Lesson 11
papamoi seltadni
More Lojban Numbers
*** lojbo namcu
11.1
On ni'u and ma'u
me zo ni'u .e zo ma'u
"ni'u" is the Lojban cmavo that represents the 'minus sign' for a
negative number. "ma'u" is the corresponding but little-used
'plus-sign'. Unlike English, the word for 'minus-sign' is not used in
Lojban to indicate subtraction, nor is the 'plus sign' used to
represent addition.
We most often see negative numbers in common use in temperatures and
in bad bank balances. We will be discussing money and measurement in
later lessons, and so will not give examples of these usages here.
Other uses relate to our discussion of telling time. In Lojban, if
you want to express the time "5 minutes before 6", you can do so as
"6:-5", or "li xa pi'e ni'umu". "A quarter before 12" would be
expressed as "12.-25" or "li gai pi ni'uremu".
Similarly, you can use negative numbers to do a 'countdown', and mixed
signs to express more complicated times. By convention, a negative
sign in a time will refer to all following units:
"-3;17" or "li ni'uci pi'e paze" means
"three hours and seventeen minutes before ..."
"-\3\17" or "li pi'e ni'uci pi'e paze" means
"three minutes and seventeen seconds before ..."
"3/-10/+5" or "li ci pi'e ni'upano pi'e ma'umu" means
"five seconds after ten-before three"
11.2
Indefinite Numbers
nalstodi namcu
Lojban has the unusual feature of having a lot of numbers that aren't
really numbers. Or perhaps it should be said that Lojban has a lot of
numbers that other languages can't decide on whether they are numbers.
You are familiar with the equivalents of these numbers in English: "a
few", "many", "most", "almost all", our friend "penultimate", more
vague concepts like "enough", "too much", and complex ones like "at
least 2" (or "plural").
Lojban treats each of these concepts as numbers. In fact, they are
almost identical to digits in grammar, which can lead to some very
strange digitized numbers.
We will introduce a few of these at a time over the next several
lessons. There are a lot of them, and most are rarely used, though
some are vital when they are needed. Rather than burden you with
learning them in this lesson when we first present them, we will save
most of them until after you have gone through the first 900 flash
card vocabulary words.
Listing the ones for this lesson briefly, we have:
ro each cmavo for quantifier/digit
'all'
so'i many cmavo for quantifier/digit
'many of {number}' (default all)
su'e at most cmavo for quantifier/digit
'at most {number}' (default 1)
su'o at least cmavo for quantifier/digit
'at least {number}' (default 1)
These 'numbers' can stand alone, or they can be combined with others.
The most frequently such combination, is to use "pi" to express each
of these as a pseudo-decimal fraction:
piro the whole of 'all of {number}' (default all)'
piso'i much 'much of {number}' (default all)
pisu'e not much 'at most {number}' (default a little bit)
pisu'o some 'at least {number}' (default a little bit)
You may also see that these four may be combined with numbers on their
right to form other values; we will use paze ("17") for an odd
example:
ropaze all 17
so'ipaze many of the 17
su'epaze at most 17
su'opaze at least 17
or even fancier:
so'isu'opaze many of the at least 17
We won't try to figure out some of the stranger possibilities for
combinations.
11.3
Number Questions
namcu preti
Number questions are easy, and follow the pattern laid down for "mo"
and "ma". Any place where either a number or a digit can go, you
insert the number question word "xo".
li xo asks for a number (or digit, or non-numeric quantifier) to fill
the space held by the "xo"; li rexomu also asks for a number (or
digit, or non-numeric quantifier) to fill the space held by the "xo";
in context, you would general assume a single digit is desired, since:
li rexoxomu also asks for a number (or digit, or non-numeric
quantifier) to fill the space held by the two "xo"s; you would assume
here that two digits are being requested.
We will give examples of "xo" in the next section, and later in the lesson.
11.4
Quantified Description
klani selgadri
There is a lot of power in numbers, and expressing them is but the
first step. Let us push on to their most common use, the quantifying
of descriptions.
You will recall that Lojban bridi and sumti express neither singular
nor plural. Every single sentence and every sumti in those sentences
which you've seen so far could have been translated as a singular
object or action or relationship, or as a plural set of objects,
actions, or relationships.
