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.
|Sometimes, I just like to have fun with these things.
Our Brains Tell Stories So We Can Live
Without inner narratives we would be lost in a chaotic world.
And sometimes those inner narratives lead to nutjob whackaloon conspiracy "theories."
We are all storytellers; we make sense out of the world by telling stories.
Occasionally, that story is "Aliens did it."
And science is a great source of stories. Not so, you might argue. Science is an objective collection and interpretation of data. I completely agree. At the level of the study of purely physical phenomena, science is the only reliable method for establishing the facts of the world.
Facts which can then be twisted into science fiction. Hey, I'm not knocking science or science fiction, but it's important to keep the two separate in one's head.
There are no naked facts that completely explain why animals sacrifice themselves for the good of their kin, why we fall in love, the meaning and purpose of existence, or why we kill each other.
Not "completely," but we have pretty good ideas about some of these. That last one, for example. It's because you're playing what you think is "music" too loudly.
For all of the sophisticated methodologies in science, we have not moved beyond the story as the primary way that we make sense of our lives.
To get serious for a moment, I happen to agree with this. But then, I fancy myself a writer.
Let’s begin with an utterly simple example of a story, offered by E. M. Forster in his classic book on writing, Aspects of the Novel: “The king died and then the queen died.” It is nearly impossible to read this juxtaposition of events without wondering why the queen died.
It's because she said, "Let them eat cake."
Okay, look, Marie Antoinette probably never uttered those words (not even the French equivalent). Supporting this, there was a story written by Jean-Jacques Rousseau long before the French Revolution where he had a princess utter those words (except it was "brioche," not "cake," but whatever). Here. (That wiki page also has a very helpful photograph of a brioche, and now I'm hungry.)
That's a story we tell ourselves. Some stories are based on fact. That one appears to be the other kind.
Once a relationship has been suggested, we feel obliged to come up with an explanation. This makes us turn to what we know, to our storehouse of facts. It is general knowledge that a spouse can die of grief. Did the queen then die of heartbreak? This possibility draws on the science of human behavior, which competes with other, more traditional narratives. A high school student who has been studying Hamlet, for instance, might read the story as a microsynopsis of the play.
Nah, I'm sticking with the French Revolution. Vive la guillotine!
The pleasurable feeling that our explanation is the right one—ranging from a modest sense of familiarity to the powerful and sublime “a-ha!”—is meted out by the same reward system in the brain integral to drug, alcohol, and gambling addictions.
Which goes a long way toward explaining why so many writers have drug, alcohol, and/or gambling addictions.
The article goes on to discuss the science behind this. I couldn't think of any jokes about it, but it's a good read.
An efficient pattern recognition of a lion makes perfect evolutionary sense. If you see a large feline shape moving in some nearby brush, it is unwise to wait until you see the yellows of the lion’s eyes before starting to run up the nearest tree.
I'm too old to run up trees, and besides, who runs up a tree? I'd want to pet the kitty. It may be the last thing I ever do, but it'd be worth it.
Science is in the business of making up stories called hypotheses and testing them, then trying its best to make up better ones.
That's... actually a really good synopsis of science.
But there is also a problem. We can get our dopamine reward, and walk away with a story in hand, before science has finished testing it. This problem is exacerbated by the fact that the brain, hungry for its pattern-matching dopamine reward, overlooks contradictory or conflicting information whenever possible.
Hence why I'm always rambling on about confirmation bias in here. There are other biases and fallacies, of course, but that's the one I know I'm inclined toward.
Because we are compelled to make stories, we are often compelled to take incomplete stories and run with them. With a half-story from science in our minds, we earn a dopamine “reward” every time it helps us understand something in our world—even if that explanation is incomplete or wrong.
And now they've just explained 90% of the internet.
Good science is a combination of meticulously obtained and analyzed data, a restriction of the conclusions to those interpretations that are explicitly reflected in the data, and an honest and humble recognition of the limits of what this data can say about the world.
Nowhere is this illustrated better than in the insistence of certain authors to ascribe mystical properties to quantum phenomena.
The article has a lot more than I'm quoting here, and I think it's important to read. It shows, at least in part, why I'm sometimes in here ragging on science reporting, while still praising (most of) the science on which it reports.
And it helps me to remember that, believe it or not, I, too, am not always right.