Showing posts with label Advanced Mathematics. Show all posts
Showing posts with label Advanced Mathematics. Show all posts

Friday, January 25, 2013

Sesén


First one hundred, then ourteen and now this. The other day I’s waiting for a long while at the post office to send a package and I heard a boy giving his mother a Maths lesson. I couldn’t retain all genius enunciated that day but what I remember I document.

First lesson’s all about the 111, or how he described it, the one and the one and the one. But know that if you read that as one hundred eleven, you’re very very wrong. The kid couldn’t be more explicit about it: “the one and the one and the one is a number that is called ten-one.”

The mother hardly payed any attention to him. His next drop of wisdom was about sequence. After the ten-one comes the twenty-seven, then the twenty-eight, then the twenty-nine, and then the sixty-eight. I don’t remember how sixty-eight was written in numbers, but it was something equally crazy.

Then he began to explain what happens with numbers’ properties when you modify their digits’ order. The 12, for example (of better put: “if you put the one in front and the two behind”), is called twelve. While if you switch the drawing, “the two in front and the one behind”, it’s called thilty-one. I wouldn’t know if the L was a pronunciation defect or part of the made-up name. What surprises me the most, in fact, is that the boy ignored stuff as basic as the formation of twenty-one, but handled perfectly the “front” and “behind” stuff with words, that I always mix up when I don’t think about it half an hour prior to talking.

The mother, at this point, actually heard what her son was saying and she corrected him. She explained that though it’s true that 1 and 2 make a twelve, 2 and 1 actually form the twenty-one. The kid’s answer was solid: “No, mom, there is no twenty-one.”

And the last of the teachings I remember’s one of the last ones he said: “There is a number called sesén.” Now sesén, pronounced seh-SEN or something like that, are actually the first two syllables of sesenta, which is Spanish for sixty. The mother looked at him with an insistent look on her face, waiting for that last syllable, but it never came. The number is called sesén. How is sesén written? “A three with a five and a five.”

I could say what happened was what I described in Ourteen, a kid trying to pretend he knows how to count. Imitating what he perceives of his teacher, for example, when he teaches the numbers to them. Imitating, in fact, what he understands of which is taught to him. And there is some of that, but I’m not sure that’s the whole story.

’Cause what I had described was my little sister making numbers up in a low voice, mumbling with the intention that no one would pay too much attention, that anyone could think by default “well, if she’s counting she must be counting properly.” This boy, on the other hand, was preaching his truth, completely confident and explaining the tables of combination of digits as far as he understood ’em.

It wasn’t just that he didn’t understand the Maths and he presented them vaguely. He didn’t understand the Maths and he had replaced them decidedly with something else entirely. My theory is the boy was actually thinking about Alchemy. And what an Alchemist! He treated every number as a compound with mystic properties, which could react with any other one and form a new number, a surprising one, that we’d have to run and add to the encyclopedias. He mentioned numbers as one mentions pokémon, elements memorized from a table, that can be found in nature and react differently to different treatments. Some combinations simply didn’t exist, digits you could put together but wouldn’t generate any real number.

And the worst is, in the end numbers can be a little like that.

Thursday, January 24, 2013

Ourteen


Another one ’bout numbers. I had the entertaining pleasure of watching by little sister grow up from a minuscule and insignificant baby to a full grown adolescent. And of course, I saw her and talked to her while she learned to count.

Once I heard her as she set out to count from 1 to whatever she knew. The thing started well the first ten numbers. Until the fourteen she managed too. After fourteen, however, came ourteen. And later see-one, and after that ateeseven. And so on.

I couldn’t really say which were the numbers she invented that day, but they were all very interesting. Her behavior fascinated me. In the same way she had many a time tried to convince me that she knew how to read, only not aloud, and she kept staring at a written sheet of paper with a concentrated look on her face, now she was trying to pretend she knew all numbers that came after the fourteen.

It’s very common that children imitate behaviors they see in adults, like counting for instance. Though they don’t know exactly what’s the purpose of the actions, or the details and knowledge required to carry ’em out, they try to mimic the symptoms, the superficial part they can identify. And in reality we adults do the same, only one of the behaviors we already learned is to identify which behaviors are harder to fake in front of the people who handle them better than us.

And that’s the interesting part of it, innit? That we live every day in this society with human beings who ignore, for example, the sequence of natural numbers, and how unambiguous and unforgeable it is. And nonetheless we can talk with ’em and discuss with ’em and feel for them almost all emotions we can feel for the folks our age, and even more. They’re people who ignore how precise, how distinct the chain of natural numbers is for someone who already knows it. But they don’t have any way to find out ’cept by pretending they know it.

Neither they have any way to know if they can mimic crying. And later maybe they find out they do, they can make some adult believe they’re effectively crying. They don’t have any way to distinguish between crying and counting, which actions are unforgeable and which are more left open to interpretation. In the same way that we, until we try, don’t know if we can pretend we laugh when in fact we didn’t get the joke. Or pretend we walk inattentive on the street when in fact we’re thinking whether we look silly or not. Or pretend we know how to do some paperwork when in fact we’re reading the form in hope that it’ll shed some fucking light on the matter. Or pretend our life is interesting when in fact we’re asking ourselves how come all things always happen to everyone else.

So one of this days I’ll send it all to hell and see if I can count up to ateeseven all by myself.

Wednesday, January 23, 2013

One hundred


I’ve a memory related to numbers from the time I’s a child. I asked my mother if the number 100 was big or not. I had surely recently learned to count to 100. She answered me that it depends, and gave me examples of situations in which 100 of something was a lot and others in which 100 of something was too little. I don’t remember the examples, but they ain’t hard to imagine: 100 lions to hunt are a lot, 100 hairs on a head are too few, 100 empanadas to cook is a lot, 100 grains of rice too few. Etcetera.

I also remember getting mad at her answer. Not mad, really, but I did think it ungraciously dodged the whole point of the question. ’Cause I wasn’t asking for the number 100 in relation with the stuff you can count with it, I was asking for its intrinsic size. Now OF COURSE the number 100 was big. If any number was smaller or greater than another one, then all numbers must have a certain size. Regardless of what stuff you could count with ’em. And the size of 100 was “big,” no doubt.

I see now that actually my mother’s answer made a great deal of sense. No number has an intrinsic size really. What happened was that by that age I didn’t know anything that, coming in hundreds, were too few. Or at least, if I knew it, I never had counted it, ’cause until then I hadn’t known how to count to 100.

And indeed, thinking about it today, I believe what at that moment I interpreted as intrinsic size (though I probably didn’t know what “intrinsic” meant to be honest) was not the number’s size, but the size of the effort needed to count till that number starting from 1. And I also didn’t suspect, I guess, that the effort required to count to 100 was relative too, and depended on who was counting.

So the only answer is there is no answer. And that’s why the question’s so interesting, and it keeps coming back to memory. Because in the end, is the number 100 big or is it not?