## Failed Bijections

Today was day one of graduation practice torture. For the nth time, where n is an extremely large positive integer, I learned that a) most seniors (or people for that matter) at my school are morons, b) my school administration is incredibly dumb, and c) It is very difficult to set up a bijection between two sets of unequal cardinality. More specifically: at graduation, it is *essential* that every boy is partnered with a girl and vice versa. Now I’m not very good at estimating, but first let’s assume (completely unfounded assumption) that the number of seniors who are to attend the graduation ceremony is even. Then let’s say there are 2n of these seniors. Then the probability that there are the same number of boys as girls is equal to {2n\choose n}\over 4^n. It seems to me that when n gets large, {2n\choose n}\over 4^n gets very small. In fact, it gets very close to zero. Therefore, it is highly unlikely that such a bijection can be accomplished. But that’s Homestead administration for you. They don’t understand such simple concepts as bijections.

So when we started this bijective process, we had lines of boys and lines of girls and we were supposed to pair up. I was following someone else in a line, and he decided to move somewhat to the left. Then, for whatever reason, the people behind me all decided to move forward one position in the line. Then the person behind me accused me of not being able to follow directions, so of course I told him that it was his fault for not being able to establish such a trivial bijection. He must have been one of the people at my school who doesn’t know any math, because he seemed very confused. I really wonder why they don’t make understanding bijections a necessary condition for graduation. It’s not very hard.

Fortunately, they decided that people would be allowed to sign yearbooks during the ceremony, so I felt justified in reading math books. But it was noisy, and I find it difficult to concentrate with >100db noise, so I didn’t learn a whole lot. At around 11:00, after we had been there for three hours, it suddenly became hot, and so of course the *brilliant* slaveholder (erm, I mean assistant principal) decided to threaten us with keeping us for even longer. But it was not to be, and at around 11:40, we were released from prison (erm, I mean graduation practice).

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.
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### 7 Responses to Failed Bijections

1. rippledance says:

If this is supposed to foreshadow my graduation…I think I’ll run and hide.

2. blenrock says:

When I read the title of your post, I knew exactly what the entry was going to be about. Hmm. Or maybe I saw the word “graduation.” In any event, my middle school did the same thing four years ago. But get this – when there were ~10 guys left at the end, the teacher in charge got mad at them for not being able to find girls to match up with. I vaguely recall her saying something like, “If you’d been faster, this wouldn’t have been a problem.” Hehehe…

• Simon says:

That reminds me of one of my more, shall we say, idiotic classes last year in which my *brilliant* English and history teachers tried to break a class of I believe 65 students (but for sure more than sixty) into twelve groups of no more than five students each for a project. Sorry genius teachers, but there’s this little detail called the pigeonhole principle that doesn’t allow such things to happen. I won’t mention the names of the teachers because I know aknoln doesn’t want to remember their names.

• Simon says:

I should mention another mathematical failing of theirs in that class. They had us play a game, and for some reason, they were trying to convince us to play one strategy, even though the alternate strategy was clearly dominant over their preferred strategy. And they wondered why some of the more intelligent people in that class hated them.

3. Anonymous says:

Our teachers were trying though.
VERY trying.

4. Simon says:

Trying to be stupid?