result 8,000 in 282 billion. Simplifying, that's about 1 in 350 million.
As Adam and Jamie might say "Totally busted".
That was too much work.
Figuring out the number of 8 letter phrases wasn't hard, but there was an easier way.
Before I went searching for an appropriate dictionary I thought, "Most common words are short. I could just count up all the 2 word combinations amongst the 1,000 most common words." That would have been 1,000 x 1,000 or 1,000,000 combinations.
That's pretty darn close to the 800,000 estimate I got after all my counting and mathulations. Since I already knew I was going to be comparing it to 282 billion, a huge, huge number by comparision, I could have saved all that work.