beauty
October 2008 
blogging leads to mathematics, beware!
Posted on Sep 6th, 2007
by 
tinkonthebrink
tinkonthebrink
I don't know how Aley's blog entry about blogging as a daily ritual morphed into a discussion of mathematics, but in my mind that's how it went.
So anyway, I decided I'm way too self-involved in this response to post this as a comment (hi aley, thanks for being a provocateur!):
I grew up thinking maths wasn't my thing. Not that I was ever bad at it, just that I wasn't "that kind" of person.
But I always loved puzzles and games and once you get past the basics, thats all maths really is.
So I took calculus when I started high school and I did well, but still, really thought my skills were in other areas.
Took my SATs early because I wanted early admission to college (please, get me away from mom and dad as soon as possible).
I was absolutely stunned that my scores were within 10 points of each other, verbal and maths.
I honestly didn't believe I had missed anything on the verbal.
And I would have been happy to scrape by on maths. Really, I thought I was mostly guessing, and it was multiple choice after all.
So I took them again six months later. Exactly the same numbers, only reversed this time, verbal ten points higher.
This made me realize, first of all, that I had an enormous bias about creativity. And second, that my ideas about who I am aren't necessarily the same as who I am at all.
The quality I get enamored of in all forms of puzzle-solving is elegance - in the physics sense. Nothing extra, nothing left out. The most precise, perfect path to the destination, a destination you don't even know yet when you set out on the journey, and not necessarily a straight line at all. It's what drives maths and physics, but also obtains in poetry and visual art and storytelling and music...not the straight line, but the perfect line. The solution you don't see coming, the surprising resolution, and when the mathematics is a calculation of beauty and delight, a poem, a story, a photograph, a piece of music, the calculation of what's essential and what's superfluous is much more elusive.
But it's still there.
And it's there whether you think you're that kind of person or not.
So anyway, I decided I'm way too self-involved in this response to post this as a comment (hi aley, thanks for being a provocateur!):
I grew up thinking maths wasn't my thing. Not that I was ever bad at it, just that I wasn't "that kind" of person.
But I always loved puzzles and games and once you get past the basics, thats all maths really is.
So I took calculus when I started high school and I did well, but still, really thought my skills were in other areas.
Took my SATs early because I wanted early admission to college (please, get me away from mom and dad as soon as possible).
I was absolutely stunned that my scores were within 10 points of each other, verbal and maths.
I honestly didn't believe I had missed anything on the verbal.
And I would have been happy to scrape by on maths. Really, I thought I was mostly guessing, and it was multiple choice after all.
So I took them again six months later. Exactly the same numbers, only reversed this time, verbal ten points higher.
This made me realize, first of all, that I had an enormous bias about creativity. And second, that my ideas about who I am aren't necessarily the same as who I am at all.
The quality I get enamored of in all forms of puzzle-solving is elegance - in the physics sense. Nothing extra, nothing left out. The most precise, perfect path to the destination, a destination you don't even know yet when you set out on the journey, and not necessarily a straight line at all. It's what drives maths and physics, but also obtains in poetry and visual art and storytelling and music...not the straight line, but the perfect line. The solution you don't see coming, the surprising resolution, and when the mathematics is a calculation of beauty and delight, a poem, a story, a photograph, a piece of music, the calculation of what's essential and what's superfluous is much more elusive.
But it's still there.
And it's there whether you think you're that kind of person or not.
Access: Public
Elegantly put, Jeannie. And I didn't see your conclusion coming - just as you said. An Aha blog, for sure. (Like an Aha moment?)
Oh thank you!
I wish I could have found the beauty…for me it was the beeauty of a “C” to pass the damn thing that made me happy!
I am glad you had a different experience!
:)
Aley
. . .
. . .
. . .
Connect all 9 dots with four straight lines, without lifting the pencil.
Think outside the box.
Okay, try this, smarty pants. Here you have to think a little more mathematically.
.
.
.
.
. .
. .
. .
Draw three circles so that each dot is isolated from the others, i.e. no two dots are contained any intersection of the three circles
Good one, d. I saw that one not too long ago; a very interesting puzzle.
My love of mathematics, which led to a degree in it, came down to calculus, both differential and integral, particularly the theory of each. My interests are far less pragmatic and much more ethereal: the simple contemplation of the symbology covering a page would–and still does–stop me, putting me into an almost immediate meditative state. I'll lose myself in that page and resurface many minutes later.
I'm by no means a genius in the subject; I have to work very hard to understand anything, where it comes quite naturally to so many others. Too, I am bored by discussions of mathematics–they devolve almost inevitably into pissing contests virtually from the get-go–nor am I particularly jazzed by all the applications mathematics covers. But drop me headlong into something like this–
Assume that we have a 2π-periodic, piecewise continuous function f with Fourier series
f(x) ~ ∑n αneinx, where αn = (1/(2π))∫-ππ f(t)e-intdt.
The partial sum SN(x) is given by
SN(x) = ∑n=-NN αneinx = ∑n=-NN (1/(2π))∫-ππ f(t)einxe-intdt.
Because the “integral of the sum is the sum of the integrals,” we see that the partial sum SN is
SN(x) = ∫-ππ f(t)DN(x-t)dt,
where DN is called the Dirichlet kernel, and is defined by
DN(u) := (1/(2π))∑n=-NNeinu.
–a discussion of pointwise convergence of a Fourier series, and I'm off into another world for a while.
Speaking of which, the above looks really interesting …
See ya' all in a while.
:–)
Shawn (the ubernerd)
I was gonna just going to say two quarters and a dime.
Donny, you suck.
This woke me up at 4am.
Give me another night to dream through it and I'll figure it out.
Shawn, you really are an ubernerd. What you need is sidewalk chalk.
Andy, it's hard to spange online.
Alright Donny, I've got a bit of brain lodged in my skull and it's starting to hurt.
Praveer recommends marzipan. I tried gummi bears and got mixed results.
I ordered this do-it-yourself brain surgery DVD, but it turned out to be a bunch of crap about Jesus. Save your money.
Oh Donny, thank you for the tip, but I decided a long time ago that watching something, really anything, while doing brain surgery on myself was just too darn distracting.
Alright, Donny, I give. I've resisited looking up the solution on the interwebs, but I can't make it happen unless I reorganize the dots a bit. How does this work?
I'm just guessing here, Jeannie, but did you try doing brain surgery on someone else while you're working this out? Because I quite agree - doing brain surgery on yourself and working out the connect-the-dots-thingummy can lead to taxidermy.