Re: OT: coins and currency (was: [Theory] Types of numerals)

--- In conlang@yahoogroups.com, Jefferson Wilson <jeffwilson63@F...>
wrote:
>
> Paul Bennett wrote:
> > On Fri, 06 Jan 2006 08:11:15 -0500, Mark J. Reed
<markjreed@M...>
> > wrote:
> >
> >> In US currency, for instance, there are essentially 4 sub-dollar
> >> denominations (1, 5, 10, 25), since half dolalrs are very rare.
As a
> >> result, some values require up to 9 coins (e.g. 94¢ and 99¢).
> >> Reintroduction of a commonly-circulated half-dollar would cut
that
> >> down by one coin; a two-cent piece would reduce it by two more.
That
> >> would yield six denominations and a maximum minimum (:)) of six
coins
> >> per value.
> >
> >
> > I'm sure you're aware of the British system, which is partitioned
1, 2,
> > 5,  10, 20, 50, 100, 200, 500, etc. I have a gut feeling that
it's more
> > optimal than the US system of (essentially) 1, 5, 10, 25, 100,
500,
> > 1000,  2000, which strikes me as more organic but less wieldy.
> >
> > Of course, it shouldn't take much math to prove that the most
optimal
> > system would have units of 1, 2, 4, 8, 16, 32, etc., provided of
course
> > that the general populace could be made sufficiently familiar
with the
> > concept.
>
> Depends on whether you want the lowest number of _coins_ or the
> lowest number of _types_.  Binary is good for the former, but for
> the latter you get the series: 1, 3, 6, 12, 24, etc.  (Something
> to keep in mind for those of us with duodecimal numbering systems
> I think.)  Hmmm, take this series up to 96, round each value to
> the nearest number divisible by 5, and you have the American
> coinage system.
>
> --
> Jefferson
> http://www.picotech.net/~
>
As far as minimizing the [number of coins] (not the number of types
of coins) you have to get and/or give in change, and keep carrying
around in your pocket-or-whatever (not the number in existence),

the optimum ratio is either 3 or 4.  That is, each coin (or
denomination of note) is either 3 or 4 of the next lower, and either
one-third or one-fourth of the next higher.

So, 1, 3, 9, 27, 81, 243, 729 ... is a good series;
1, 4, 16, 64, 256, 1024, 4096 ... is a good series;
1, 3, 12, 36, 144, 432, 1728 ... is a good series;
1, 4, 12, 48, 144, 576, 1728 ... is a good series.

----

A base for a number system has extra conveniences if it has many
factors.  Defining, for the moment, a "good base" to mean "a number
that has at least as many factors as any smaller number", we get the
following "good bases";
 2 factors:  2, 3
 3 factors:  4
 4 factors:  6, 8, 10
 6 factors:  12, 18, 20
 8 factors:  24, 30
 9 factors:  36
10 factors:  48
12 factors:  60, 72, 84, 90, 96, 108
16 factors:  120, 168

and so on.

Natlangs, and ordinary uneducated people, aren't likely to use bases
greater than about 40 (in spite of the Mesopotamian/Egyptian/Greek
scholars' fondness for base 60).

Besides, the base 12 -- a "good base" -- fits neatly with the third
and fourth example series I wrote towards the beginning of this reply.

So, I plan to use base 12.
I might use something like:
1 "knuckle" or "joint"
3 knuckles = 1 "finger" or "digit"
12 knuckles = 4 fingers = 1 "hand"
36
144
432
1728
... etc.

Or, since I'd rather have the higher factor used first, I could use
the series
1
4
12
48
144
576
1728
... etc.
but then I don't know what I'd name them.

---
Tom H.C. in MI

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