Mystery solved: the Paris edition

Filled-in windows next to the gate of the Cordeliers campus of the École de médecine, Paris. Picture source: me.

Adam Gopnik’s Paris to the moon is the best writing that I know of on the experience of being an American ex-pat in Paris.  He maintains that the only really important difference between Paris and New York is the latitude: Paris is, in fact, so far to the north that in the wintertime, days are super-short here.  For me, it’s the one and only problem with this place—the winter darkness is crushing, a weight that I often think I can feel physically. 

Screen Shot 2017-11-22 at 05.17.57
Google’s autocompletes when I looked for the origin of Paris’s nickname, “The City of Light.” Note: Paris is NOT dirty.

In this city often called the City of Light, light actually is often an issue.  If you live on one of the lower floors of the typical 7-story Hausmannian apartment buildings that make up about 60% of Paris, the sunlight only actually shines into your home for a short time every day, even in the summer—in the winter, it’s a sort of perpetual gloom, even if you have big windows, just because of the height of the surrounding buildings.   Your windows are everything here, as far as I’m concerned.

Bricked-up windows, someplace or other in Paris. Picture source: me.

Consequently, it’s always been a surprise to me to see things like you see in the photo to the left.  You’ll notice that a number of the windows have been bricked up.  In a city where sunlight is at a premium, why the hell would you do that?

A wonderful tour guide told me the answer: once upon a time, buildings were taxed by the number of windows.  Brick up your windows, and you paid less in taxes.  At the time, Parisians mostly rented their apartments (today it’s common to own your apartment), and from the landlord’s perspective, it made sense—if you didn’t think that you could make up the tax difference by charging more rent, you might as well brick up your windows, pay less taxes, and your renters be damned.

Bricked-up windows overlooking a little café on the rue des Écoles. I accidentally learned the word “braguette” here when I walked inside to pay–with mine open. Picture source.

Interesting, but I was never able to find any documentation of the old tax rule that the tour guide had told me about, and I don’t typically write about things on this blog if I can’t find a source to cite.  Fast-forward a few months, though, and I find myself reading Victor Hugo’s Les misérables.  I was expecting a nasty cop trying to throw a guy in prison for stealing two loaves of bread; instead I’ve read  chapters and chapters about a really nice priest.  Is this book ever going to go anywhere?  I have no clue.  But, then I came across this.  Remember: as I said, the priest is really nice.  At one point, he gives this sermon:

« Mes très chers frères, mes bons amis, il y a en France treize cent vingt mille maisons de paysans qui n’ont que trois ouvertures, dix-huit cent dix-sept mille qui ont deux ouvertures, la porte et une fenêtre, et enfin trois cent quarante mille cabanes qui n’ont qu’une ouverture, la porte. Et cela, à cause d’une chose qu’on appellee l’impôt des portes et fenêtres. Mettez-moi de pauvres familles, des vieilles femmes, des petits enfants, dans ces logis-là, et voyez les fièvres et les maladies ! Hélas ! Dieu donne l’air aux hommes, la loi le leur vend. Je n’accuse pas la loi, mais je bénis Dieu. Dans l’Isère, dans le Var, dans les deux Alpes, les hautes et les basses, les paysans n’ont pas même de brouettes, ils transportent les engrais à dos d’hommes ; ils n’ont pas de chandelles, et ils brûlent des bâtons résineux et des bouts de corde trempés dans la poix résine. C’est comme cela dans tout le pays haut du Dauphiné. Ils font le pain pour six mois, ils le font cuire avec de la bouse de vache séchée. L’hiver, ils cassent ce pain à coups de hache et ils le font tremper dans l’eau vingt-quatre heures pour pouvoir le manger. — Mes frères, ayez pitié ! voyez comme on souffre autour de vous. »  — Victor Hugo, Les misérables


Hugo, a champion of the poor, had it right: search for impôt des portes et fenêtres and you’ll find the Wikipedia page on the subject.  Turns out the tax was first instituted during the Revolution of 1789, but it comes from an older Roman tax scheme called the ostiarium.  In effect until 1926, the original goal was to have a progressive tax, i.e. one that falls proportionally more heavily on richer people.  As it turned out, it had a bad effect on the renters.  From Wikipedia:

Cet impôt fut accusé de pousser à la construction de logements insalubres, avec de très petites ouvertures, donc sombres et mal aérés, et il conduisit à la condamnation de nombreuses ouvertures, ainsi qu’à la destruction, par les propriétaires eux-mêmes, des meneaux qui partageaient certaines fenêtres en quatre, ce qui augmentait substantiellement l’impôt.  Wikipedia

Sombres et mal aérés–exactly as Hugo described them.

