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== Lesson 4: Numbers, and a few more articles ==
See also [[jbocre: Abstract Algebra|Abstract Algebra]]


One of the first things you learn in a new language is how to count, and
*prime: [http://www.lojban.org/jbovlaste/dict/m mulna'usle]
*unit: jicmu namcu: [http://www.lojban.org/jbovlaste/dict/c cmuna'u]


this course is no exception. However, in Lojban, numbers include much
**A unit in an integral domain is a number that every number is divisible by; e.g. the units in Z are 1 and -1, and the units in the Gaussian integers are 1, i, -1, and -i.
 
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:
 
# '''''pa'''''
 
# '''''re'''''
 
# '''''ci'''''
 
# '''''vo'''''
 
# '''''mu'''''
 
# '''''xa'''''
 
# '''''ze'''''
 
# '''''bi'''''
 
# '''''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 '''sew'''ing ('''''.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'''''!)
 
# 35
 
# 4,802
 
# 6,000
 
# 7.54
 
# 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. [[jbocre: 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.
 
# All babies are beautiful.
 
# The pack of three cats bite the dog.
 
# What a surprise! Mei Li loves two men. (use an attitudinal indicator)
 
# Most men love at least one woman.
 
# It is not true that all men love at least one woman.
 
# The group of four women kiss Ricky Martin.
 
# It's a shame that no-one likes Bill. (use an attitudinal indicator)
 
# The baby bites two people (separately).
 
# One in three women like David Bowie.
 
# No more than 15% of Buddhists eat meat. ("Buddhist" is '''''budjo''''', as you may remember from Lesson 3).
 
# 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 ====
 
# 35 = '''''li cimu'''''
 
# 4,802 = '''''li vobinore''''' or '''''li vo ki'o binore''''' (the spaces are optional)
 
# 6,000 = '''''li xa ki'o'''''
 
# 7.54 = '''''li ze pimuvo''''' (again the space is optional)
 
# 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 ====
 
# '''''ro lo cifnu cu melbi'''''
 
# '''''lei ci mlatu cu batci le gerku'''''
 
# '''''.ue la meilis. prami re lo nanmu'''''
 
# '''''so'e lo nanmu cu prami su'o pa lo ninmu'''''
 
# '''''ro lo nanmu na prami su'o pa lo ninmu '''''
 
# '''''lu'o vo lo ninmu cu cinba la rikis.martin.''''' (give yourself a pat on the back if you got that one right!)
 
# '''''.uinai''''' [[jbocre: or '''''.uu'''''|or '''''.uu''''']] '''''no lo prenu cu prami la bil.''''' or '''''na su'o pa lo prenu cu prami la bil.'''''
 
# '''''le cinfu cu batci re lo prenu'''''
 
# '''''pafu'ici loi ninmu cu nelci la deivd.bo,is.''''' (note that "Bowie" is not pronounced '''''bau,i''''' or as in "bowie knife")
 
# '''''su'e pipamu loi budjo cu citka lo rectu'''''
 
# '''''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.

Revision as of 17:07, 4 November 2013

See also Abstract Algebra

    • A unit in an integral domain is a number that every number is divisible by; e.g. the units in Z are 1 and -1, and the units in the Gaussian integers are 1, i, -1, and -i.
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