Wednesday, October 03, 2007


As per today's discussion, what do you guys consider to be beautiful?

How do you justify it?

Has it ever impeded/aided you in acquiring knowledge?

How does in interact with knowledge issues?


Dani said...

To answer my own question...(kinda lame but I was excited about it)

1) I consider a lot to be beautiful, but most recently (yesterday, 8th hour), I was sitting through AP stats, messing around with the Fibonacci sequence (all the stuff were doing in class was done in math studies last year). I didn’t see how the sequence was relevant or significant still I started try horizontal addition (13= 1+3= 4) and it starts a whole other Fibonacci sequence.

13→ 4
21→ 3
34→ 7
55→ 10 → 1 (1+0=1)
89→ 17 → 8
144 → 9
233 → 17 → 8
377 → 8
610 → 7 (because 8+8 (above) =16, and 1+6=7)

Finally, if you just keep reducing it to one digit there’s a pattern that repeats over and over (or at least as far as I got, but so far the theory holds up):

2) Even though I don’t know if this holds true throughout the infinite numbers, I find it beautiful because despite the increasingly, seemingly random numbers, they all work to start another pattern. The fact that this pattern repeats itself, through seeming chaos, I see it as beautiful because it’s perfect. The symmetry out of randomness is like doing a derivative from the definition, it’s perfect, logical, and therefore beautiful.
This is totally an emotional association, and purely because of how I am personally (weird thing is, I usually hate math. But this is more of a pattern than hard math I guess). I think I find it similar to a perfectly symmetrical flower, or leaf or other form of nature that seems to be inherently perfect.
I know that this isn’t really much justification, but I’m not exactly sure why I find what I do to be beautiful.

3) I believe it can do both, logically, there’s motivation to find it if you have faith in that the result will be beautiful. However, this also leads to bias because you could be making connections and "finding" something that doesn’t really exist merely because that’s what you want to find.

4) I think that the primary issue it presents is bias as everyone's view of what is beautiful is different. Also, like we discussed earlier, maybe people look harder for beauty and therefore find what they want to see, even if it's flawed.

* Finally, if this isn’t true, and doesn’t work out, please, please, please don’t tell me. Let me live in my ignorance (at least its pretty)

Dani said...

I'm sorry that the arrows are messed up! I hope you can still understand it...

katrina337 said...

I consider everything to be beautiful. I've really never considered anything to be ugly. Some things are more appealing than others, of course, but I've never really considered something not beautiful...
Justification? I suppose sense perception and self-awareness.
Impeding/aiding acquiring knowledge...I'm not sure. I'm not sure if it's ever effected it.
Same with knowledge issues, I have no clue.

I can understand what the arrows are supposed to do, I think that's interesting.

SamanthaJo said...

I can definitely relate to that math pattern being beautiful.. At first when I started reading that you thought something about math was beautiful, I had to do a double-take. Most people consider beautiful things to be in the sense that you discussed later, about nature and flowers. But math? I understand exactly what you're saying about the pattern just being beautiful.. it's perfect, makes sense, and just gives the person doing the math a sense of accomplishment.

What I consider beautiful as well are people. The whole idea that everyone is unique. If you just take the time to look at the people around you, you will find that all of them are beautiful in some way. Whether it's in their appearance, mind, or heart. I truly believe that everyone has some amount of goodness in them as well, which also makes them beautiful. This may sound kind of naive, but from my experience I have justified to myself that this is true. When I see someone doing something nice for somebody else just because they want to, something as simple as holding the door open for somebody who has their arms full, I really appreciate the beauty of humanity.

This may have impeded my acquisition of knowledge because I am determined to find the goodness in people. I am more reluctant to believe someone, perhaps from history, is pure evil or their actions were purely selfish. This does not mean I believe everyone is all good all the time, in fact I do become angry when people are downright mean. I observe it and I disapprove of it. I'm also not saying that I am always a saint and perfectly kind to everyone, but I do try my best.

Anyway, to wrap-up this long ramble, I believe people are beautiful. I also believe considerate actions by a person can say a lot about who they are and what is important to them. To me, goodness will always be an important quality I look for in others.

Dani said...

I totally agree, people are beautiful.
Has anyone (please say yes otherwise I'm gonna feel really weird) just sat and watched a group of people interact? Or have you ever had a really good group to work with in class? Where everyone just works flawlessly together? Thats beautiful.
I think the reason I find math beautiful is because of the symmetry and how everything fits. Like a puzzle, or even a zipper. something that functions perfectly is beautiful.

Sierra Tamkun said...

Since everyone talked about symetry being beautiful, how patterns are beautiful, I think I'll produce a counter-claim (yah for the essay) and write about beauty in things that are not the conventional. In class, we discussed how we see people as beautiful because of symetry, good proportions and such. Don't call me crazy, but I prefer people who are not well proportioned. I like the imperfections. I mean, sure, I love perfectability, don't get me wrong, but I like seeing that people are perfect, that something doesn't make sense, it just is. I love it when people make mistakes, and realize what they've done, and then have to fix it. I think that that, the process of fixing things, is beautiful. I think that when things don't work out, but people deal with anyway, in a manner that doesn't hurt or hinder anymore, that that is beautiful. When people have to work for something: that is beauty. And of course I agree with the flowers. But not open flowers. I think that brand new flowers, roses before they fully open, when they are still growing, that is beautiful. Trees without any leaves, though they appear dead, covered in snow, the white contrasted against the dark bark, wind blowing off the cold blankets in waves, forcing the crystals back to the ground again, that is beautiful.

katrina337 said...

Dani: Yes, to all of those questions.

Dani said...

fantastic point...but i think theres a way to find symmetry in almost everything. maybe not perfect mathematical symmetry, but a kind of symmetry or balance nonetheless.
also, without the imperfections, how would we know what symmetry was? Sort of like having to have sad days to know when the good ones are, or having to have bad teachers in order to know the good.

SamE said...

Dani - What happens when you divide the numbers of the Fibonacci sequence by 9? What remainders do they leave?

Dani said...

thats pretty cool, thanks

SamE said...

It's an example of what math people call "modulo 9", where we just look at the remainders when we divide by 9. As can be easily verified, you can do almost everything that you can with normal equations (add, subtract, multiply) with "equations" (they're really called congruences) modulo 9. Since the Fibonacci sequence is defined by addition, the sequence modulo 9 follows the same rules, as long as we subtract by 9 if we get a sum more than 9 (try this with your sequence!).

Since two consecutive numbers define the rest of the sequence, and there are only so 81 different pairs of numbers from 1 to 9, the sequence can only visit 81 different locations, defined by these pairs. Therefore, it will be bound to come back to the pair 1,1, which will begin a sequence that looks exactly like the entire sequence. In other words, this argument shows that your sequence will repeat (try it!).

Now, my question for the rest of you is, is something like this beautiful if you can explain it? Does Dostoevsky, the Northern Lights, the Fibonacci sequence, the Mona Lisa, or the conquest of Alexander the Great remain "beautiful" if it can be explained?

Dani said...

If anything, explanations can make things even more beautiful, especially when it expands on the perfection, or symmetry of something further.

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