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Lesson 4: Numbers, and a few more articles

One of the first things you learn in a new language is how to count, and this course is no exception. However, in Lojban, numbers include much more than just counting; for example, in Lojban, "some", "many" and "most" are numbers.

Basic numbers

The numbers from one to nine are as follows:
  1. pa
  2. re
  3. ci
  4. vo
  5. mu
  6. xa
  7. ze
  8. bi
  9. so
This leaves zero, which is no (think "yes, we have no bananas"). You may have noticed that the numbers repeat the vowels AEIOU. Since you can't get by without memorising numbers, try to think of mnemonics for the unfamiliar ones. For example, although the sound is different, xa has the X of "six", and I remembered so by thinking of the proverb "A stitch in time saves nine," which is about sewing (.oi).

Numbers from 10 onwards are made by putting the digits together, just like you'd say a telephone number. For example:

pano
10
zebi
78
xanoci
603
vomusore
4,592
4,592 has a comma in it (or a full stop in some languages, just to make things confusing). We can't use a comma in Lojban, because that means "separate these two syllables" (as we saw in Lesson 1 with Lojbanised names like zo,is. for "Zoe"). What we say instead is ki'o. We don't have to use ki'o, but it can make things clearer. It also has the advantage that if the following digits are all zeroes, we don't need to say them, so 3,000 is ci ki'o. You can remember ki'o easily if you think of "kilo"—a thousand.

Just as we have a word for a comma, we also have one for a decimal point: pi (don't get this mixed up with the number "pi" - 3.1415... !). So 5.3 is mupici. In fact, pi is not always decimal—it's the point for whatever system you're using.

Question: What is the difference between the following numbers?

pareci

li pa li re li ci

The first one, as we've seen, has to be "one hundred and twenty-three," so the second is "one, two, three." li is the article for numbers.

Exercise 1

What are the following numbers in Lojban? (don't forget li!)
  1. 35
  2. 4,802
  3. 6,000
  4. 7.54
  5. 6,891,573.905

Numbers and articles

So far, we've looked at three articles: la, for cmene, le, for sumti and li for numbers. So li bi is "the number eight." Actually, outside mathematics, li is not used very much. What we usually want to say is things like "three people," or "the two women."

Note for mathematicians: Lojban has a number of words to deal with basic mathematics, and also an incredible number of words to deal with just about any mathematical expression you can think of in a separate subset of the language. But come on guys, this is a beginners' course.

We can use numbers either before or after le. For example,

ci le gerku
means "three of the dogs", while
le ci gerku
means "the three dogs."
What do we do, though, if we just want to say "three dogs"? For this we need another article, lo. The logic of lo is pretty complicated, but it basically means "something which really is," which nine times out of ten is the same as English "a" or "some" (translating Lojban grammar into English like this is a mortal sin, but even so, this is the best thing to do with lo at this stage!).

Note for logicians: lo prenu cu klama expresses the proposition "There exists at least one person, such that that person goes."

ci lo gerku therefore means "three of those which really are dogs", or in plain words, "three dogs". lo ci gerku, however, means that there are only three dogs in the world, which is not something you'd really want to say (mathematicians and logicians can look up the relevant parts of The Complete Lojban Language if they want clarification on this issue).

Let us now consider the English sentence "Three dogs bit me." This actually has two possible meanings. The one we would expect is that I was attacked by a pack of dogs, and all of them bit me. However, I could be an extremely unfortunate person who was bitten by three separate dogs on three different occasions. Lojban is a logical language, and so does not tolerate this confusion! If I say ci lo gerku cu batci mi, I just mean that three dogs bite me. Maybe one dog bit me in the morning, one in the afternoon, and one at night, or maybe I mean that I have been bitten by a dog three times in my life. However, if I say lu'o ci lo gerku cu batci mi, I mean that a group of three dogs bit me. lu'o means "the mass composed of" and in effect converts a bunch of individuals into a coherent unit. If you're a fan of computer strategy games, think of lu'o as like the "group" command for units (there's also an "ungroup" command, lu'a).

