response to And: MEX

[Logical Language Group <cbmvax!uunet!grebyn.com!lojbab>]

One difference that has been identified between ratios and quotients is that
the latter is an evaluated function, while the former generally remains
a fraction or ratio.  I think, though, that these two gismu would get used
in totally unrelated circumstances.

3/4 parbi leni broda leni brode
.75 dilcu 3 4

The latter is pretty much a mathematical operation; the former tends to be
used over a broader applied-math context.

There exist gismu for some mathematical operations, and presumably lujvo and
le'avla can be created for any others that are needed.  Using these, you can
talk ABOUT mathematics.

The MEX grammar exists, not to talk about mathematics, but to EXPRESS math-
ematics.  Specifically, it is to express mathematics as it is written by
mathematicians.  The rules for the international system of mathematical
expression are not those of Lojban.  International math uses a combination
for forethought (Polish) expressions like f(x), infix, and in some cases
(HP calculators) postfix/reverse Polish.  Lojban cannot change the way
math is written by mathematicians.  We needed a way that a person can read
off in Lojban a mathematical expression such that the expression unambiguously
reflected what was written, including the style of expression (which is i
important when you are trying to teach the difference between these forms
of notation if nothing else).  The reading off has to be as close to
obvious or automatic as possible.

Unfortunately the grammar of international math is not perfectly unambiguous,
so a little compromise had to be made.  And we have had internal debates over
whether mathematical operators should have assigned precedences, or whether
the speaker should speak in full parentheses, since some mathematics uses
conventions wherein e.g. 'times' does not have precedence over 'plus'.

The main reason for the few gismu in the mathematical realm was that I saw
some potential for semantic metaphor using them.  Certainly, for example,
one can talk about exponential increases without a full understanding of
the mathematics involved.

lojbab