On the plus side, the lack of any prolonged sunshine on my windows means that my apartment never gets very hot in the summertime.  When the days get short, I pull a light box out from under my little water heater (which turns out to be related to another Parisian mystery, but more on that another time), and half an hour a day in front of that makes the crushing winter darkness feel less…crushing.  Spring will be here before we know it.

French notes

Dieu donne l’air aux hommes, la loi le leur vend.  “God gives men the air, the law sells it to them.”  What interests me about this is the double pronominal objects: le leur vend, “sells it to them.”  I have a terrible time with that kind of double-pronominal construction, and as it turns out, a lot of French people do, too–ask someone how to say I give myself to you and you give yourself to me, and I’ll bet that they have to think about it for a minute.  The most common answers that I get are along the lines of Je me donne à toi and Tu te donnes à moi, where the indirect object pronoun (in this case, the person to whom something is being given) is not placed in front of the verb, but rather after it, in a prepositional phrase–contrast those with le leur donne, where both of the pronouns are pre-verbal (before the verb).  Native speakers, got any help for us anglophones here?

Speak to us of drinking, not of marriage

The feeling was like what gay friends have described to me when they first learned that they weren’t the only guys in the world who wanted to have sex with other men.

A Basque joke about the alleged difficulty of the Basque language: The Devil wanted to tempt the Basques to sin, so he decided to learn to speak Basque.  He quit after seven years, only having learned the word “no.”  The Devil did better learning Basque than I’ve done learning French, because I still don’t know how to say “no” in French.  My stumbling block: the second clause in a contrast.  My father speaks Portuguese, but I don’t.  We have pinot noirs in Oregon, but not Brouillies.

Jean Girodet’s magisterial Pièges et difficultés de la langue française to the rescue.  According to Girodet, the issue comes up in what he calls ellipticals.  In this situation, he says that literary language tends to prefer non, while the spoken language tends to prefer pas: 

Dans les tours élliptiques, la langue littéraire préfère en général non, la langue familière pas.

He gives these examples:

Non Pas
Veut-on réformer la société ou non Qu’il travaille ou pas, je m’en moque !
Il néglige son travail, moi non. Elle aime le ski, moi pas.
Cette parole est d’un marchand et non d’un prince. J’irai en voiture, pas à pied.
Il habite une villa, non loin de Cimiez. Il tient un café, pas loin d’ici.
Il veut créer un art tout nouveau, pourquoi non ? Partir tout de suite ? Pourquoi pas, après tout.

OK, good so far: you can use either, with non sounding more literary, and pas sounding more casual.  But, why do you occasionally run into both of them together??  Here’s a clear elliptical in Girodet’s sense of the word: the refrain of the song Parlez-nous à boire, “Speak to us of drinking (not of marriage).”  There are many recordings of it available (sometimes with minor differences in the lyrics), but my favorite du moment is this one from the film Southern Comfort.  Lyrics follow, from

Oh parlez-nous à boire, non pas du marriage
Toujours en regrettant, nos jolies temps passé

Si que tu te maries avec une jolie fille,
T’es dans les grands dangers, ça va te la voler.

Si que tu te maries aves une vilaine fille,
T’es dans les grands dangers, faudra tu fais ta vie avec.

Oh parlez-nous à boire, non pas du marriage
Toujours en regrettant, nos jolies temps passé

Si que tu te maries avec une fille bien pauvre,
T’es dans les grands dangers, faudra travailler tout la vie.

Si que tu te maries avec une fille qu’a de quoi,
T’es dans les grands dangers, tu vas attraper des grandes reproches.
Fameux, toi grand vaurien, qu’a tout gaspillé mon bien
Oh parlez-nous à boire, non pas du marriage.


Native speakers, can you help this poor, lost anglophone?  (Note: I’m guessing that jolies temps passé should be jolis temps passés, but what do I know?)

My source for the Basque joke: I don’t remember, but it’s probably one of Mario Pei‘s many books.  Pei was a linguist who wrote tons of popular-press books about language between the 1930s and the 1970s or so.  Running across one of them in a used bookstore  was the first time I ever heard of “linguistics.”  After a lifetime of mostly keeping quiet about my unending obsessions with language, the feeling was like what gay friends have described to me when they first learned that they weren’t the only guys in the world who wanted to have sex with other men.

How can you be 17 years old and 4 months old?

