Thursday, April 9, 2015

Root Differences

When I was in high school, I noticed a curious pattern: one plus three equals four, plus five equals nine, plus seven equals sixteen, and so on. Each whole square was a certain number greater than the next, and the difference between the squares would increase by two every time. When I mentioned this to a math teacher, she either did not see it that way or misunderstood my phrasing, for she dismissed it as simple coincidence, not a natural law. After class, however, I was not convinced. Stubbornness is both a vice and a virtue of mine, and I continued to puzzle over how a series of odd numbers, increasing by two each time, connected to the succession of perfect squares.
Eventually, I drew the pattern out on scrap paper and saw something interesting: each square on a grid increases by the addition of new units to a side; being two-dimensional, they increase by two new units each time--one for each dimension.
We came up with an equation that represented the pattern. Since we want to look at the difference between squares (how much you add to get the next whole square), we added 1 to r, which stands for the square root. There’s the 2 pattern!

(r+1)2 = r2+2r+1

But I was still not fully satisfied. Something felt missing. I reasoned that if one could calculate differences between squares, surely a similar pattern might hold true in three dimensions--that is, whole cubes. The formula would be more difficult to visualize, but fortunately, my friend Ray owned a bowl of small cubes which we used to crack this puzzle. Three new squares would need to be added with each successive layer, and by holding cubes together, we discovered that the edges between sides would also need to be accounted for.
[insert “cube edges” visual]
We determined that the formula is:

(r+1)3 = r3+3r2+2r+1

Applied fascination, when shared with other curious thinkers, spurs the creation of wonders.

Thursday, April 2, 2015

Why We Love Dragons

Among various fantasy-geek communities, dragons seem a prevalent source of admiration.
Of course, dragons are awesome.

But why? What has kept them from turning out as, say, vampires did?

I cannot speak for everyone, but I feel that they possess a combination of remarkable traits:

  • They often embody elements (usually fire), and the four Classical elements continue to play a role in both fantasy and reality. Some dragons also spit venom or work magic.
  • They combine several animalistic features that fascinate humans: flight, scales, horns, a spaded tail, barbels, feathers, fur... (Not all dragons possess all of these aspects, obviously. I am aware of wyverns, drakes, wyrms, knuckers, etc.)
  • They are at once distant and nearly human. Whether they have humanlike greed and malevolence (like Smaug) or empathize with human emotions (like Saphira), I find that anything so physically different from us that still thinks like us is something our minds find intriguing.
  • They represent flight--literally as well as of the human imagination. Discounting planes and the like, humans cannot fly, and we love to imagine the "what if...?" scenarios of being able to do so.
I'm sure I missed several things, and some fascinations are simply difficult to justify, but these are my two cents at the moment.

Of course, dragons are hugely diverse in literature, cinema, and folklore, as I mentioned, but they will likely always hold a special place in my heart. Perhaps a plug of Oberon Zell-Ravenheart and Ash "LeopardDancer" DeKirk's book, Dragonlore, is in order here. It contains a wealth of information about mythological dragons, from Pa snakes to the Stoorworm to Chinese Lung dragons to the Tarasque, and beyond.

May the stars watch over all of you!

Major Waffling

Ever since my later high school days, I've been indecisive about my career path. Ideally, I'd major in English and minor in Creative Writing. However, I also feel that I ought to take advantage of the presented opportunities to learn new things and secure a career.
I feel that a job in STEM would enable me to further forge paths of research (not to mention pay off loans more quickly), but I feel that the liberal-arts half of my brain would lend me a more rounded education. And besides, don't the sciences require just as much creativity as the arts? Without radical, outside-the-box thinkers, we'd have neither Apple nor Microsoft. Conversely, many successful science-fiction writers had a firm grip on real science. Combining vastly different elements in unique ways is no guarantee of success, but it certainly doesn't seem to harm one's chances or mindset.
I currently intend to double-major in English Literature and Computer Science, with possible minors in any combination of two or three of the following: Classics, Physics, Mathematics, Art, or a foreign language. Eventually, I'd like to write full-time, but I wouldn't mind a job in the software business while my written endeavors take off. I could even blog about technology in addition to writing fiction and screenplays (and occasionally, poetry).
We need to stop pigeonholing careers and educational paths. Often, a fresh perspective is just what the world needs.