So, I’m through Newsweek this weekend, and I run across a quote from Goucher College mathematician Robert Lewand, where he said:
“Somebody in the governor’s office was just having a little fun.”
What Dr. Lewand was describing was the result of a recent veto by California Governor Arnold Schwarzenegger. So, what could have brought this so much attention?
Well, it turns out that the statement accompanying Gov. Schwarzenegger’s veto came with a subliminal, more obscene message. Here’s what the actual statement said:
“For some time now I have lamented the fact that major issues are overlooked while many unnecessary bills come to me for consideration. Water reform, prison reform, and health care are major issues my Administration has brought to the table, but the Legislature just kicks the can down the alley.
Yet another legislative year has come and gone without the major reforms Californians overwhelmingly deserve. In light of this, and after careful consideration, I believe it is unnecessary to sign this measure at this time.”
Seems harmless enough, right? Well, if you look at the actual statement, and especially the first letter in each line of this statement, you’ll see the intended message of “f–k you”. (To read more about the story, you can go here…)
You might be asking – how does anyone know that anyone intended anything? Couldn’t this just be a coincidence? Well, it could be, but we have to ask ourselves a couple of questions: One, how likely is it that this arrangement of letters occurred by accident? And two, how likely is it that someone in the Governor’s office arranged the letters on purpose?
In science, we ask ourselves these questions all the time to figure out which one leads to the right answer. So, let’s start with the second question first – how likely do we think that a government staffer actually played with the sentences to make the message read this way? I don’t know, but I’m sure it’s pretty unlikely, but let’s say that the odds of this happening is… oh… 1 in a million. Let’s even put it out there more – let’s say the likelihood of this happening is about 1 in 1 billion. That’s certainly pretty rare!…
Now, what we do next is to figure out how likely it is that these seven letters came out the way they did by accident. Well, if you look at how often letters actually occur in the Engligh language, you can calculate this likelihood. I went to Wikipedia and found these occurrence probabilities, so I calculated the likelihood for myself.
(if you don’t mind, I’d rather not list the letters here – don’t want the obscenity police coming after my blog…)
But here’s something that was interesting. Originally, when I heard that Professor Leward said it was a 5.5 in 1 trillion shot for this arrangement of letters to be random, I didn’t believe him. I thought he was off.
Starting simply, if there are 26 letters in the alphabet, then assuming that each letter is equally likely (which it isn’t, but this is where I started…), then 1/26 = 3.846%, and then multiplied seven times for the 7-letter message, this would be about 1 in 8 billion. So I thought, “Wait! This mathematician is wrong, isn’t he?!”… Well, it turns out that I was… But then again, I wasn’t (I’ll get to that below…)
So I did the calculation using the actual letter frequencies that I found on Wikipedia, and that’s where I got the same answer as Professor Leward – 5.5 in 1 trillion, or 1 in 185 billion… (it turns out that the letter “k” is actually quite rare – only 0.77% as opposed to the letter “f” which occurs 3.78% of the time…)
But wait, there’s more. It turns out that Professor Leward should in fact revise his calculations. The letters of the obscene message actually occur as the first letter of each word, and the letter frequencies for being the first letter of a word are different than the letter frequencies regardless of where the letter shows up.
So, if you use the letter frequencies for the first letter of each word (also on the Wikipedia page), you get a likelihood of 1 in 485 billion or about 2 in 1 trillion, about 2.7 less likely than Professor Leward’s original calculation.
Now, which cause for the “FY” memo is more likely? Well, now what we do is compare the likelihoods, and the one that has the greater likelihood is the best explanation. So, even though it would be very rare for a staffer to embed coded vulgarity into the Governor’s statement (1 in a billion), it’s still nearly 500 times more likely that this is the cause than for these letters to have arranged themselves by accident. Using our likelihood ratio analysis, we can have a lot of confidence that some staffer is going to get a spanking sometime soon…
So is this proof? It depends on what you mean by proof, but nothing is absolute – you can only compare how likely things are to cause what we see. This is how science works, and how we all make our decisions…
Obscene messages happening at random and government staffers arranging for obscene messages to show up in official documents are both very, very rare events. However, it’s far more likely that Gov. Schwarzenegger’s F-bomb veto is the result of purpose than of accident…