Humans are so good at “resolving” ambiguities that they usually don’t even notice them. Computers, though–computers have no such abilities, unless their designers give them to them.


One of the properties of every known human language is that they are ambiguous.  Being “ambiguous” means that something can have more than one interpretation.  Humans are so good at “resolving” ambiguities (i.e., figuring out the intended interpretation) that we rarely notice them, but in fact almost everything that you will hear/read or say/write today will be ambiguous in some way or another.

Humans are indeed quite good at resolving ambiguities.  If you want to get a computer program to do anything whatsoever with language, though, you have to give it the ability to deal with ambiguity–computer programs are just as incapable of ignoring ambiguity as humans are capable of resolving it.  So, one of my standard exercises for students in natural language processing (treatment of language by computers) courses is to have them go through some texts and find the ambiguities.  I typically have them do that with cartoons, since their humor is often based on playing with ambiguities.  Tomorrow, though, I’ll be teaching at the EUROLAN “summer school” on biomedical natural language processing, so I feel obligated to give the students a biomedical example.  Here’s what it’ll be.  It’s a text that would be completely typical in a health record (but it is not from an actual patient).  I read through it until I found 10 ambiguities, and then stopped–so, you should be able to find at least 10 points of ambiguity here–in just the first two sentences:

CLINICAL HISTORY: This prolonged video/EEG was performed on a 17 year and 4 month-old female.  This study was done to completion of Phase I surgical evaluation

TECHNICAL SUMMARY: The patient underwent…

Now, if you’re a normal human, you will not, in fact, be able to find 10 ambiguities in this text–we just don’t notice them, for the most part.  And that, in fact, is the point of the exercise.  I’ll follow the exercise with an illustration of those 10 points of ambiguity, many–or most–of which the students won’t have noticed.  Their computer programs, though–their computer programs won’t be able to miss them, and it’s their very ubiquity that beginning researchers need to have pounded into their heads.

See how many you can come up with, and then watch this space for the (or, at least, some) answers!

Go ahead, end this sentence without a preposition–if you can…

Of all of my students, this is the one on whom my work habits rubbed off. 

Déteindre sur: to rub off on. Ton pull à déteint sur ma chemise–il ne fallait pas les mettre ensemble au lavage.   (Collins French-English Dictionary)  Why ensemble and not ensembles, I have no clue…

On being stared at

At some point in their life, everyone should spend some time in a place where they’ll be stared at

Picture source: me.

It’s 1981, and my ship has pulled into Istanbul for a week.  Being a stupid young sailor, I’m wandering around alone.  I pass some old men sitting on a stoop drinking tea (a common pastime for old men in Turkey).  One of the old men gets up, walks over to me, spits on a finger, and tries to rub one of my many tattoos off.  When he can’t, he shakes his head in disgust and sits down again.

It’s 1981, and my ship has pulled into Istanbul for a week.  Being a stupid young sailor, I’m wandering around alone.  Going down a busy street, I suddenly find myself surrounded by a crowd of young men.  One of the guys emerges from the crowd, and in broken English starts translating for the rest of the crowd, telling me everything that they have to say about how much they love my tattoos.

It’s 2016.  I’m waiting in line at an art show in China.  A guy walks up to me: excuse me, I can take picture of you with my children?  Sure, why not?  Smiles all around as pictures are snapped, and we all go back to waiting in line.

My job and my pastimes take me far and wide, and in some of the places that they take me, I look unlike anyone else.  Japan, Guatemala, China, Mexico, Turkey–in all of them, I am a “white guy,” a light-skinned, blue-eyed guy in a country where everyone else is brown-skinned, with black hair and brown eyes.  In some of those countries, I go places where I may be the only “white guy” that I see all day, and in those countries, I get stared at–a lot.  It’s not just me–it’s the experience of any Westerner in those places.

What I’ve learnt in those countries: how good it can feel to be smiled at.  This morning I took a walk along the riverfront in Hangzhou, China.  Men (and a couple women) did tai chi alone.  Women (and a couple men) did synchronized dancing to music.  Grandmothers pushed strollers, and grandfathers jogged–often in business casual–occasionally omitting a loud yell or two.  (I have no clue what the purpose of the yells is–native speakers, do you have any insight into this?)  For 45 minutes, I was the only “white guy” that I saw.

It was unusual for people not to stare at me.  Sometimes out of the corner of their eyes, and sometimes quite openly, but almost everyone stared.  Some of them, though–some of them smiled at me, too.  你好, they might say.  你好, I would answer.  I waved at little kids, and their grandmothers smiled–and made them wave back at me if they were too shy to do it on their own.  Not big-deal interactions–but, it always felt so good.  What it cost them: nothing.  What it gave me: a lot, actually.

