The Squeeze Theorem

If you haven't heard me talk about the navigational applications of the Squeeze Theorem before, you've been missing out.  (Hey watch it, I can see your eye-rolls!)

For those of you who didn't take, or don't remember, first-year calculus, the Squeeze Theorem is a mathematical nicety that helps you if, say, you need to know what value a function (a particular type of equation) will have as a variable on which it depends goes to infinity (i.e., as you take the limit).  If you're lucky, you don't need the Squeeze Theorem, and you can calculate the limit directly.  But if you can't perform that calculation, you might be in luck if you know that your function is bounded (i.e., always bigger than one thing, and smaller than another thing) by two other functions that go to the same limit.  That is to say, your function of interest gets "squeezed" to its limit by the bounding functions.  Ta-da!

All right, that whole paragraph was utterly useless (and probably not mathematically accurate).  But the Squeeze Theorem, that most glorious concept, is not!  Because, you see, the Squeeze Theorem is vitally important to everyday life -- specifically, to finding your way around in strange places.

Consider the following:

• You are Holly.
• You want chocolate.
• Chocolate occurs in discrete patches.  For example, in Ghirardelli Square, at the tip of the San Francisco peninsula.
• Therefore, if you head generally North while in the city (creating your own wandering function as you do), and do not swim across any bays or oceans (your bounding functions), you shall reach chocolate.

I've used the Squeeze Theorem to find chocolate, and also to burn it off (it worked remarkably well during long marathon-training runs in Boston, which, like any decent city, has a river to aid in bounded navigation).  And my friend Adam has reported that it works rather nicely in Minnesota, where the land is so flat that you can see your boundaries for miles (never mind that those boundaries happen to be ten miles apart).

And, wonder of all wonders, it turns out that Canterbury plans are the perfect for some Squeezing.  Allow me to present photographic evidence:

Imagine you are biking along a perfectly anonymous road.  You are surrounded by cropland, and it's very flat (i.e., the plains of Canterbury).

Perfectly Anonymous Road

 You might think you are lost.  But no!  Simply look left, then right!

To your left, some power lines (which are a useful North-South
bound once you get the hang of the place), but more importantly,
the Southern Alps!

To your right, the Canterbury hills!

Now securely bounded, you know you are traveling Southward!  Don't ask me how far apart the hills and the mountains are... that's why I've memorized road names. :)