Re: Issue 855 in lilypond: fix the command index

[Graham Percival]

On Thu, Dec 23, 2010 at 11:37:11AM +0100, Werner LEMBERG wrote:
> >> A long time ago I've seen a demonstration how to count up to 100 (or
> >> more) with a single hand.  Unfortunately, I've forgotten all details.
> > 
> > hmm... if you use the hand position/orientation, you could "easily"
> > add another 5 bits, which would give 1024.  The "left-right"
> > positions aren't terribly comfortable for me, so let's call it 3
> > more bits -- which still gives 256.
> 
> Well, the demonstration showed a system which was (or still is) in
> practical use.  The normal binary system doesn't belong into this
> category.

Maybe it was "counting for practical purposes", i.e. accurate to
the nearest 5% ?  So for numbers 1-20, it's completely accurate,
but beyond that it might be off by a few numbers?  Or maybe it was
"counting with the aid of one's fingers", i.e. you count up to 5
(or whatever) in your head, and use the fingers to keep track of
how many 5s you have?

I don't have any references handy, but I'm pretty certain that
it's a basic theorem/theory/law (I can never remember which one is
which, especially when sick) of information theory that you cannot
store more information than you have states in which to store it.
There's only 2^5 different ordered permutations/combinations (see:
sick) of 5 bits, so it's impossible to represent more than 2^5
different numbers.

Of course, another way to get around the 2^5 limit would be to
have more than 2 states for each finger.  If we had 3 states
(fully closed, half-open, fully open) then we'd have 243 different
states.  I could certainly imagine somebody inventing an easy way
to count with that system.
(they'd probably want to avoid having the 3rd finger fully open
and the 4th finger half-open, since that's a difficult hand
position for most people -- oh, and I'm using violinist fingering
here, i.e. thumb is 0, not 1 like the pianists do that.  I've had
so much confusion when teaching cello to piano students over this!)

Cheers,
- Graham