I maintain that at some point in their life, everyone should spend some time in a place where they’ll be stared at.  It’ll teach you the value of a smile for someone who doesn’t seem to fit.  Lots of people get stared at in today’s America–Muslim women in hijab.  Black men in nice hotels/white neighborhoods/academic conferences.  Any woman at all in a computer science department.  A smile at someone else costs nothing–and can give a lot.

English notes

on being stared at: I include this one in the English notes because of the commonly-taught, commonly-believed old bullshit that there’s something wrong with ending a sentence with a preposition.  Is on being stared at English?  Absolutely.  Is there any other way to say it?  Not that I know of.

their life: This is a good example of the use of a third-person plural pronoun to refer to a singular person.  Since there is no reason to assume any particular gender here, some dialects of English use their gender-neutral pronoun, which looks like the plural pronoun, but in this context is not.  You can read more about this phenomenon here.

Picture source:

stoop: Besides being a verb with a number of different meanings, stoop can also be a noun.  Merriam-Webster defines it as  a porch, platform, entrance stairway, or small veranda at a house door.  How I used it in the post: I pass some old men sitting on a stoop drinking tea (a common pastime for old men in Turkey). 


Once a year I spend a week in Antigua, Guatemala, where I interpret for a group that does free surgeries for people for whom even the almost-free national health care system is too expensive.  I spend a lot of time in the recovery room. It’s a challenge–you’re interpreting for people who are half-asleep, and often wearing an oxygen mask–and I do like a challenge. (This use of do explained in the English notes below.)  Sometimes the challenges are unexpected ones, though.

One day last year a recovery room nurse asked me to tell a little boy to cough. That’s not unusual in a recovery room–sometimes post-operative secretions in your lungs cause a minor drop in the amount of oxygen that you’re getting, and a cough or two will clear them right up.

Tosa, I said. The kid looked at me uncomprehendingly.  Hmmm, I thought to myself–does the kid not speak Spanish?  That’s not uncommon in Guatemala, where 70% of the population is indigenous and over 20 Mayan languages are spoken.

The father looked at me and smiled. Tosá, he said. The kid coughed. So: no cough when I said tosa, but tosá elicited the desired response.

The father was using a verbal form that’s used in Guatemala and a few other places in Central and South America. Indeed, it’s probably the most distinctive thing about Guatemalan Spanish. However, although I know a few local regional nouns and usually get a happy laugh when I use them, I had never learnt this particular verbal form–Americans would rarely have an occasion to use or to hear it, as it’s used only in the context of particular social relationships, and it wouldn’t be at all typical for a foreigner to have one of those.

My “voseo” lesson at Maximo Nivel, a Spanish language school in Antigua, Guatemala. Picture source: me.

The verbal form in question is called voseo. It’s used in very close relationships–between friends of long duration is the typical one.  In Guatemala, the tu form of verbs is used in many situations in which the usted form would be used anywhere else in the Spanish-speaking world–for example, waiters in restaurants and the ubiquitous vendedores ambulantes (people who stroll constantly through the tourist areas selling stuff, primarily Mayan women of a variety of ethnicities from the surrounding pueblos) will typically address you with the formal terms señor or señora (sir or ma’am)–and then use the tu form of verbs with you, which even on my fifth time in-country sounds weird.

So, you’re wondering: how does one form this mysterious conjugation?  For starters, let’s go over the present indicative.  It’s almost entirely regular, and very easy to relate to the three classes of Spanish verbs.

Spanish verbs end with either -ar, -er, or -ir, with the -ar verbs mostly being homologous with the French -er verbs.  (Sorry–I havent even thought about the others!)  To form the voseo present indicative of almost all verbs, you keep the vowel of the infinitive, add the -s that you would expect in the tu form of the verb, and put the stress on the final syllable.  So:

  • escribir – escribís
  • decir – decís
  • venir – venís
  • tener – tenés
  • comer – comés
  • volver – volvés
  • tomar – tomás
  • buscar – buscás
  • caminar – caminás

Of course, just because Ive learnt the voseo forms doesnt mean that I have anyone with whom to use them–as I said, there are only some relationships in which its OK.  I did use them with the dog at my host familys apartment.  I listened carefully, and they use the formal usted form with him,  but he didnt seem to mind my voseo–although I was sneaking him treats, so who knows…

Enjoying these posts from Guatemala?  Why not make a small donation to Surgicorps International, the group with which I come here?  You wouldn t believe how much aspirin we can hand out for the cost of a large meal at McDonalds–click here to donate.  Us volunteers pay our own way–all of your donations go to covering the cost of surgical supplies, housing for patients’ families while their loved one is in the hospital, medications, and the like.  Scroll down for the English notes, per usual.

