September 1st, 2006

krazy koati

At finding max and minimums, I'm simply just miraculous

If you're going to get any calculus done at all you just have to get a function. Finding a function can be an adventure, which is why students often begrudgingly accept mass-produced functions turned out in textbooks and homework assignments. What a function even is can be the subject of weirdly intense debate. Many will tell you a function is just a rule by which you match one collection of things to another -- possibly the same -- collection of things. This is a sign of permissive parenting. You really want something with some self-discipline. A decent function is the kind where you give it some number or numbers to start, and get some number or bunch of numbers back when it's done. Do not interrupt it while it is working, as functions are prone to anger.

Once you have a function (you can get one in aisle four, below the off-brand toys with two years' worth of dust on them; remember to rinse yours off after getting home) about the most natural thing is to differentiate it. Differentiating a function can be as satisfying an exercise in craftsmanship as building your own furniture or baking a complicated meal, and it involves fewer nails, butterfly joints, or chances to spill batter on the cats. While a function may complain during the process, it will appreciate the results, as the differentiation makes it stand out and improves its chances of finding a mate.

You start differentiating a function by finding what its value is for some number, which is called the point of differentiation. Then you pick some other point and find out what the function is there, so you know how different the function would have been if you went to this second point to start with. Some functions are wary, however, and if they suspect what you're up to will jump back to the first value they had, making it look like they didn't intend to change at all. Some will even have their parents call you repeatedly to swear they'd never think of changing without permission. You may have to change your number, ideally not to the one the function gives you.

The solution is to try a second point, which is the third one you've picked, that's even closer to the point of differentiation than the first point, which was the second. But the faster functions will have jumped back, so you need a third point, your fourth, closer to the first point than your first and second, which were the second and third points overall. And so you carry on, until you finally pick a point that was the same as your first point, and find that your function didn't change when you didn't change your point, at which point you take the ratio (which ratio? Answer in 250 non-expletive words or fewer) and there's your differential. Are there any questions?

Trivia: The bill bringing the United Kingdom to the Gregorian calendar was brought through Parliament by Philip Stanhope, the Earl of Chesterfield. Source: Mapping Time: The Calendar and Its History, E G Richards.

Currently Reading: Asimov's Science Fiction, September 2006. Something's made the covers crumple up right by the spine, though the pages are standing firm.