The Bises Problem

So when I idly posed the following math problem in my last post, I wasn't really thinking about it, but it's actually a little bit interesting. 

The Question: If a party of nine people is breaking up, in which there are five girls, four guys, and no relations, how many kisses will be exchanged?

The Assumptions: Any pairing involving a girl (that is, girl-girl or girl-guy) will result in two kisses (one on each cheek). Since none of the guys are related, any pairing of two guys will result in no kisses.

To warm up, let's consider the Handshake Problem: If a roomful of n people all shake hands with one another, how many handshakes will be exchanged? For simplicity's sake, let's say n in this case is 10. That means each person in the room shakes hands with 9 other people, so you might be tempted to multiply 10 by 9 and arrive at 90 handshakes. Actually, though, you've double-counted each handshake, since A shakes hands with B and B shakes hands with A, but that's only one handshake total. So you divide by 2 and arrive at 45 handshakes. Or, more generally, in a room with n people, you will have [n*(n - 1)]/2 hanshakes.

My problem is a little more complicated, since the guys don't faire les bises among themselves and instead of one handshake, we have 2 bises. If you look at the picture (sorry, it's not the most beautiful graph ever, since I drew it by hand and photographed it with my webcam, but it will have to do), where G = girl, B = boy, and each line = 2 bises, all the girls are connected to everyone else but the boys are only connected to the girls. For the moment, let's pretend kisses are like handshakes, i.e. one between two people. All you have to do is calculate the number of kisses for a normal group of 9 and then subtract the number that aren't being exchanged by the group of 4 boys, in other words:

(9*8)/2 - (4*3)/2 = 36 - 6 = 30

Now, remembering that each exchange of bises actually involves 2 kisses, we multiply by 2 to arrive at 60 total kisses in the above scenario. In other words, Elizabeth wins!

(Is it glaringly apparent how much I miss math?)

Les Expressifs

Starting yesterday, there's been some sort of street fair going on on downtown Poitiers called Les Expressifs. The idea seems to be to get together a bunch of street performers, plus some musical groups. I heard very loud rock music coming from the tent in the square in front of the Hôtel de Ville this afternoon, and this morning I watched a guy engage in pseudo-juggling (à la Renfest, rolling them down his arms and around his body and such). I'm pretty sure the story he was telling to go with it was some sort of political allegory, but a) I couldn't hear very well and b) I don't know enough about politics to get it even if I'd understood. There were a lot of crunchy-granola types (or whatever they're called in France) in attendance; in fact, I have a feeling this whole festival would be very at home in Vermont.

The actual point of going into town today was to get my receipt for my application for a titre de séjour (residency permit), which took all of five minutes but required an hour of waiting in line at the Préfecture. Everything administrated by the government, from drivers' licenses to citizenship applications, goes through the Préfecture - not very efficient, in my opinion. Waiting at the DPS is bad, but at least you're only waiting behind other people wanting their drivers' licenses. So that was a pleasant way to pass an hour's worth of my afternoon. On the other hand, I bought a nice scarf in order to blend in more readily with the French population (staying warm being a secondary motive).

I went to Bible study again last night, which was great fun (much more lively discussion/analysis of the text this time around), involved another dinner of crepes (never a bad thing), and was like a miniature cultural education in and of itself. I think I've finally properly decoded the ritual of les bises (cheek-kissing). If there's a female involved, two kisses are pretty much automatic (but occasionally just one; for example, you've boarded a bus and see four or five of your friends and are trying to greet them all while not falling down or knocking anyone over). When two guys greet each other, if they're related, they'll probably kiss on one cheek (more on greeting people you're related to later); if they're not related, they'll shake hands, varying from a warm clasp to a manly grasp depending on the age of the parties involved (manliness being inversely proportional to age, amusingly enough). That being established, the question is obviously when this ritual is necessary. It doesn't appear to be normal to thus greet people you live with (hence the two-related-men scenario only occurs if, say, Bruno's older son who lives in an apartment comes over to visit), unless you haven't seen them in a few days and/or they're leaving for a prolonged period. On the other hand, anyone you have even a passing acquaintance with is fair game, which means you'll probably end up faire-ing les bises with half the students in any given class every time it meets. People you don't know at all are equally fair game, sometimes as a precursor to an actual introduction, sometimes just to be friendly (several girls in my history class greeted my like this three weeks in a row before I actually figured out their names). If it's obvious you're foreign (like me), there's more likely to be hesitation on the part of the other party, though usually they can't overcome the impulse. Other foreigners are the trickiest, especially if you have no idea what part of Europe they're from: to faire or not to faire, is always the question. And the most tiresome manifestation of the habit is when leaving a gathering, whereupon you are morally obligated to kiss everybody in the room, which takes absolutely forever if everyone is leaving at once.

