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Speed Limit

While I was doing my impromptu pre-summer tour up and down the East Coast and Tennnessee, I was thinking about math. (Yes, I’m a geek even when I’m driving.)

So you’re on an interstate for, say, eight hours (give or take pit-stops for gas). The speed limit on said interstate is 70. (Unless you’re on I-81 along the ass-edge of Virginia where they’re speeding-ticket happy for no good reason, and then it’s 65. But I digress.) So you’re trucking along for the good part of the day, until you hit that last hour of your trip, where your destination is so close you can taste it on the wind.

That last hour is always hell. You suddenly have to pee like your life depends on it, but you’re determined to hold it so you can just GET THERE. You probably should have stopped for gas at that last exit, but your dash swears you have enough to coast into the driveway on fumes. You’re stomach is rumbling like its just eaten a maniac (or his hands). You’re sick of your iPod, your books-on-tape, your mixed CD collection, and there’s nothing but God and jazz and hip-hop on the radio so you’ve started scanning for car commercials.

As if that all wasn’t enough–to make matters worse, the closer you get to your destination, the lower the speed limit becomes. 70 turns to 65. 65 turns to 55. 55 turns to 45…and sometimes less if there’s construction. Once you hit the neighborhood it’s 30, or even 25. 15 if it’s a school zone and classes just let out. You begin to feel like the closer you get to your destination the slower you’ll have to go, until you’re stopped right there in front of your sister’s driveway: you can see the house, but you can’t go in. You will never go in. The Speed Limit won’t let you.

There’s a mathematical concept very much like this dilemma that’s called–appropriately enough–a limit. In layman’s terms, it’s one of those numbers that goes on forever, like 1.99999999999999…etc. 1.99999999 approaches 2, but it never really ever gets there. In some circles, it’s decided that eventually 1.99999999999 gets SO close to 2 that it better be using contraception, so for all intents and purposes, 1.9999999999999 = 2.

I think about this as I slowly walk up the steps to my sister’s house, as x (essentially the number of 9s) becomes infinitely large, and I am thankful to those mathematicians who have decided that my limit is infinity enough to bridge that increasingly small gap and ring the doorbell.

My hat’s off to you, sirs and madams. Safe journeys to you all.

Originally published at AletheaKontis.com. You can comment here or there.

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( 2 comments — Leave a comment )
codimension4
Jun. 28th, 2010 05:52 pm (UTC)
"In some circles, it’s decided that eventually 1.99999999999 gets SO close to 2 that it better be using contraception, so for all intents and purposes, 1.9999999999999 = 2."

In other, more mathematical circles, they post annoyingly precise proofs, such as the one below, which recasts your above observations in a more rigorous light.

Let x = 1.9999999...
Then 10x = 19.999999...

10x = 19.9999...
- x = 1.9999...
----------------
9x = 18
x = 2

=> 1.99999... = 2
QED

In this case, the nines don't get there, they're just already there. There are limits where we approach something at infinity, but this is not an example. Normally, limits are applied to functions that change over some variable (say, as x changes). In the case of 1.9999..., however, nothing is changing. It's just a graphical representation of a (static) number. Instead of thinking about adding on 9's one after the other (which would be getting closer and closer to 2), you have to accept the mind blowing premise that all of the 9's are already there.

...Okay, so I lack your gift for the poetry of language, but I felt it important to point out. You know. For the children.

In some circles, I have no friends.

Love,

your favorite mathematician (after Oberly, I mean)
princessalethea
Jul. 7th, 2010 06:22 pm (UTC)
I love that you took the time to answer this properly.
:-)
( 2 comments — Leave a comment )

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