Introductory
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:
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; providing a vocabulary of commonly used mathematical terms which can readily be expanded to include newly coined words using the full resources of Lojban; permitting the formulation, both in writing and in speech, of unambiguous mathematical text; 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.
Lojban numbers
The following cmavo are discussed in this section: pa PA 1 re PA 2 ci PA 3 vo PA 4 mu PA 5 xa PA 6 ze PA 7 bi PA 8 so PA 9 no PA 0 The simplest kind of mekso are numbers, which are cmavo or compound cmavo. There are cmavo for each of the 10 decimal digits, and numbers greater than 9 are made by stringing together the cmavo. Some examples: 2.1) pa re ci one two three 123 one hundred and twenty three
2.2) pa no
one zero
10
ten
2.3) pa re ci vo mu xa ze bi so no
one two three four five six seven eight nine zero
1234567890
one billion, two hundred and thirty-four million, five hundred and sixty-seven thousand, eight hundred and ninety. Therefore, there are no separate cmavo for “ten”, “hundred”, etc.
There is a pattern to the digit cmavo (except for “no”, 0) which is worth explaining. The cmavo from 1 to 5 end in the vowels “a”, “e”, “i”, “o”, “u” respectively; and the cmavo from 6 to 9 likewise end in the vowels “a”, “e”, “i”, and “o” respectively. None of the digit cmavo begin with the same consonant, to make them easy to tell apart in noisy environments.
Signs and numerical punctuation
The following cmavo are discussed in this section: ma'u PA positive sign ni'u PA negative sign pi PA decimal point fi'u PA fraction slash ra'e PA repeating decimal ce'i PA percent sign ki'o PA comma between digits A number can be given an explicit sign by the use of “ma'u” and “ni'u”, which are the positive and negative signs as distinct from the addition, subtraction, and negation operators. For example: 3.1) ni'u pa negative-sign 1 -1 Grammatically, the signs are part of the number to which they are attached. It is also possible to use “ma'u” and “ni'u” by themselves as numbers; the meaning of these numbers is explained in Section 8.