While we pay a lot of attention in English to singular and plural,
they are not important in many circumstances; in others they are
obvious from context. Sometimes English assignment of singular/plural
seems rather arbitrary. Why are water, rain, snow, and information
singular? Can you show me a water?
The truth is that English and related languages require 'number', the
property of singular/plural, in order for you to keep its highly
irregular grammar straight. A second property, 'person', also bears
on the grammar. A third, 'tense', can significantly affect the other
two properties. Each of these properties can cause verbs to change;
English requires 'agreement' in tense, number, and person between the
subject of a sentence and the verb. Other languages add the confusion
of gender to the problem of agreement, and may require adjectives and
other parts of the sentence to agree as well as the verb.
Lojban does away with all of this. The structure is carried in all
those sometimes elidable scope markers, and the other cmavo that label
pieces of a sentence by type. Wherever possible, if information is
not vital, it can be omitted, there are no modifications for 'person'
or 'number' or 'gender' or 'tense'. If you wish or need to insert
markers representing any of these concepts and their related
information, you can. But they are simple insertions. If you put
them in the right place, your sentence need not be modified in any
other way. It will be grammatical, and presumably will be understood.
Lojban expresses 'number' with numbers (How odd!). There isn't truly
a concept of 'plural'. That concept is simply the 'number' of "at
least two" ("su'ore", from the last section).
When you want to say that "the two people greet (each other)", you
quantify the description selbri in the natural way:
le re prenu [ku] cu rinsa
This type of quantification means that you have two specific things in
mind, which you are describing as 'people'.
You can also say:
re le prenu [ku] cu rinsa
"Two of the people greet ..."
In this example, you aren't saying how many are in the set that you
have in mind. When you put the quantifier before "le", you are merely
selecting two of that unspecified set as the basis for your
description.
Commercials say "9 out of 10 people prefer ...". You can combine both
types of quantification to express this in Lojban as:
so le pano prenu [ku] cu cuxna
You can use numbers and non-numeric quantifiers with pro-sumti as
well, finally being able to specify, or at least imply, the 'number'
of these variables. In general, quantification of pro-sumti should be
considered the 'selective' variety of quantification:
xa ti cu culno means
"Six of these are-full"
which implicitly says that the number of ti is su'oxa ("at least six").
You can similarly quantify "mi", "do", "ko'a", and even "ko":
ci ko cu cpacu ci ko'a re mi
"Three of you, get three of them from two of 'us-excluding-you' "
There is a lot to be said about interpreting the 'implicit
quantification' (the defaults to be assumed) for sumti and pro-sumti.
It is a complicated subject that we will leave for later. The
approximations we've described here will be adequate for your needs
until then.
Let's look at examples of quantified sumti:
11.4.1
la .alis. cu klama .i la rik. cu klama .i la djos. cu klama
.i la fred. cu klama
Alice goes. Rik goes. Joe goes. Fred goes.
.i la djos. cu nanmu .i la rik. cu nanmu .i la fred. cu nanmu
.i la .alis. cu na nanmu
Joe is-a-man. Rick is-a-man. Fred is-a-man. Alice is-not-a-man.
.i la .alis. cu zutse .i la djos. cu zutse .i la rik. cu na zutse
.i la fred. cu na zutse
Alice sits. Joe sits. Rick does-not-sit. Fred does-not-sit.
>From these circumstances we can say:
ro le prenu [ku] cu klama
Each of the people go.
.i piro le prenu [ku] cu klama
The whole of the persons go.
.i le vo prenu [ku] cu klama
The four people go.
pe'u. suzn. .i xo le prenu [ku] cu zutse
Please, Susan? How-many of the people sit?
.i pa le nanmu [ku] cu zutse
One of the men sits.
.i re le nanmu [ku] cu na zutse
Two of the men do-not-sit.
.i re le vo prenu [ku] cu zutse
Two of the four people sit.
.i ro le vo prenu [ku] cu klama
Each of the four people go.
.i ro le nanmu [ku] cu klama
Each of the men go.
