[lojban] jimc on MEX

["And Rosta" <a.rosta@pmail.net>]

From: "And Rosta" <a.rosta@pmail.net>

jimc:
> Since we're stirring the pot about mathematical expressions (MEX), I
> thought I'd toss in some comments about -gua!spi.  I also was not entirely
> happy with the specialized grammar for MEX.  A few small changes from
> Loglan/Lojban practice allowed an elegant solution.
> 
> First, following a common mathematical practice, numbers are defined as
> equivalence classes of equal-count sets, e.g. "the number 2" means "the
> class of all pairs".  The obvious extension is assumed to be feasible for
> extension rings and fields (e.g. fractions and decimal numbers).

I've never had any trouble with defining positive integers in this way,
but feasibility of "the obvious extension" is not at all apparent to my
unmathematical mind. As far as I can see, only positive integers are
valid set cardinalities, while other numbers can be derived by operations
on integers but not on sets.

> Next, mathematical functions are named by predicate words /brivla/ of the
> usual kind, defined to take such objects as arguments.  First place
> occupants have the property of being in the result set; thus
> /lo'i/ (veridical set) should be the article used when an argument
> /sumti/ is made from the expression.  "The sum of 2 and 3" is interpreted to
> mean "the sum of (the class of all pairs) and (the class of all
> triplets)", which comes out to be "the class of all pentads".  

I don't understand this. That is, I don't understand how classes can
be summed, especially not in a way that gives the results you describe.

> Getting this definition to work right takes a little thought in the area of 
> eliminating duplicate members while also not mixing triplets and quads with 
> the pentads, but mathematicians have worked this out.

Have they worked out a way to help me grock it? %-[

> The language's usual syntax for embedded arguments is used
> when a complex sub-expression occurs as an argument of the containing
> expression. - -gua!spi has a very simple syntax for embedded arguments.
> The syntax of Lojban is perfectly useable in this application.

Can't Lojban already do the equivalent by using the ordinary apparatus
or integers and variables plus the maths gismu?

> Units of measure are defined to multiply the second place argument (a
> number or other expression) by the unit.  They would normally be used in
> restrictive subordinate clauses.  "I weigh 70 kilograms" in Lojban would
> come out /mi tilju poi kilgrake lo'i mei ze no/.  

ze no mei? And that poi doesn't seem to make sense. I weigh the set
of ninesomes that are kilogrammes? I don't have a gi'uste here, but
I wonder whether something like "mi se kilgrake lo'i ze no mei" is valid
and at least a partial improvement - "I weigh in kilos the set of
ninesomes". Mind you, I still can't get my head round it. "I weigh in
kilos the defining property of the set of ninesomes" would make more
sense: "mi se kilgrake lo ka ce'u ze no mei". Excuse my creakingly
rusty Lojban.

> Assuming I haven't botched something in rusty Lojban, the unit of measure is
> actually semantically valid with current (?) place structures.
> I'm not presently able to say if this vision of MEX is presently 100% valid
> usage in Lojban, or if the only thing you need to use it is changes to the
> (non-baselined) place structures of the math functions.  But I offer it as
> a simple and effective MEX grammar that's coherent with the core grammar of
> Lojban.

Now, if only I could understand it.

> For more on -gua!spi see
> http://www.math.ucla.edu/~jimc/guaspi/guaspi.txt
> (it's really in TeX, sorry for not having html for you to read).  The
> discussion of MEX is about 80% through.  The sample story that follows (550
> words), intended to show that -gua!spi can express material from daily
> life, actually turned out to include a MEX naturally but essentially.

Last time I read the guaspi file (admittedly, some years ago now) I found that 
you seem to share my unfortunate gift for writing expositions that are 
supposed to be, but aren't, intelligible to the general reader ;-)

--And.

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