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In high school I came up with a geeky mathematical analogy for… - The Life and Thoughts of Zach

Nov. 29th, 2004

12:14 pm

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In high school I came up with a geeky mathematical analogy for relationships.

A relationship is a smooth analyzable (continuous and continuously differentiable) well behaved function with 2 "hole" discontinuities. The beginning and the end. You know how you got to the beginning and you know where you went after the beginning, you know how you got to the end and and later you will know where you went from the end.

But those moments -- the moment of beginning and the moment of ending -- are insanity. Unanalyzable, discontinuous, not differentiable. Everything goes to infinity or division by zero, the path/graph you were walking on falls out from under you. You just have to keep counting until the function returns to normal and existence proceeds.

ETA (2009/09/12): I was just looking for this post, and before I found it on LJ, I found an old email in which I also characterized the same theory with slightly different words:

Have you heard my "hole in the graph" theory of relationships? That the arc of relationships tends to be uniformly continuous and differentiable at all points EXCEPT at the moment of getting together and at the moment of breaking up. You see where it's heading, you see where you've been, you see what's likely to come....but even if you see being together or being apart as the logical outcome of the current course of things, everything still falls apart at those moments of transition. You have no data. Math breaks down. Prediction breaks down. Understanding of how you got there or why breaks down? It's chaos. It's change. It's intense. And later in retrospect, if you ignore the hole in the graph, it all seems to make so much sense. But if you look at that hole you get lost again.

Comments:

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From:desert_fox
Date:November 29th, 2004 06:34 pm (UTC)
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My guess is that the asymptotes hold some transcendental value. Some other inexplicable application of Pi.
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From:skywind8
Date:November 29th, 2004 06:39 pm (UTC)
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And the holes sometimes hold glimpses of the function value at a different point in time. Maybe sorta transcendental there too.
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From:zarfmouse
Date:November 29th, 2004 06:47 pm (UTC)
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Exactly! From a distance you can infer the existence of the beginning and end. You can see where they are, even though they aren't there and they can't be understood. Where the function went afterwards usually follows directly from where it was heading beforehand.
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From:skywind8
Date:November 29th, 2004 06:38 pm (UTC)
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Hehe! I like that description. I think that's the most accurate model for it I've seen yet.
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From:flutastic
Date:November 29th, 2004 06:43 pm (UTC)
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I like it. It definitely draws out a picture of what relationships are like. Ah, polynomials. Haven't thought about those in years.
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From:logodaedaly
Date:November 30th, 2004 02:58 am (UTC)
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I <3 this post. Added to memories. You rule, Zach. :-)
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From:soulsong
Date:November 30th, 2004 08:37 am (UTC)
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Did kids pound you at school a lot? :)
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From:zarfmouse
Date:November 30th, 2004 08:44 am (UTC)
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I went to a math and science academy for high school as did most of the folks posting their approval in these comments. :)

Such thinking was the norm among us geeks, not a grounds for pounding. :)

(Which isn't to say there wasn't a lot of *ahem* pounding going on among the kids of that school...but that was the fun kind where no one was hurt.)

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From:soulsong
Date:November 30th, 2004 09:01 am (UTC)
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Explains a lot :p
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