.i su'o le klama [ku] cu ninmu
At least one of the go-ers is-a-woman.
.i su'oci le klama [ku] cu nanmu
At least three of the go-ers are-men.
.i so'i le prenu [ku] cu nanmu
Many of the people are-men.
11.4.2
ti cu kabri .i le ckafi [ku] cu nenri le kabri [ku]
.i le ladru [ku] cu nenri le kabri [ku]
This is-a-cup. The coffee is-in the cup. The milk is-in the cup.
.i piso le nenri [ku] cu ckafi
Nine-tenths (.9) of the thing-which-is-inside is coffee.
.i pipa le nenri [ku] cu ladru
One tenth (.1) of the thing-which-is-inside is-milk.
11.4.3
ti cu botpi .i le sodva [ku] cu nenri le botpi [ku]
.i le botpi [ku] cu culno le sodva [ku]
This is-a-bottle. The soda is-in the bottle.
The bottle is-full with the soda.
.i piro le nenri [ku] cu sodva
The whole (point-all) of the thing-which-is-inside is-soda.
11.4.4
djos.: ko [cu] kancu le pinsi ku pe'u. Rik. .i xo le dacti [ku] cu pinsi
Count the pencils, please, Rick. How-many of the objects are-pencils?
rik.: vo le dacti [ku] cu pinsi
Four of the objects are-pencils.
djos.: xo le pinsi [ku] cu blanu doi .alis.
How-many of the pencils are-blue, O Alice?
.alis.: ci le vo pinsi [ku] cu blanu
Three of the four pencils are-blue.
djos.: ko lebna le ci pinsi ku pe'u doi fred.
Take the three pencils, please O Fred.
fred.: mi [cu] na jimpe .i le ci ki'a pinsi ku doi djos.
I don't-understand. The which-three pencils, O Joe?
djos.: ko [cu] lebna le ci blanu [ku]
Take the three blue-things.
fred.: mi [cu] lebna
I take.
11.4.5
le nu klama [kei] [ku] cu cacra li re
The go-ing is-in-hours-of-duration 2 [i.e. It takes 2 hours to go.]
11.5
A Song Activity
selsanga selzukte
We get to do something different at this point. We will practice
numbers, abstraction, and pronunciation, by singing a Lojban
translation of a familiar song:
le sosoboi dacti cu botpi le birje
.i le sosoboi botpi cu galtu
.i nu pa le botpi cu farlu le loldi
.i le bitmu cu ralte sobiboi le botpi
The song is translated in the answer key in the back of the book, in
case the instructor wants to use this as a group or individual
exercise. The elidable "ku"s and "kei"s have been omitted for the
sake of the rhythm, whereas some of the "boi"s, all unnecessary, seem
to help that rhythm.
You will find, of course, that the translation is not identical to the
English, but is close enough that you will be able to identify the
song and its tune. When the class knows what the song means, it can
then be sung as a group pronunciation exercise, with a little quick
thinking on your numbers necessary in order to do later verses.
Note the use of the abstraction as an observative bridi. This is a
fairly unusual occurrence; it would be hard to find a better or more
appropriate example of when it is useful.
The instructor should have pre-written the song in large print on a
board so you can talk about the translation if needed, and so you can
point to lines as they are sung.
After a couple of verses, the instructor can speed up the activity and
make it more challenging by having more than one bottle fall. Just
say (or change on the board):
xa le botpi cu farlu
and indicate that the students are to continue. If necessary, help
them out by writing in numerals (not text), the new number of bottles.
Pre-plan the numbers to be subtracted so that you use all of the
digits, and have the answers in front of you so you don't make a
mistake. It is a good idea to have rehearsed this one with your
partner.
Translation of the Activity Song
Ninety-Nine Bottles of Beer on the Wall
le sosoboi dacti cu botpi le birje
"The ninety-nine things are-bottles containing beer."
.i le sosoboi botpi cu galtu
"The ninety-nine bottles are high."
.i nu pa le botpi cu farlu le loldi
"(Observe!) One of the bottles is-falling to the floor."
.i le bitmu cu ralte sobiboi le botpi
"The wall retains ninety-eight of the bottles."