With le things are simpler. While le pano ninmu means "the ten women", lei pano ninmu means "the ten women treated as a group or mass". Let's imagine that ten women I have in mind kiss me on ten separate occasions. I could then say le pano ninmu cu cinba mi, in which case I'd consider myself quite fortunate. However, if I say lei pano ninmu cu cinba mi, I mean that the ten women kiss me en masse, in which case I would consider myself either blessed or harassed (maybe I'm a rock star or something). However, it does not necessarily mean that each and every woman kisses me, simply that I was mobbed by a group of ten women and kissed by one or (probably) more in the process.

Proportions

Warning: this section gets into some tricky logical stuff. Skip it if you're not interested.

Question: If le ci prenu means "the three people," and re le prenu means "two of the people, how do you say "two of the three people"?

You probably go this one pretty easily: re le ci prenu. If, however, we use lo, the meaning changes. We can't say re lo ci prenu to mean two out of any three people (i.e. two thirds of the population). This is because while le ci prenu means the three people that I have in mind, by the same logic, lo ci prenu means the three people that actually exist, i.e. that there are only three people in the universe. You would therefore only use the number+lo+number formula if you knew the actual numbers rather than just the proportions, e.g.

re lo mi ci mensi cu nelci la rikis.martin.

Two of my three sisters like Ricky Martin.

This states two facts: that I have three sisters (not actually true!) and that two of them like Ricky Martin (it doesn't actually state that my third sister hates him—she may be indifferent to him, or never have heard of him). If I use le in the same sentence, it isn't actually wrong, but it allows the possibility that I have, say, five sisters, but I'm only talking about three of them! This is one of the few areas where le and lo are not like "the" and "a/some".

One way out of this is to use fi'u, which is like the Lojban slash sign. So "two out of every three people" is really "2/3 of people", or refi'uci lo prenu

Quantities

I've said that words like "most" and "many" are numbers in Lojban, which is pretty logical if you think about it. The following "numbers" are particularly useful:
no
none (we've already seen this as "zero")
ro
each / all
so'a
almost all
so'e
most
so'i
many / a lot of
so'o
several
so'u
few
su'e
at most
su'o
at least
Some examples:
no le ninmu cu nelci la bil.
None of the women like Bill.
no lo ninmu cu nelci la bil.
No women like Bill. [because lo ninmu potentially includes all women that exist]
coi rodo
Hi, everyone
mi nelci ro lo mlatu
I like all cats.
mi na nelci ro lo gerku
It's not true that I like all dogs. (this is not the same as "I don't like any dogs", which would be mi nelci no lo gerku or mi na'e nelci rolo gerku—"I other-than-like all dogs")
so'i lo merko cu nelci la nirvanas.
Many Americans like Nirvana (the group, not the mystical state).
so'u lo jungo cu nelci la nirvanas.
Few Chinese people like Nirvana.
su'e mu le muno prenu cu cmila
No more than five out of the fifty people laugh(ed) (let's say a comedian told a bad joke).
su'o pa lo prenu cu prami do
At least one person loves you.
This last one is logically the same as lo prenu cu prami do, which means "there exists at least one person such that that person loves you," but it makes the meaning clearer and more emphatic.

Exercise 2

Translate the following sentences.
  1. All babies are beautiful.
  2. The pack of three cats bite the dog.
  3. What a surprise! Mei Li loves two men. (use an attitudinal indicator)
  4. Most men love at least one woman.
  5. It is not true that all men love at least one woman.
  6. The group of four women kiss Ricky Martin.
  7. It's a shame that no-one likes Bill. (use an attitudinal indicator)
  8. The baby bites two people (separately).
  9. One in three women like David Bowie.
  10. No more than 15% of Buddhists eat meat. ("Buddhist" is budjo, as you may remember from Lesson 3).
  11. Nine out of ten cats like "Whiskas." (use a cmene)

Number Questions

Remembering the sentence re lo mi ci mensi cu nelci la rikis.martin., how would I answer the following question?
xo le mensi cu nelci rikis.martin.
The answer, of course is re, which means that xo is the question word for numbers (though not all questions that can be answered with a number have to take xo, as we'll see in the next lesson).
xo is also used in mathematics, as in
li ci su'i vo du li xo
3 + 4 = ?
A few more examples:
xo le botpi cu kunti
How many of the bottles are empty?
xo lo prenu cu klama ti
How many people come here?
do viska xo lo sonci
How many soldiers do you see?
Note: It is not actually necessary to include the lo after xo. In fact, it isn't necessary after any number—for example ci lo gerku could be simply ci gerku, if you prefer. However, many Lojbanists prefer to keep the lo for the sake of clarity.