English notes

I do like…  This use of do emphasizes something.  As far as I can tell, the primary use, although not the only one, is to emphasize something that is contrary to expectations.  For example, in this Dashiell Hammett quote

I do like a man that tells you right out he’s looking out for himself. Don’t we all? I don’t trust a man that says he’s not. And the man that’s telling the truth when he says he’s not I distrust most of all, because he’s an ass and ass that’s going contrary to the laws of nature.

…you wouldnt expect anyone to like a person who is looking out for himself (a very Trumpian behavior, particularly if youre only looking out for yourself)–hence the do.  How I used it in the post:

It’s a challenge–you’re interpreting for people who are half-asleep, and often wearing an oxygen mask–and I do like a challenge.   Liking a challenge is presumably at least somewhat contrary to expectations–hence, the do.  

In-country: being or taking place in a country that is the focus of activity (such as military operations or scientific research) by the government or citizens of another country (Merriam-Webster)


White House leak template for journalists: You speak more English/French/Spanish than you think you do

For me, it became clear that we had crossed some horrible line between sanity and madness when journalists started laughing during news stories. On the plus side, this leads to a discussion of the role of recursion in language.

For me, it became clear that we had crossed some horrible line between sanity and madness when journalists started laughing during news stories.  Leaks of stories of hallucinatory misbehavior, treason, criminality, and just plain evil have been coming out of the Trump government so fast that it’s become surreal.  Potential reasonable reactions include despair, and humor.  Taking the second option, the New York Times web site recently published a satire piece called The White House Leak Template for Journalists.  You click on various and sundry choices…

Screenshot 2017-06-18 20.24.59
Picture source: screen shot from the New York Times web site,

…and it generates a little news story about a leaked Trump administration scandal for you.

Scroll to the bottom of this page, and you’ll find screen shots of the whole thing.  It’s sadly hilarious, but behind the hilarity is an important point about how language works.

One of the things that’s interesting about language is that every human language (what we call in my line of work “natural” languages, as opposed to computer languages) is capable of saying an infinite number of things.  “Infinite” is a big claim, and you’re right to be skeptical about it.  So, let me just show you that with even a very small amount of knowledge of a language, you can say an enormous number of things–much more than you might ever have thought–and as you’ll see at the end of the post, this is a fact that has important implications for the many people reading this blog who are trying to learn a second language.

Let’s suppose that you know how to say a simple declarative sentence in some language or another–my dog ate my shoes.  You’ve got a subject, a verb, and an object.  Suppose that you know 10 nouns and 10 verbs.  You can now say the following number of sentences:

10 nouns * 10 verbs * 9 nouns = 900 sentences

Why only 9 nouns in the object position?  Because I’m assuming that you won’t use the same noun for the object as you did for the subject.  So, whichever noun you pick for the subject, you now have nine choices left for the object, rather than the 10 that you started with.

Let’s suppose that you have a language–like French or Spanish–that inflects all verbs differently for singular versus plural subjects.  Let’s also suppose that in our calculation above, we included only singular forms of the verbs.  Add the plural form of the nouns and the plural form of the verbs, and now you have the following additional sentences:

10 plural nouns * 10 verbs * (9 plural nouns plus 9 singular nouns) = 1800 sentences

To recap: 900 sentences if you only know the singulars, plus another 1800 if you add the plurals, so you’ve got 2700 sentences that you can say.

Note: this post relies heavily on a branch of math called combinatorics.  I stink at combinatorics, so please be kind!  Corrections are welcome in the Comments section.

To this point, we’ve only been using nouns and verbs.  Let’s add a new kind of word: and. Even if we didn’t know the plural forms of the verbs, and lets us say a truly remarkable number of sentences with just our 10 singular nouns and our 10 singular verbs.  Recall how many simple declarative sentences we could say with just 10 nouns and 10 verbs:

10 nouns * 10 verbs * 9 nouns = 900 sentences

Once you’ve picked a noun for the subject, you have 9 nouns left for your object, leaving eight unused nouns.  Suppose that you’re going to use and in your object: you have 9 possibilities for the first noun (since you used 1 for the subject) , and 8 possibilities for the second one (since you used one for the subject, and you’ve already used one in the object).  So, with and, you have the following number of possibilities:

10 nouns * 10 verbs * (9 nouns + and + 8 nouns) = 1700 sentences

…and if you’re keeping track, that’s 900 + 1800 + 1700 sentences, or 4,400 sentences.

