Tuesday, September 21, 2010

I've reached my limit and it looks a lot like sin(1/x)


My life is all about limits these days. Crash Kid is getting a crash course in the mathematical sorts of limits. He's taking AP Calculus — a year's high school course compressed into a semester. This course moves. He's had lots of questions for me, running along the lines of "how do you analytically find the limit of sin x2/ x as x → ∞ ?"

Since I'm in the incredible minority of people who on occasion have an actual use for mathematical limits in their work*, I'm not a bad person to ask. (I almost said "have a practical use" but that's an entirely other post about whether quantum mechanics can ever be said to be practical!). Still, my take on limits leans heavily toward the pragmatic. Crash is best off asking the resident mathematician when he wants to know about the theoretical underpinnings of these great mysteries. So sometimes I say, "Go ask your father!"

There's no escaping at work though. Evaluating the usability of some mathematical functions for quantum mechanics requires that you take a limit - and so my students have been dropping by my office all week to ask various questions about limits.

"Enough," I want to say, "I've reached my limit when it comes to limits!" And since it's the start of a new school year, I'm still working out the limits of how many plates I can keep spinning and how well I can keep the camels confined (cue the occasional crashing plate and spitting camel here). I made some remark at the dinner table to this effect tonight — at which point Math Man turned to Crash and said, "I'd say Mom's life is a bit like sin(1/x) as x approaches zero." They both snicker.

Don't get the joke? Check out the graph of sin(1/x) in the picture. The closer you get to zero, the more wildly the function oscillates, until it's just quivering.

There's nothing quite like getting snarked with math by your 16 year-old at your own dinner table. Especially when he's right on the money. Sigh. I think I need to set a few more limits.

*My Fermi calculation suggests the population of people who might take a limit as part of their job is less than 0.01% of the population.

7 comments:

  1. [notarealcontributiontooscillationandwhatnot]

    Whenever you say (write) "camels", I imagine them in your backyard, and the thought makes me laugh. Thank you!

    [I also find the rendition of "Go ask your father!" amusing.]

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  2. Lastly, I hope you do not approach 0. In philosophy we might add "or 0 does not approach you". We like to play with the rules.

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  3. Me too. I think it's that kind of week.

    That is all.

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  4. One quick correction: It is a year long course, so I have more time to study...and suffer

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  5. Ah, the spitting camels. Don't forget to keep that tent flap closed sometimes. :) As for the math joke, nice zinger...and true I think.

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  6. Being a theologian, rather than a mathematician or scientist, I read the title as "...it looks a lot like sin"! (Probably also cause I just got back from retreat, which inspired a confession appt on Sunday! Pray for Mtr. Susan and me, please, and I will pray for your camel management.)

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  7. Rev. Dr. Laura,

    I think there is another post there about sin and sin! Prayers, yes, for grace-filled shriving....

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