Friday, October 30, 2009


Gimme an "F"!...

Many of you have probably heard about the Governator’s playing with steganography — specifically, an acrostic:Governor Schwarzenegger’s veto letter

Of course, everyone’s buzzing about whether it could possibly have been accidental, as his staff claims, or whether it just had to be intentional. My opinion: I think it was intentional. But, opinions aside, let’s take a look at it for a moment, without trying to pull out actual numbers (there are plenty of folks posting statistical analyses that do have numbers, so you can look for those if you like).

The chances, of course, of writing some text that spans seven lines and happens to have the first letters of each line spell “Fuck You”, are exceedingly, vanishingly, teeny-tiny. Really, really, really, really small. Even more so if you consider capitals, and the paragraph break between the two words, forming the “space”. Minuscule.

But not zero. It is possible, however unlikely it may be, for it to happen by chance.

But back up and consider that there are many combinations that might have appeared there and been thought noteworthy. It could have said “kiss ass”, for example, or “eat shit”. It didn’t even have to take all seven letters: if it said “bite me”, and the first or seventh letter were unrelated, we’d probably still hear about it and wonder if he’d meant to do it. We’d even wonder about “x no way x” (substitute your favourite irrelevant letters for the x’s).

So the chances of getting something that we’d notice and put in the newspaper are, while still not at all high, not as tiny as it seems when we look at the single phrase that did show up.

And, in fact, the chances that there’d be something sensible there at all, even if it were, say, “tadpole” are actually pretty good (especially if you consider incomplete strings, like the “no way” example). This is what sucks the bible-code lunatics in, when they think they can find secret messages from God hidden in the bible. On the surface, it seems to us that “discovering” a convoluted pattern that we can make sense out of in light of something we know (or would like “evidence” of) means something. In fact, it means only that we’re good at artificially finding meaningless patterns.

How likely is it that “1 2 3 4 5” will come up in tonight’s lottery drawing, in that order? How likely is “37 12 83 7 22”? Exactly the same (both very, very unlikely). Yet we perceive the former to be “impossible” — if it should ever show up, we could be sure of a fraud investigation, and a likely re-draw — while accepting the latter as a normal “random” set of lottery balls.

If we should fairly and thoroughly shuffle an unarranged deck of cards, what’s the probability that we’d end up with the four aces on top? What’s the probability that the top four cards, in order, will be the jack of hearts, the three of spades, the seven of hearts, and the ten of diamonds? The former is actually much more likely than the latter (because the order doesn’t matter... 24 times more likely, 1 in 270,725 vs 1 in 6,497,400), but we’re inclined to think otherwise. We do not have a good intuition about probabilities, and we overemphasize what appear to us to be “obvious” patterns.

Of course, there’s a difference between playing with the layout of bible text until we can find some pattern that we interpret to be a fuzzy message about the JFK assassination... and straight out seeing “fuck you” as an acrostic in something someone wrote yesterday. Yeah, I think Governor Schwarzenegger (or his staff) was having some fun. And my sincere thanks to the Governor for making today’s blog topic easy.


Nathaniel said...

In the 1980's at CMU I wrote an algorithm that generated filenames as unique ID's of 18 characters, using something very close to today's base64. Then I wrote another piece of software that told all the users the names of all files being written or read from the remote file system (AFS). Sure enough -- and a picture of this is in my book Programming as if People Mattered -- one of my users complained when one of the 18 character strings incuded "FuckYOO" -- even though it was surrounded by 11 other characters.

Barry Leiba said...

Too bad no one knew about the bible-code people then — you could have told the user it was a message from God.

The Ridger, FCD said...

It's actually 8 lines, since the first one fits, too.

Barry Leiba said...

Sure, if you want to make it fit. I've never heard anyone say, "I fuck you!", as a statement of defiance.

Of course, the desire to include the first line to extend the pattern rather demonstrates my point.