I leave you with a math problem: if a party of nine people is breaking up, in which there are five girls, four guys, and no relations, how many kisses will be exchanged?

Vignettes

I'm very thankful today is Sunday: nothing on the schedule that requires doing battle with the bus system. I went to church with my host mother this morning. It was...different. It's called the Église chrétienne (Christian Church), and is exactly what I expected from the name: not actually in a church, praise and worship music, about as non-liturgical as it gets. Lots of spontaneous praying and hand waving. The pastor is American and speaks French worse than I do. All he did was give a sermon; he didn't even serve or particularly bless the communion; you go up and take it "as the spirit moves you," I guess you could say. Me, I like the ceremony and tradition of liturgical churches. But living in Mignaloux, with no buses on Sunday, I'm not sure what other options I have. We'll see.

Mignaloux does have its plus side, being small and cute. Today there was a big market thing, basically an all-town garage sale (it reminded me strongly of the Kolache Festival, sans kolaches, and with sausage in a baguette rather than on a stick). I saw lots of interesting stuff, including an amazing number of matched sets of beer glasses, piles and piles of the little china figurines that come out of King Cake, Readers Digest condensed classics in French, and tons of vinyls, which Bruno collects (he came home with Johnny Cash and Sting, among others). It was pretty fun. However, it greatly disturbed me that they planned on selling the rabbits at the petting zoo for eating. That's just wrong.

To backtrack a bit, we tried to register at the Scolarité des Sciences on Friday and had all sorts of trouble with our American health insurance not being accepted. The nicest of the ladies told Lauren and me to go to our class anyway and we'd get it worked out later, so we did...and we're not going back. I came to that conclusion more quickly, having understood less of the computer science related material than her, but it's not what either of us was looking for. So I'm ditching math for the semester, which leaves this week pretty much free.

We did two walking tours of the downtown area, one Friday afternoon and another Saturday morning, with M. Fabrice Vigier, a history professor at the university. We saw a lot of churches, including some that have been repurposed. It was all quite interesting, and also damp - it's rained every day so far, and the forecast predicts rain for the foreseeable future. Charming. Tomorrow I'm planning to go into town in the afternoon, when there's at least a chance at sun and I am nearly certain the buses are running to/from Mignaloux, to explore inside a few of the churches at my leisure. I love old churches, and devoutly wish people still habitually built in stone. Though it's awful to see the graffiti and ugly paint and electric lights and other indignities people inflict on beautiful old churches. Progress is all well and good, but it should stay away from certain arenas.

I finally bought a cell phone, which is pretty cute and weighs almost nothing, being as basic as it gets (which is exactly my cup of tea). I had to go with the cards to add minutes, because you can't sign up for a month plan without a French bank account - a credit card doesn't cut it. Minutes are kind of ridiculously expensive, as previously noted, but all received calls are free and work even if you don't have any credit to make calls, and emergency numbers are free as well, so it's good for being reachable and in case of emergency.

In general, I'm getting a bit more settled in, though everything is inordinately tiring, including talking to people. I can understand French if one person is speaking in a relatively quite environment, but start adding people to the conversation and I completely lose it. Hopefully that will get better quickly.

L'épuisement

Today was exhausting. Don't ask me what I'm doing blogging about it instead of sleeping; I wouldn't have a good answer. It's a relief to write in English again - we signed the Language Pledge today, so no more cheating by speaking English with my host mother, but communication with friends and family is sort of exempt, so I'm filing blogging in that category. As the day wore on, my French got worse, not better - when I'm tired, I lose all grasp of syntax, grammar, vocabulary (I forgot the word for "dog" this afternoon), pretty much everything you need to communicate effectively. Oh well.

This morning we met with Viviana and M. Paoli for introductions, lectures about French university life, classes, professors, all the logistics. We had lunch at a RestoU, but I haven't really been hungry since I got here (between the walking, the worrying, and the lack of appetite, I'm going to lose weight instead of gain it), so I can't really report on the quality of the food. The afternoon was more lectures and then, for three of us, meetings with professors in the math and science departments. It seems that math professors are the same everywhere - quiet, awkward, hard to engage in conversation - and I felt that he underestimated Lauren's and my level of proficiency. We're both taking Combinatoire (combinatorics) this semester, which is a third-semester course, and for next semester I had to talk him out of wanting me to take courses I've already covered. As it is he barely agreed to let me into a fourth-semester course in Euclidian/Hermitian spaces that I think I'm quite well-prepared to take. Oh well. Lauren and I present ourselves at the Université at 8h30 tomorrow morning to register for our math class, and the class itself starts at 10h30 and goes till 12h30. We'll grab something to eat and take the bus to centre ville to meet M. Fabrice Vigier, a history professor, who's taking our group on a walking tour of Poitiers. Then I'm going to take the bus home and go to sleep.