Of course, we’re not done with and yet–since you’ve learnt to use the plural forms of verbs, you can use and in the subject, too.  The calculation of the number of sentences that you can make with and in the subject (but just a single noun in the object) is similar to what we just did:

(10 nouns + and + 9 nouns) * 10 verbs * 8 nouns = 1520 sentences

…getting us to 5,920 sentences.

Of course, you can have two nouns in the subject and two nouns in the object, as well–you can do the math.  What’s cooler is that you can use and to join together two sentences, too.  Let’s take the “formula” that gave us the smallest number of sentences: singular subject, singular verb, singular object.  Remember how we calculated the number of sentences that we could make with only 10 nouns and 10 verbs:

10 nouns * 10 verbs * 9 nouns = 900 sentences

How many sentences can you make by joining two sentences together with and? The possible assumptions are numerous.  Can you repeat the subject?  Why not?  (Dogs chase cats and dogs chase balls.)  Can you repeat the object?  Why not?  (Dogs chase cats and children chase cats.)  Certainly those are weird, though, so let’s estimate that maybe 10% of our possibilities aren’t going to be OK, and just calculate from the numbers that we used for the simple declarative sentences.  That gives us this:

10 nouns * 10 verbs * 9 nouns and 10 nouns * 10 verbs * 9 nouns = 1800 sentences; subtract 10% of that for the ones that repeat too much and you still went from 900 sentences to 1620 sentences with just one additional word.

…in other words: as soon as you throw and into the mix at the level of sentences, you double the number of sentences that you can make.  (The last time we tried to total how many sentences we could make, we had 5,920.  Double that with and, subtract 10% for the sentences that repeat too much, and you have 10,656 sentences.)

What happens if you add or to your armamentarium?  You just doubled the number of sentences that you can make again.  How about throwing but in there?  You just doubled it again.  (We’re around 40,000 sentences right now, even with our 10% adjustment for repeated things.)  Add one more tense and you just…well, it just got really, really big.  And let’s review what you know–it’s very little:

  • 10 nouns, singular and plural
  • 10 verbs, singular and plural
  • two tenses
  • and
  • or
  • but

For those of us who are as math-challenged as I am: that’s 23 words and two tenses to give you around 40,000 sentences.  Throw in some adjectives…  Learn how to turn a simple declarative sentence into a question…  Learn a few names…  Learn to say he, she, and it…  Add because…  

Now, I know what you’re thinking: I know a hell of a lot more than 10 nouns and verbs in French, but it sure doesn’t feel like I know how to say very many things.  Remember, though: as we discussed recently, you can get a surprisingly long way on a pretty small amount of a language.  This is a skill that you can develop with practice: think about simple ways to communicate your wants and needs, and I bet you’ll come up with creative ways to work around your lack of knowledge of a language.

A technical excursus: recursion

When we got into and, we touched on an important mechanism of language that leads to the fact that every human language is capable of saying an infinite number of things.  Called recursion, it has a specific definition in mathematical formalism that you can find here; for our point of view, it means that some things in language that we care about, such as sentences, can be made up of other things of the same type.  For example, we used recursion when we made the sentence Dogs chase cats and dogs chase balls out of two sentences: dogs chase cats and dogs chase balls.  We could also use recursion to make noun phrases (the groups of words that make up the subjects and objects in our examples): the noun phrase my dog and your cat is made up of the noun phrase my dog and the noun phrase your cat.  In principle, is there any limit to this?  No, actually.  You would die before you could say an infinitely long sentence, and even if you could live long enough to hear one, by the time you got to the end you would most likely have forgotten the beginning.  But, that doesn’t change the fact that the language, by virtue of having this fundamental property of recursion, can produce an infinite number of things to say.

If no one could ever say an infinitely long sentence, who cares about understanding how and why languages can produce the things?  For one thing, infinity is a pretty big deal, and if you’re dealing with a system of any sort that’s capable of infinity, then if you want to be able to understand how it works, you need to understand that aspect of it.  I believe it was Chomsky (who in many ways was a horrible thing to have happen to linguistics) who made the analogy that just because no marathon runner can run forever doesn’t mean that it’s not useful and important to understand the physiological mechanisms that let them do it.

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