A final question

Lojban has no difference between singular and plural—"the dog" and "the dogs" can both be le gerku. But suppose you wanted to make a distinction between the two—how would you do it?

Summary

In addition to numbers, this lesson has entered the dangerous waters of Lojban articles. Lojban articles may seem difficult at first, but they are perfectly logical. In fact it's probably because they are logical that people have problems with them to start off with - you have to learn to think in a slightly different way. For the curious, here are the main articles and article-like words:
la
that named
le
that described
lo
that which really is
li
the number (lu is not an article, it's a quotation mark!)
la'e
the referent of (not really an article, as it takes a full sumti or pro-sumti, as in la'edi'u—the thing the last sentence refers to, as opposed to the words of the last sentence)
le'e
the stereotypical
lo'e
the typical
lai
the mass named
lei
the mass described
loi
the mass which really is
la'i,
the set named
le'i
the set described
lo'i
the set which really is
We also looked briefly at lu'o, which turns a set into a mass, and lu'a, which turns a mass into a set of individuals ("group" and "ungroup"). Strictly speaking, these aren't articles, though.

If all this looks terribly complicated, don't be discouraged! As you can see, these articles are all really variants on la, le and lo, which are normally all you will need. My personal advice (not official Lojban policy!) is when in doubt, use le. This is because the only time le is completely wrong is with a cmene (which needs la, of course). If you use le where another article would be more appropriate, you may not express yourself as clearly as you wanted, but at least you will not be talking nonsense, like you would in German if you said "der Frau".

Answers to Exercises

Exercise 1

  1. 35 = li cimu
  2. 4,802 = li vobinore or li vo ki'o binore (the spaces are optional)
  3. 6,000 = li xa ki'o
  4. 7.54 = li ze pimuvo (again the space is optional)
  5. 6,891,573.905 = li xa ki'o bisopa ki'o muzeci pisonomu (if that looks long, try writing it as a word in English!)

Exercise 2

  1. ro lo cifnu cu melbi
  2. lei ci mlatu cu batci le gerku
  3. .ue la meilis. prami re lo nanmu
  4. so'e lo nanmu cu prami su'o pa lo ninmu
  5. ro lo nanmu na prami su'o pa lo ninmu
  6. lu'o vo lo ninmu cu cinba la rikis.martin. (give yourself a pat on the back if you got that one right!)
  7. .uinai [or .uu] no lo prenu cu prami la bil. or na su'o pa lo prenu cu prami la bil.
  8. le cinfu cu batci re lo prenu
  9. pafu'ici loi ninmu cu nelci la deivd.bo,is. (note that "Bowie" is not pronounced bau,i or as in "bowie knife")
  10. su'e pipamu loi budjo cu citka lo rectu
  11. sofu'ipano loi mlatu cu nelci la .uiskas.

A final question

"The dog" would be le pa gerku. Normally, we wouldn't bother with the pa though, unless we wanted to make it quite clear that we only have one dog in mind. "The dogs" would be le su'o re gerku (or lei su'o re gerku, if we're thinking of them as a group)—"the at least two dogs". However, it is hard to think of many situations where you would need to say this. Like some other languages (e.g. Chinese), Lojban normally leaves number up to context. You guessed it—you've just spent all this time learning to say how many people, dogs etc. there are, and piso of the time, you don't need to! But, like many features of Lojban, it can be very useful when you want it, so please don't feel tricked.

Last modified: Mon Jun 27 23:13:35 PDT 2005

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