Christian_Szegedy comments on Open Thread: July 2010 - Less Wrong
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Information theory challenge: A few posters have mentioned here that the average entropy of a character in English is about one bit. This carries an interesting implication: you should be able to create an interface using only two of the keyboards keys, such that composing an English message requires just as many keystrokes, on average, as it takes on a regular keyboard.
To do so, you'd have to exploit all the regularities of English to offer suggestions that save the user from having to specify individual letters. Most of the entropy is in the intial charaters of a word or message, so you would probably spend more strokes on specifying those, but then make it up with some "autocomplete" feature for large portions of the message.
If that's too hard, it should be a lot easier to do a 3-input method, which only requires your message set to have an entropy of less than ~1.5 bits per character.
Just thought I'd point that out, as it might be something worth thinking about.
This is already exploited on cell phones to some extent.