Speaking of buses, so far I haven't gotten too lost. I almost took the wrong bus this morning, but la conductrice fortunately asked me where I was going (I guess I do look like a foreigner) so it all ended up all right. Living in Mignaloux (a suburb of Poitiers) puts me closer to the campus that most people, but it's a bit of a hassle with the bus system. The routes end early in the evening (we ate dinner in centre ville tonight, so my host mother kindly came and picked me up from the closest bus stop to Mignaloux that I could get to) and you have to call ahead of time to get a bus on Saturday. They don't appear to exist on Sunday at all. I'm thinking of buying a bike, as it's not too far to the Parcobus Champlain stop (though a bit far for walking) where buses run much later and more frequently. We'll see.

I'm pretty nervous about my first class tomorrow, but at least Lauren and I will be together. I'm looking forward to settling into a schedule, at least; hopefully one that permits more sleep than I'm currently getting. I still need to buy a cell phone. I feel slightly naked without one, but they're so expensive here! If you use the pay-as-you-go variety, it's about €40 for the phone, and then €30 for two hours of call time (which comes out to about $0.75 a minute). I'm trying to decide if a one-year plan is worth it. Hopefully I'll have some time to figure that out on Saturday. And now I'm going to bed.

Dear Math

This abusive relationship needs to stop. For all the time I devote to you, I'm not getting the love and respect I deserve. We've been going steady for a while now - it's time to stop playing hard to get. I can't hold this relationship together by myself. I need some positive feedback from you. You've got me on an emotional roller coaster. Most days I just don't understand you at all; you keep me up at night trying to figure you out. I'm tired of crying over you. I want to quit you, but every time I'm ready to walk away, you remind me how interesting and beautiful you are. I remember how great life is when we're getting along, the exhilaration I feel when I discover something new about you. I want it to work between us, but I can't do it alone. Enough with the enigmas - open up and let me know you love me back!

Love and confusion,
Hallie

This Is Why I Love Math

Today in calculus, my professor was scribbling definitions and examples on the board in full flow when he hit the end of the board. He jokingly suggested that for his birthday, he wanted a round room with a neverending chalkboard. Somebody in the class called out to ask him when his birthday is. It's sometime in October, but I don't think anybody in the class remembers the date because we were all too busy trying to work how old he'll be. His age will be a product of primes for the third consecutive year, and this is the first time in his life that this has occurred. I love how he already had that worked out and didn't even have to think about it. So, how old will Professor Schmitt be?

Do What You Love

Life is full of pithy but overly simplistic bits of advice like the above. How do you know what it is you love? What if you love too many things? I had more than a few crises as I neared the end of my first year of college (I can't believe I've finished a year of college), but I finally made up my mind to double major in French, which was basically a given (and on the practical end of liberal arts), and math, because I really think it's what I love. I realize many people find math unlovable. I loathed it through middle school, was skeptical through pre-calculus, and only really started to appreciate it when I got to calculus. They don't usually teach you the cool stuff, like linear algebra, in high school. Remember chemistry class when your teacher told you the only way to balance chemical reactions was an educated version of guess-and-check? Actually, there's a simple, foolproof method involving matrix reduction that will give you every possible way to balance an equation every time, including some solutions it would be basically impossible to arrive at by the eyeballing method. Nifty. Well, a lot of subjects have cool tricks up their sleeves. How do I know math is what I want to do for the next three years of my life? It was a small clue when my first meeting with my potential adviser turned into an hour-long lecture on the braid group and I didn't get bored. That evolved into my going to office hours on the (legitimate) pretense of getting homework help, but really just so I could sit and listen to the math professors talk. I heard rants ranging from how the sciences are corrupting pure math, to how math in movies is invariably wrong (and how the professors here invariably know the people hired to be math consultants in said movies), interspersed with mini-lectures about arcane principles of mathematics. As terrifically nerdy as it sounds, those were some of the best conversations I had all semester, and those are the people I want to spend the next three years learning from. I will leave you with a joke that, even if you never find mathematics lovable, you have to admit is pretty hilarious:

Q: What do you get if you cross a mosquito with an elephant?
A: (mosquito)(elephant)(sinθ)

Q: What do you get if you cross a mosquito with a mountain climber?
A: Trick question. You can't cross a vector with a scaler.