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Okay, that clears up a lot for me. Thanks.
stevo
On Tue, Dec 20, 2011 at 12:53 PM, Alex Fink <[log in to unmask]> wrote:
> On Tue, 20 Dec 2011 12:27:20 -0500, MorphemeAddict <[log in to unmask]>
> wrote:
>
> >I'm confused by the way you're using 'bit'. A single unicode character
> >(4-digit hex) uses 16 bits, so 80 bits is just 5 unicode characters. How
> >are you getting "a 10 word phrase" out of that?
> >And what does "the OED has ~250k words (~= 18 bits)" mean? How is about
> >250000 words approximately equal to 18 bits?
> >stevo
>
> We're talking about bits of entropy; you can think of this, loosely, as the
> number of bits it would take to store the data in question if you used _the
> densest possible (decodable) encoding_ for such data.
>
> At 16 bits per letter, Unicode is certainly not the densest possible
> encoding for English words! You could get away with 5 bits per letter with
> 00000 = 'a', 00001 = 'b', ..., 11001 = 'z'. And even that isn't the best
> possible; if e.g. you gave shorter codes to more frequent letters and
> longer
> codes to rare ones, you could get away with fewer bits (on the average, and
> it is the average that counts). Etc.
>
> If I have a piece of data and you know it's a word from the OED, then I can
> convey which word it is by telling you only 18 bits, with the following
> scheme: look up which position it comes in in the OED ("a" is word 1, "a2"
> is word 2, "a1" 3, "aa" 4, "aal" 5, "Aalenian" 6, ...) and write down that
> number as an 18-bit binary number. Hence there's (at most!) 18 bits of
> entropy in choosing one word from the OED.
>
> Here's a different way to ask Sai's question: provide a list of 2^80
> different English sentences so that
> a) they are valid, if very absurdist, English phrase (eg "Barnaby
> thoughtfully mangles simplistic yellow camels" is fine),
> b) ---
> c) each one is short enough to be easily memorized, and
> d) you can write down the list (in theory) without use of any external
> service, i.e. it could be implemented with a small amount of client-side
> code plus a canonical static dictionary file
>
> Alex
>
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