TWSB: Back on the Chain Gang
This week’s science-related blog has to do with CALCULUS because calculus is awesome and because we actually just got tested on using the Chain Rule on Wednesday. The Physicist over at AskAMathematician.com responded to this question awhile back: “Is there an intuitive proof for the chain rule?” Which, when you think about it, is a really interesting question. We’re taught in calculus that when we’ve got a function “embedded” within another function [e.g., f(g(x))], when we take the derivative of that function, we take the derivative of the “outside function” f’(x) and then multiply it by the derivative of the “inside function” g’(x) to get f’(g(x))g’(x).
But why the heck do we need to do that?
As the Physicist very elegantly points out, it all has to do with slope. When you multiply a function by some amount, you squish it up by that same amount. Using their same example, say you’ve got a function f(x) and it’s “squished” function f(2x). These two functions are the same when x=6 and x=3 respectively, but that’s not the case for their slopes. The squished function 2x will have a steeper one by two. When you take the derivative of this function, then, you have to re-multiply it by two to deal with the squishing.
So how does this work out in general? If you replace the 2x with a more complicated function g(x), you get f(g(x)), and the slope of the whole thing depends, then, on g(x). So when finding the slope (taking the derivative) of f(g(x)), you have to re-multiply it by the slope of g(x) (or the derivative of g(x)) to deal with whatever g(x) is doing to the whole of f(g(x)).
And there’s your chain rule!
Take a look at the actual article. They’ve got pictures and actually have the derivatives and functions written out like I can’t do here.
VERY FREAKING COOL, PEOPLE.
Pardon me while I go throw up for a bit
Holy freaking crap, have any of you been in the bathrooms in the Mines building? I opened the door to the third floor women’s bathroom by the College of Science office and I almost had a seizure.
I felt like I was in one of those glass-floored checkered rooms that they put babies in to test and see if they’ve got depth perception yet.
It’s like PULLING THE TEETH OF MY MIND
CRAP GUYS, I have a long essay due in Non-Fiction class next Friday and I have no idea what the hell to write about. I originally wanted to write about my lack of olfaction since I’ve never really written about that before in any sort of formal context, but my teacher and I thought that would be better for the second long essay because I kind of want to take a literary journalism-type approach to it.
So now I’m currently at a loss for the first essay.
I’d actually like to write about Vancouver (or at least my walking around Vancouver) but I’ve repressed all that crap and I think that if I try to bring it to the forefront of my mind would cause physical pain.
But right now it might have to happen, ‘cause I’ve got no other ideas.
Haha, and you think I would, too, considering all the random crap I’ve been through the past year or so.
This week is INSANITY.
MY MOM IS HERE YAY.
Also, why don’t they make this stuff for adults? I can’t be the only one whose ostentatious style leaves room for such BADASS SHOES.
I think I’m a witch, guys
Remember that whole creepy-beating-the-odds thing with the 13-digit number last week? Well today my TA returned a stack of homeworks to me so I brought them to my office and started in on alphabetizing them. This involved splitting the big pile into two smaller ones. So I attempt to do that, but it turns out that the unsorted pile was actually naturally divided into two sections: the first containing last names starting with A – L, the other containing last names starting with M – Z.
Which is creepy on its own.
So I go through the A – L pile and alphabetize, then I go on to the M – Z pile. Well, guess what?
IT WAS ALREADY ALPHABETIZED.
Please keep I mind that my TA does not attempt to alphabetize the homeworks as he grades and has told me that he usually grades them in the order they are in the original pile I hand him.
So yeah.
Creepy stuff, man.
Redefining
So I can’t REALLY complain about Vaio II losing his life. I mean, the dude lasted through the damp, dark hellhole that was Van Land for two years, plus being carted around North America a whole bunch of times.
Also, I saved about 98% of the stuff I had on him because his hard drive was too small for all my crap and I’d moved everything to an external a few months ago. So my stories, my pics, my music, my internet nonsense [AND MY BLOGS]…all saved.
So I really can’t complain.
But I’m going to anyway, because one of the things I DID lose was my playcounts for my songs. Which is a big deal for me, because I very often sort my songs by playcount and pretty much had a whole hierarchy going on where I defined my “top 50” songs by playcount.
Well, that’s all gone now, so next comes the arduous task of redefining my favorite songs.
That’s hard for me.
But exciting, too. I think with the nearly three years of downloading a new song every day, my musical tastes have evolved a bit. So things that were on my “favorites” playlist from before that may just have been on there due to past playcounts—even though I haven’t played them in months—have all been removed. Time to start anew!
Haha, I know none of you care, but this is pretty much the most exciting non-school-related thing to happen since September.
Happy birthday.
Eigenblogger 