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Tuesday, July 04, 2006

Letters, Words, and Big Numbers, Oh My!

So, I was bored and... decided to play around with license keys some. Everybody hates license keys, right? Especially in cases like Neverwinter Nights, where they have 35 alphanumeric characters (!). We're currently in the process of making some changes to how the system works at work, and one of the results is that we'll now be using license keys for something. So, what can we do to make them more friendly?

Let's apply some basic psychology to the problem: the brain only has so many registers (bits of information that it can hold readily available without requiring effort to memorize the information; I think the exact number is like 5), with each one able to hold a symbol (remember that the brain's processing abilities are highly symbolic). For a random alphanumeric string, each character must be stored in a separate register (if you think that's dehumanizing, you should see the occasional debates me, DB, and BZ - all of us programmers, but all of us also interested in biology - have on the topic of reproduction and evolutionary psychology; and yes, I am aware that "me" isn't technically a subjective pronoun). For a string of, say, numbers where a pattern is evident, the brain can apply compression to the string, and store a larger number of numbers in its registers than it would be able to if there was no pattern.

So, my idea is simply this: use symbols larger than letters and numbers in the license key. This one dictionary I picked for this purpose has 16,100 English words of 7 characters or less (a somewhat arbitrary limitation I established), and that's not even including conjugations of most verbs.

Let's see how well this works. If we take the NWN key, the maximum number of theoretically possible keys is about 3*10^54 (36^35; quiz: how many bits is that?). I can remember about 5 characters at a time, meaning I will have to look at the key 7 times to type it in, if I don't type as I'm reading it (which is reasonable for people who aren't secretaries or programmers). It would take 13 words to represent this key (log(36^35) / log (16,100)). I can remember about 4 of these words at a time, meaning I can type them in 3-4 groups, almost half as many as for the string of random characters.

However, there's one more thing to consider, which is actually a facet of something already mentioned: most people aren't secretaries or programmers. They probably can't type even half as quickly as I can. In addition to the previously stated implications, this also means that they're going to have at least twice as long as I do to remember the words/characters, and 13 words would be a total of 75 characters (average word length of 5.75 letters). And unlike registers in a CPU, the brain's registers lose the information they were holding fairly quickly. Unfortunately, I don't really have any way of quantifying this effect, like I was able to benchmark how much I could remember and type in, so this really remains an unknown.

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