On a Tangent

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You might be thinking, what is that?  And what does it have to do with me?  Or maybe you’re just thinking: Gosh, that looks beautiful – I wish I knew how to make such pretty pictures.

For the latter sort, you could get a math degree, or you could take a shortcut and read my tutoring blog, where I explain other marvels and will soon get into some more technical detail about today’s work of art.  But for the former, read on.

We start off with some really weird curve (read: I mashed a few keys in a graphing program and worked with what came up).  Now, if you were an ant on there looking close up, how would you visualize that curve?

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Maybe you’d think that it was just a line, a line heading off at that same angle that you currently find yourself.  Maybe, as you walk along, you’d constantly revise your view of the world:

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Such an ant could manage themselves just fine.  As long as they keep looking at where they are, they can make it around the curve.  But their conception of the world at large is completely off.  Almost every single judgement they would make about other points on the curve would be wrong.  The ant can live in the “now” as long as they keep it to themselves.

But our ant could be a little more sophisticated:

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This second ant is still using data merely from their local environment; they just estimate a curve of best fit, instead of a line (in mathese: they find a tangent conic, instead of a tangent line.  In worse mathese: they use a truncated Taylor series as calculated at that point, the general technique for all estimations in this post).  This curve still doesn’t match the overall pattern very well, but it does a darn sight better at making decisions about the neighbourhood.

A third ant might be a little more resourceful, and come up with this:

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Or this:

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Now, this ant can start making broader claims about the world.  The ant will still be off, but significantly less so than the previous two.  And finally, we have genius ant here:

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Again, this ant’s knowledge is not perfect – but she absolutely nails entire portions of the world, using just the information that is at her immediate fingertips.  She doesn’t have a larger view of the world, she has a deeper view.  Maybe she still lives in the “here and now”, but she doesn’t rest content with mere appearances.  She doesn’t just calculate how things are, or how they are changing, but how change changes, and so on (technically, up to 8th derivatives).  By assuming that everything is changing, including change itself, she can understand.

And as a bonus (which I’m not sure has any analogical value, but which looks cool), here’s all of the approximations together in one animation:

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Adjusting

I was filling out the most recent batch of PC paperwork last week. (For the record, it never ends. The initial application is not a hurdle; it is a plateau.) I had to send out a resumé and a statement of aspiration to South Africa so that they’ll know what to do with me once I am over there (I’m sure my family could narrow it down to two words: padded room). Funny thing is that I have to talk about how I plan to do a job when I don’t quite know what that job is or even exactly it will be (for an example of my quandary: you’re told you will teach in the US. Will that be in the UP? Kansas? Texas? Southern California? Virginia? Now, what if each spoke their own language as well? Though I guess Texas already does…).

However, I do know something about the job. I will be teaching children. And by “children”, I mean 6 – 15 year olds. I had a bit of a panic attack on realizing this. Wait, me, hang out with kids all day? The guy who expressly requested when working at camp to be placed on maintenance instead of counseling? Being placed with the one group of human spawn with whom I have no experience teaching?

Examine the typical life-cycle of my interests. I become intensely enthused, study excessively, find a problem, freak out, whine and complain and annoy people around me. Fortunately, the next few steps are usually to calm down, tell myself to shut up and deal with it, learn about what I was panicking about, and find out that it actually is more interesting than I thought. Lather, rinse, repeat.

So I’m at the calming down stage now and picked up some books on primary education pedagogy from the library. And really, I like the idea of teaching young children much better than teaching blasé college students. It is a chance to actually make a difference, to shape habits when they are most moldable. I mean, I still won’t be working wonders, but there’s something to be said about teaching science to students who want something more than the “practical” applications of it, or of teaching medical habits when they might actually become instilled. And in addition, I’ve reframed it to myself as a challenge. Dealing with children and breaking up information into easily digestible pieces are not strong suits of mine. Therefore, I should get better at them.

I’m still working on getting myself excited about teaching arithmetic and word problems, however.

Details

I have the official information now. I will be in South Africa, with orientation starting 10 July. Evidently, my job description in the invitation packet is that of “primary education”, without many specifics in the way of math. I’m not sure what to make of that, other than that I will be maintaining flexibility in the months to come. The two provinces I may be in would be Mpumalanga and KwaZulu-Natal, two of the easternmost provinces. But the specific site won’t be decided until I’ve been overseas for a month and a half, or so I gather. All info is subject to change, of course.

I’m currently adding and revising links over in the right sidebar so that people can have some basic info on the country I’ll be visiting. As I read up on history and culture, I’ll post some of that here too.

Invitation

Got the email today. I’m in. July, teaching secondary ed mathematics. Where and when, you ask? That I’ll find out in the next 10 business days as the physical invitation is mailed to me. But it’s official.

I think this calls for a martini.

Update on the medical stuff (since I know that no one wanted to see that at the top of this message): the problem was not necessarily my asthma, but rather that I have been to urgent care recently and they needed to find a site that was within 4-6 hours of medical care, should I need it. So I won’t be way, way out in the boonies (which, actually, I kinda would have liked). But they found something for me, so I am happy.

Updates

I went to a PC networking event last night. There were a bunch of other prospectives, as well as returned volunteers and families for all involved. It was interesting hearing people’s stories of where they had been. I also had some good chances to talk to people who had recently been in Africa. They speculated that I would probably be placed in Burkina Faso (or, the country formerly known as Upper Volta), since it is the only country in West Africa that they know of that both speaks French and needs math teachers. Since speculation is all that I have at the moment, we’ll go with that. And who doesn’t want a capital called Ouagadougou?

Although I might have more soon. See, there are four separate evaluations – medical, dental, legal, and placement. I finished the placement eval earlier this week, and just got notice this morning that my medical eval was complete and that I’ll receive the results in the mail soon. (Of course, that could mean that I was deferred or something – but I like my version better.) So it’s just legal and dental. Dental was received at the same time as medical, so I would think that it should be processed soon, and I don’t have any major surgeries or anything that need to be done. Legal, well, there’s that stupid document I forgot to sign. But I sent that in a few weeks ago, so hopefully that should be done soon as well.

So I might find out sometime relatively soon where I’ll be going. There are a lot of hopefullys in the above paragraph. But after listening to all the people last night who have been waiting a year and a half to find out their placements, I figure that I’m going through this whole process rather quickly, one way or another.

UPDATE: Legal has been cleared. So I’m just waiting on dental, and then for the different groups to get together and discuss placement options. Fingers crossed….