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March 07, 2009

Two-Bit Players Communicating Via Signs

This is, to me, one of the most effective demonstrations of Shannon and Weaver's Theory of Communications, which discusses transmission of information through a channel in the presence of noise:

Shannon and Weaver's information model describes an information source, a transmitter, a signal, noise, the received signal, a receiver, and a destination. It's the basis of almost all modern information theory.

Claude Shannon went on to offer a quantification of information in units he called "bits", binary digits. Our modern discussion of gigs and megs are just multiples of Shannon's bits.

We can calculate the bits of information exchanged by the two characters via their notes using this formula:

The messages they exchanged are, "take a photo im kidding stacey jason nice 2 meet u nice 2 meet u 2 i have a secret i was watching u first do u want to meet i got promoted we should celebrate absolutely do u want to meet thought youd never ask hi". (For the purpose of this discussion, we're avoiding the images: the tictactoe, the torso, the face.)

A string length of 215 characters, in a 27-character set, conveys 27^215 bits of information, or 5.5361684267445E+307 bits, or 5.53 * 10^307 bits. Less than a googolplex.

Romantics and non-engineers might say, Oh No! To limit our understanding of their communications to just their text signals is so inappropriate! You lose all the nuance and texture!

Of course, it is a gross oversimplification to say that all of their communication was across the channel of their signs - they saw each other, they exchanged non-verbal signals, they laughed, etc. Her signaling with a mirror was a clear communication. A lot more information than 5.53 * 10^307 bits was communicated between them.

For the calculation to be valid, the only communication between them would have been the messages. Where would we see such an artificial exchange? In telegraph- or email-mediated correspondence, which is to say: text messaging. Does anybody believe that the movie would have ended the same way if they had only communicated via text messages?

Which, thank you, brings me to my point about communicating via text messages and email. It's not nearly as effective to text/email somebody as it is to speak to them, and it's not nearly as effective to speak/phone somebody as it is to meet with them.

So, we start with a love story, we middle with Shannon's calculation of bits over a narrow channel, and we end with a generalization: it's more effective to meet people than to exchange text messages with them.

I'd like to thank Chris Briem of Nullspace for pointing me to, where I found this movie. It really is fascinating from an information theory point of view.


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