Re: measuring systems (was: Selenites)

-----Original Message-----
From: Nik Taylor <fortytwo@...>
To: Multiple recipients of list CONLANG <CONLANG@...>
Date: Monday, September 28, 1998 11:04 PM
Subject: Re: measuring systems (was: Selenites)


>Carlos Thompson wrote:
>> in older text, even with the Arabic/Indian notation, parts of units where
>> given as fractions, then 1/5 was nothing complicated as
0.249724972497...,
>> but 1/5.
>
>True, but with fractions, the base doesn't really matter, now does it?
>So as far as a "basal notation", duodecimal is easier with common
>fractions, while with fractions both are equally easy.
>
>P.S., how did the Romans do multiplication with Roman numerals?  I can't
>imagine trying to multiply XXIII by XIV without converting into Arabic
>numberals.
By substitution and cancellation.  Pretty mindless, but slow (because it
requires a lot of rewriting).  Remember, each digit (except 1) is a power of
10 or half of a power of 10.  The powers of 10 are X=10, C=100, M=1000, and
so on.  Half of the powers of 10 are V=5, L=50, and (if memory serves)
D=500, and so on.  So, for X times X, you substitute C; and for X times V,
you substitute L; and so on.

In your example, XXXIII times XIV, here's how I proceed:
X(XXXIII)=CCCXXX
I(XXXIII)=XXXIII
V(XXXIII)=LLLVVV

Note that XXXIII is a negative quantity because "I" precedes "V" in XIV.
(Any digit is negative if, and only if, it precedes a greater digit.)  So
the first 2 numbers -- CCCXXX and XXXIII -- can be written on one line like
so -- XXXIIICCCXXX -- and 3 negative and 3 positive X's cancel each other
other, leaving IIICCC.

Next, we rewrite the third number -- LLLVVV -- as CLXV (simply substituting
C for LL and X for VV, since C=L+L and X=V+V), and add that third number to
the result of combining the first two numbers: IIICCC+CLXV=IIICCCCLXV.  But
the negative III cancels out 3 of the 5 units in V, yielding CCCCLXII.

Then we substitute CD (meaning 100 less than 500) for CCCC, because there's
a rule that says we can't let any digit appear more than 3 times in a
number.  This shortens CCCCLXII to CDLXII.


-- Tommie