Re: decisions of Wed.

Calling all lojban-listers!  Lojban Central has an internal debate going on
over the meaning of Lojban numeral strings.  Lojbab and I (who are on opposite
sides) need your input.  I am solely responsible for the following writeup,
which therefore probably slants toward my position.

Background information:  Lojban numbers are represented by numeral strings,
where each numeral is a cmavo.  For example, "recivo" means "234" and represents
the number two hundred and thirty-four.  There are cmavo for each digit,
for the decimal point, for positive and negative signs, for the slash in
fractions like 1/2, and for a few special numbers like pi, exponential e,
imaginary i, and so on.

The dispute arises over the meaning of numbers which combine the regular digits
with the special numbers.  Any string of numeral cmavo is a grammatical number,
but not all of them have an assigned meaning; for example:

	pa pi re pi ci
	1  .  2  .  3

does not have any assigned meaning, because no number can have more than
one decimal point in it.  (The use of "." to connect section, subsection,
subsubsection, etc. numbers is represented by a different cmavo altogether.)

Likewise, the meaning of:

	pa fi'u re fi'u ci
	1  /    2  /    3

is shaky at best:  is it (1/2)/3 = 1/6 or 1/(2/3) = 3/2?  Once again, there
is an entirely different cmavo for the operation of division, as in a/b.

It is common in mathematics to write "2pi" to represent 2 times pi.  Lojbab
has it that the corresponding numeral string:

	re pai
	2  pi

should also mean 2 times pi in Lojban.  My view is that since Lojban does not
allow you to omit multiplication operators in general -- for example:

	(m + n)(m + n)

is

	vei my. su'i ny. ve'o pi'i ve'i my. su'i ny. ve'o
	(   m   +    n   )    *    (    m   +    n   )

and it is ungrammatical to omit the "pi'i" -- it follows that:

	2 pi

must be

	re pi'i pai
	2  *    pi

and simple "re pai" has no defined meaning.  This principle may be extended
to other analogous cases.

Argument pro:  not allowing implied operators in numeral strings will tend
to prevent confusion (why is "2 pi" = "2 * pi" whereas "23" = "2 * 10 + 3"?)
and will allow expansion space, as undefined number strings may be put to
newly devised uses if not pre-empted for things that can be said otherwise.

Argument con:  "re pai" is shorter and (having the syntax of a number) can
be used in places where a full mathematical expression cannot.  Expressions
other than simple numbers must be parenthesized when used as quantifiers, so
"2 pi people" requires a "vei" (left parenthesis) in front of the expression
"2 times pi".

Special note on "imaginary i":  I am willing to allow a special role to
"ka'o", the cmavo for "i", because "3+4i" can reasonably be thought of as
a conventional way of notating the point <3,4> on the complex plane, rather
than as a multiplication by "i" and an addition.  I do not believe this
argument carries over to "2 pi" or "2 e".

Please give us your comments!  I am in the final stages of rewrite on a
paper about Lojbanic mathematics, and this point must be nailed down.

-- 
cowan@snark.thyrsus.com		...!uunet!cbmvax!snark!cowan
		e'osai ko sarji la lojban