Chapter 18: lojbau mekso: Mathematical Expressions in Lojban
The following cmavo are discussed in this section:
mei MOI cardinal selbri moi MOI ordinal selbri si'e MOI portion selbri cu'o MOI probability selbri va'e MOI scale selbri me ME make sumti into selbri me'u MEhU terminator for ME
Lojban possesses a special category of selbri which are based on mekso. The simplest kind of such selbri are made by suffixing a member of selma'o MOI to a number. There are four members of MOI, each of which serves to create number-based selbri with specific place structures.
“-mei” creates cardinal selbri. The basic place structure is:
- x1 is a mass formed from the set x2 of n members, one or more of which is/are x3
✥11.1 lei mi ratcu cu cimei those-I-describe-as-the-mass-of my rats are-a-threesome. My rats are three. I have three rats.
Here, the mass of my rats is said to have three components; that is, I have three rats.
Another example, with one element this time:
✥11.2 mi poi pamei cu cusku dei I who am-an-individual express this-sentence.
In ✥11.2, “mi” refers to a mass, “the mass consisting of me”. Personal pronouns are vague between masses, sets, and individuals.
However, when the number expressed before “-mei” is an objective indefinite number of the kind explained in c18-§8, a slightly different place structure is required:
- x1 is a mass formed from a set x2 of n members, one or more of which is/are x3, measured relative to the set x4.
✥11.3 lei ratcu poi zvati le panka cu so'umei fo lo'i ratcu the-mass-of rats which are-in the park are a-fewsome with-respect-to the-set-of rats. The rats in the park are a small number of all the rats there are.
In ✥11.3, the x2 and x3 places are vacant, and the x4 place is filled by “lo'i ratcu”, which (because no quantifiers are explicitly given) means “the whole of the set of all those things which are rats”, or simply “the set of all rats.”
✥11.4 le'i ratcu poi zvati le panka cu se so'imei The-set-of rats which-are in the park is-a manysome. There are many rats in the park.
In ✥11.4, the conversion cmavo “se” swaps the x1 and the x2 places, so that the new x1 is the set. The x4 set is unspecified, so the implication is that the rats are “many” with respect to some unspecified comparison set.
More explanations about the interrelationship of sets, masses, and individuals can be found in Chapter 6.
“-moi” creates ordinal selbri. The place structure is:
- x1 is the (n)th member of set x2 when ordered by rule x3
✥11.5 ti pamoi le'i mi ratcu This-one is the first-of the rats associated-with me. This is my first rat.
✥11.6 ta romoi le'i mi ratcu That is-the-allth-of the rats associated-with me. That is my last rat.
✥11.7 mi raumoi le velskina porsi I am-enough-th-in the movie-audience sequence I am enough-th in the movie line.
✥11.7 means, in the appropriate context, that my position in line is sufficiently far to the front that I will get a seat for the movie.
“-si'e” creates portion selbri. The place structure is:
- x1 is an (n)th portion of mass x2
✥11.8 levi sanmi cu fi'ucisi'e lei mi djedi cidja This-here meal is-a-slash-three-portion-of my day-food. This meal is one-third of my daily food.
“-cu'o” creates probability selbri. The place structure is:
- event x1 has probability (n) of occurring under conditions x2
✥11.9 le nu lo sicni cu sedja'o cu pimucu'o The event of a coin being a head-displayer has probability .5.
“-va'e” creates a scale selbri. The place structure is:
- x1 is at scale position (n) on the scale x2
✥11.10 le vi rozgu cu sofi'upanova'e xunre This rose is 8/10-scale red This rose is 8 out of 10 on the scale of redness. This rose is very red.
When the quantifier preceding any MOI cmavo includes the subjective numbers “rau”, “du'e”, or “mo'a” (enough, too many, too few) then an additional place is added for “by standard”. For example:
✥11.11 le ratcu poi zvati le panka cu du'emei fo mi The rats which-are in the park are too-many by-standard me. There are too many rats in the park for me.
The extra place (which for “-mei” is the x4 place labeled by “fo”) is provided rather than using a BAI tag such as “ma'i” because a specification of the standard for judgment is essential to the meaning of subjective words like “enough”.
This place is not normally explicit when using one of the subjective numbers directly as a number. Therefore, “du'e ratcu” means “too many rats” without specifying any standard.
It is also grammatical to substitute a lerfu string for a number:
✥11.12 ta ny.moi le'i mi ratcu that is-nth-of the-set-of my rats That is my nth rat.
More complex mekso cannot be placed directly in front of MOI, due to the resulting grammatical ambiguities. Instead, a somewhat artificial form of expression is required.
The cmavo “me” (of selma'o ME) has the function of making a sumti into a selbri. It is often used to make a name into a predicate:
✥11.13 ti me la nu,IORK. [me'u] this-here pertains-to what-I-call “New York”. This is New York (or is New York-related).
A whole “me” construction can have a member of MOI added to the end to create a complex mekso selbri:
✥11.14 ta me li ny. su'i pa me'u moi le'i mi ratcu that is the-number n plus one-th-of the-set-of my rats. That is my (n+1)-th rat.
Here the mekso “ny. su'i pa” is made into a sumti (with “li”) and then changed into a mekso selbri with “me” and “me'u moi”. The elidable terminator “me'u” is required here in order to keep the “pa” and the “moi” separate; otherwise, the parser will combine them into the compound “pamoi” and reject the sentence as ungrammatical.
It is perfectly possible to use non-numerical sumti after “me” and before a member of MOI, producing strange results indeed:
✥11.15 le nu mi nolraitru cu me le'e snime bolci be vi la xel. cu'o The event-of me being-a-nobly-superlative-ruler has-the-stereotypical snow type-of-ball at Hell probability. I have a snowball's chance in Hell of being king.
Note: the elidable terminator “boi” is not used between a number and a member of MOI. As a result, the “me'u” in ✥11.14 could also be replaced by a “boi”, which would serve the same function of preventing the “pa” and “moi” from joining into a compound.