ZOMG
HOLY CRAP.
MIND HAS BEEN BLOWN.
PERSPECTIVE HAS BEEN CHANGED.
PANTS ARE OFF.
THAT LAST STATEMENT IS IRRELEVANT.
You guys probably all already knew this ‘cause you’re smarter than me, but I just learned that the inflection points of the normal distribution occur at the first standard deviation above and below the mean.
HOLY CRAP.
Inflection points, remember, are the points on a curve where the concavity changes (f’’(x) = 0).
I’m not quite sure why that’s a significant thing because I don’t think I’m quite at the math level I need to be to understand it, but I’m pretty sure that it’s a significant thing. Either way, VERY COOL.
I’mma go screw around with calculus now.
Freaking love calculus.
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.
Sweet Jesus, I love calculus
We talked about Leibniz in calculus today. My hands were shaking so badly I could barely write.
I am not ashamed.
Why are all the smart and sexy ones dead?
Apparently the derivative of a lip ring is a Monroe
Yeah. When you start finding the derivations of various facial piercings in your dreams, you know you’ve done way too much calculus the day before.
I’m totally serious, I start spacing off and then realize that I’m daydreaming about DERIVATIVES.
This is FREAKING AWESOME.
On a somewhat related note, I went to a symposium on dreams this morning. One of the presenters gave a really interesting talk in which he displayed art students’ artistic interpretations of their dreams while reading their dreams aloud to us. I thought it was pretty interesting how many of the dreamers presented exaggerated or inappropriate emotional responses in their dreams. I can only think of a few examples of my own dreams (the Boxy Boxy dream, the Maggie = Spearow dream, though I think “shock and awe” were fairly appropriate emotional responses there) where I, in my dream, acted with exaggerated or simply the incorrect emotions.
Also, according to another guy it’s pretty rare for people to dream of numbers/calculations. Those are also fairly common in my dreams, but usually to a lesser extent than they are when I’m doing crap loads of calc problems per day, and usually happen right before I wake up.
Today’s song: Angel by Sarah McLachlan
Calculus can solve many problems, BUT CAN IT FIND YOUR GOD?!
There are few things weirder than math, I think. It’s systematic, but it’s also really creepy.
Take calculus. Given some curve y = f(x) for some equation x, you’re able to find the slope of the tangent line to that curve at any given point just by finding the derivative f’(x). How do you find the derivative? There are like five main rules you need to know to be able to find it for any equation x (ignoring e and all that crazy natural log stuff for now).
I know I’ve blogged about this before, but does anyone else find that incredibly…convenient? The fact that many mathematical problems can be reduced, in some form or another, to addition, multiplication, subtraction, and division is kind of frightening.
And the fact that nearly all problems we’ve come across have some sort of mathematical explanation to them—and not only a mathematical explanation, but a mathematical explanation that works with the way we’ve defined mathematics on this little planet hurtling through space, this infinitesimally small rock in the whole expanse of the universe? Insanity!
It freaks me out that we’re able to explain things like space phenomena using our math. I’m probably just a simpleton, but it freaks me out. How has (nearly) everything we’ve found conformed to our little system of manipulating numbers? How is it that the formulae and procedures we’ve developed coincide so nicely with the workings of what we’ve seen of the universe? I really don’t know what to think of it anymore. As I’ve said, I think if there were any plausible explanation for a god, it would lie in math.
But what do I know?
Today’s song: Luna by Evgenij Anegin
I am deriving so much pleasure from calculus that I may need to integrate it into my daily life
HOT DAMN I love calculus.
And no, it’s not just because the great and glorious Leibniz invented it, either. It’s very methodical and I actually know what the hell I’m doing (for most of it). I think I hated it so much the first time around because it was at 8:30 in the freaking morning AND because it was all business-oriented. And because I didn’t really care back then. I dig the tediousness of it all—it’s less tedious than eigenvalues (thank god) but still fun. It feels weird to be doing a metric crap ton of math homework again.
Oh, and THERE’S A FREAKING ICE CREAM TRUCK OVER HERE, TOO! Totally not an imaginary one, either…I saw it go down 43rd street blasting out a lullaby.
I’m not insane. Bad ass.
Today’s song: Glycerine by Bush
She Deafened Me with Pseudoscience!
I’m starting to loathe Saturday nights. And I was actually going to post yesterday’s blog, you know, yesterday, but MySpace was being dumb.
Either way, our little “group” went to Kharah’s last night and played a bunch of games (and made a lot of stupid jokes) and shared a bunch of cheese. Welcome to grad school.
Haha, and Michael and I got into an argument over who invented calculus, it was pretty freaking awesome. How come the only cute, pudgy blonde guy I’ve met up here is a proponent of Newton?
Guess you can’t win them all.
And I think I found my Script Frenzy plot.
AND I finished the drawing of Matt. Matt, do you mind if I post it to my DeviantArt page? That way you can actually see it, haha. I can leave your name off of it if you’d prefer.
AND AND this.
Today’s song: You Belong by Northern Kind
I HAVE THE URGE…
THE URGE TO UNDERSTAND MATH!
I don’t know what it is about this subject. It terrifies the hell out of me (especially when I have to take a class in it), but yet when I don’t understand something about it I have this incredible urge to take as many math classes as my soul will allow me in order to actually “get it.”
Right now I want to take calculus again. Lots of it. Mainly because I forgot all that I learned due to losing my notes and the class being at 8:30 in the morning (whose brilliant idea was that, anyway?).
Sigh.
I guess I’m realizing that now that I’ve started grad school, I’m one major step closer to pigeon-holing my education. It’s not undergrad anymore, where nobody gave a crap what I took. I actually have to “stay on task.” Which is surprisingly difficult for me.
Whatever.
Alliteration’s Almost Always Appropriate
I’m sorry, but I must address this issue, as I had a dream about it mere hours ago (it’s like 10 AM) and if it’s infiltrated my dreams, it must be important to me.
So as I’ve stated, I’m reading The Calculus Wars. In the blog about said book, I briefly mentioned the fact that the book used the word “invented” to describe how calculus came about. As I read on, though, the author appears to switch randomly between the words “invented” and “discovered.”
As confused as I was at the beginning over this, I’m more confused now, mainly because I’m not sure which word should really be used. Really, what sounds more accurate?
If we say that Newton and Leibniz discovered calculus, that basically means that there is some sort of preexisting system of mathematics that humans are in the process of unlocking.
But if we say that they invented calculus, then it just seems kind of strange that they were able to just invent something with such mathematical power to explain all the things it explains.
But then again, I find it rather suspicious that human beings have developed these systems called “numbers” and “math” and they somehow magically explain the workings of the universe (velocity, the speed of light, rate of acceleration, etc.). I mean, don’t you find it the least bit suspicious that we can explain these things using simple formulas? It makes sense that the universe is ordered in some fashion, I just find it kind of odd that we’ve managed to gain possession of something that seems to be able to explain the patterns. It seems too easy, you know what I’m saying?
What if it’s all arbitrary?
(See, this is why I want to take freaking Metaphysics)
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