Chapter 18: lojbau mekso: Mathematical Expressions in Lojban
lojbau mekso (“Lojbanic mathematical-expression”) is the part
of the Lojban language that is tailored for expressing
statements of a mathematical character, or for adding numerical
information to non-mathematical statements. Its formal design
goals include:
- 1)
- representing all the different forms of expression used
by mathematicians in their normal modes of writing, so that a
reader can unambiguously read off mathematical text as
written with minimal effort and expect a listener to
understand it;
- 2)
- providing a vocabulary of commonly used mathematical
terms which can readily be expanded to include newly coined
words using the full resources of Lojban;
- 3)
- permitting the formulation, both in writing and in
speech, of unambiguous mathematical text;
- 4)
- encompassing all forms of quantified expression found in
natural languages, as well as encouraging greater precision
in ordinary language situations than natural languages
allow.
Goal 1 requires that mekso not be constrained to a single
notation such as Polish notation or reverse Polish notation,
but make provision for all forms, with the most commonly used
forms the most easily used.
Goal 2 requires the provision of several conversion
mechanisms, so that the boundary between mekso and full Lojban
can be crossed from either side at many points.
Goal 3 is the most subtle. Written mathematical expression
is culturally unambiguous, in the sense that mathematicians in
all parts of the world understand the same written texts to
have the same meanings. However, international mathematical
notation does not prescribe unique forms. For example, the
expression
1.1) 3x + 2y
contains omitted multiplication operators, but there are other
possible interpretations for the strings “3x” and “2y” than
as mathematical multiplication. Therefore, the Lojban verbal
(spoken and written) form of Example 1.1
must not omit the multiplication operators.
The remainder of this chapter explains (in as much detail as
is currently possible) the mekso system. This chapter is by
intention complete as regards mekso components, but only
suggestive about uses of those components — as of now, there
has been no really comprehensive use made of mekso facilities,
and many matters must await the test of usage to be fully
clarified.