by Robert Waltz
Not for the faint of art.
A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.
The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.
Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.
Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.
PROMPT May 13th
What does it mean to be a “grown up”? What do you do regularly as an adult that you dreaded having to do when you were a child? Have you found ways to maintain a sense of childhood wonder or curiosity? If so, how?
People think that I must be a very strange person. This is not correct. I have the heart of a small boy. It is in a glass jar on my desk.
What does it mean to be a “grown up”?
Having to pay taxes.
I mean, really, there's probably more, but it all has to do with other boring shit like "taking responsibility" and "being considerate of others."
What do you do regularly as an adult that you dreaded having to do when you were a child?
Pay taxes. And take pills. Sometimes I even clean my room without being threatened or bribed.
Have you found ways to maintain a sense of childhood wonder or curiosity?
Have you read my blog?
If so, how?
The defining feature of childhood, for me, was going from knowing basically nothing to knowing a few things. Some of those things turned out to be wrong, so I learned new things. Some of those will probably turn out to be wrong, too, so I keep an open mind and look for new evidence, whether it supports or contradicts what I already think I know.
Certainly, the things I learn about now are different, but it's all in the same vein. One of my earliest memories was my dad wrapping me up in a blanket and taking me out of the warm house on a cold, clear winter's night. The atmosphere is denser when it's cold, you know, with less haze, so you can see so many stars if you have the eyesight of a child. I have never stopped being fascinated by astronomy.
See, although the stars in the sky seem limitless, when it comes to viewing with "the naked eye" (a source of great amusement to Kid Me), we can "only" see about 5,000 points of light. "And," that linked article points out, "because the Earth itself gets in the way, you can only see about a half of those from where you stand."
2,500 is, of course, a tiny, tiny fraction of the total number of stars in the universe. Not even a rounding error. Going back to the article I just linked, there are probably about one septillion stars in the observable universe, the vast majority of them residing in other galaxies. That number is just mind-bendingly huge, way too big for our simple minds to comprehend, let alone be able to catalog them all.
And so it is, to delve into analogy, with knowledge itself. We know some stuff. The amount left to learn is huge. I object to a term I've seen bandied about, "near-infinite." There's no such thing as near-infinite. But there are things that might as well be infinite, for all that we will ever be able to list them all.
So that's how I stay curious, and how I maintain my sense of wonder: by periodically reminding myself that neither I personally, nor humanity in general, have done more than just put a tiny scratch into the surface of possible knowledge, and that there's always going to be more to learn because the other immutable law of the universe -- besides taxes -- is that it's going to keep changing, even as we study it.
Part of me regrets that I won't be around to watch us learn more of it. But another part rejoices, knowing that there will always be another star for someone to gaze at in wonder.
Well. Until entropy stops and the universe itself dies. But that's a really long ways away.