Encoding Information


I finished reading Katherine Neville’s new novel The Fire yesterday. It’s good and worth a read, but its prequel, The Eight, is a masterpiece. Anyway, I spent most of the time thinking about encoding information. (I’ve thought about this a lot before reading this book too.) In particular, it is interesting to think about how much information can be encoded into some (different) string of characters.

When I was at Santa Barbara, Rabbi Mendel told me a story. The entire story is not terribly relevant, but the crux was that two people had a falling-out over whether one Torah portion could contain all the information about the universe. The skeptic asked his teacher to find him in the Torah portion, and the teacher said that his name was spelled out as the second letters of some set of consecutive words in the portion.

I am unconvinced. Of course if you have enough letters, you can find various things spelled out, but presumably if someone is going to be decoding the message, that person will want some sort of criterion for determining whether any particular hidden message is intentional or not. In particular, one major criticism of Bible codes and other such nonsense codes is that they have no predictive power. I guess that’s another way of saying that there’s no way of telling whether something is intentionally encoded or not.

Here is one example of a good code from The Eight:

I have warned you but you
will not listen. When you
meet with danger,
you should not hide your head
in the sand — there’s a lot of sand in
Algeria.

The words are mostly meaningless; only of interest are the first words of each line. (The character figured this out accidentally.)

Several codes in The Fire were notable, albeit much less convincingly executed. The first was a telephone number given as (615) 263-94. Decoding that is reasonable albeit maybe a bit of a stretch: two digits are missing, so one must figure out what they are. Well, rewriting the number as 61 52 63 94 and reversing each set gives 16 25 36 49, after which it’s logical that the last set should be 64 (squares). I’ll believe that someone who is good at dealing with encoded messages could have figured that out.

The next was a message that read:

WASHINGTON
LUXURY CAR
VIRGIN ISLES
ELVIS LIVES
AS ABOVE, SO BELOW

The fourth line is easy to decode if you’ve been reading the book. (I didn’t have any trouble with it.) The person who left the message is named Cat Velis. The first three are also pretty easy: Washington is DC, luxury car is LX, and Virgin Isles is VI (I’m not sure what that’s supposed to mean exactly.) Well, those are all Roman numerals which come out to 666. That number keeps coming up in the book, although it isn’t clear to me why. However, that’s the wrong code, but I didn’t really understand the logic behind the right one. And the last line I don’t feel like trying to explain.

There are a few more overly convoluted codes in the book, as well as people who know way too much. Go and read it; I won’t tell you what happens, but read The Eight first.

When he was teaching the algebraic number theory course I took a few years ago, Agboola said that the zeta function of a number field tells you everything you could want to know about the number field if only you can figure out how to ask. But in that case we like to know everything; nothing is encoded unintentionally. (And if you want to tell me happy things about zeta functions of number fields, I’d be glad to listen.)

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About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.
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2 Responses to Encoding Information

  1. dreamyshade says:

    have you read a lot of borges stories? i don’t remember if i know. he just spends a lot of time thinking about this kind of thing too – detective stories, infinity, hermeneutics, text.

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