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Complex Numbers
Complex Numbers
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.
October 2, 2022 at 12:02am October 2, 2022 at 12:02am
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Today's article is from over five years ago, but it should still be relevant.
Why is it relevant? Well, maybe you want to sell something. Maybe that something is a story, to a publisher or to the general public as a self-publisher.
Or maybe, like me, you just want to know what tricks they're using so you can protect yourself.
Sadly, the "four-letter code" turns out not to be one starting with F.
Several decades before he became the father of industrial design, Raymond Loewy boarded the SS France in 1919 to sail across the Atlantic from his devastated continent to the United States. The influenza pandemic had taken his mother and father, and his service in the French army was over. At the age of 25, Loewy was looking to start fresh in New York, perhaps, he thought, as an electrical engineer. When he reached Manhattan, his older brother Maximilian picked him up in a taxi. They drove straight to 120 Broadway, one of New York City’s largest neoclassical skyscrapers, with two connected towers that ascended from a shared base like a giant tuning fork. Loewy rode the elevator to the observatory platform, 40 stories up, and looked out across the island.
Appropriately, the lede comes from the New Yorker School Of Not Getting To The Fucking Point.
That building still exists, by the way. It is, itself, a pretty amazing design; it's no wonder that it apparently influenced a designer.
In France, he had imagined an elegant, stylish place, filled with slender and simple shapes. The city that now unfurled beneath him, however, was a grungy product of the machine age—“bulky, noisy, and complicated. It was a disappointment.”
That's okay. We Americans feel something similar when we first visit Paris.
The world below would soon match his dreamy vision. Loewy would do more than almost any person in the 20th century to shape the aesthetic of American culture. His firm designed mid-century icons like the Exxon logo, the Lucky Strike pack, and the Greyhound bus.
Great. Two industries that deliberately contributed to our impending doom, and a bus.
To sell more stuff, American industrialists needed to work hand in hand with artists to make new products beautiful—even “cool.”
It is true that one of the only practical uses for art (for certain values of "practical") is in marketing.
Loewy had an uncanny sense of how to make things fashionable. He believed that consumers are torn between two opposing forces: neophilia, a curiosity about new things; and neophobia, a fear of anything too new. As a result, they gravitate to products that are bold, but instantly comprehensible.
I once got into an argument with a published author at a convention. She claimed that people wanted new things. I countered with evidence that they just want old things, repackaged—this was at the height of the "vampire" craze in the noughties, and everyone was talking about Twilight. I also noted that Harry Potter wasn't anything new; it just merged the classic British "boarding school" genre with high fantasy.
I lost the argument on the basis of, well, she was published and I'm not, but I still don't think I was wrong. And we may have actually been saying the same thing: what Loewy's saying here, that stories need a touch of the familiar and a touch of the novel (pun intended, as usual). So yeah, this was the bit that made me want to link this here, because it's just as relevant to selling a story as it is to selling a pack of chewing gum.
Loewy called his grand theory “Most Advanced Yet Acceptable”—MAYA. He said to sell something surprising, make it familiar; and to sell something familiar, make it surprising.
Sounds easier said than done, but it does ring true for me. And I'm just glad it's not a stupid acronym like ABC - Always Be Closing.
Why do people like what they like? It is one of the oldest questions of philosophy and aesthetics. Ancient thinkers inclined to mysticism proposed that a “golden ratio”—about 1.62 to 1, as in, for instance, the dimensions of a rectangle—could explain the visual perfection of objects like sunflowers and Greek temples.
There's still discussion about the Golden Ratio, but as far as I can tell, it may not be "the most beautiful," but it certainly doesn't suck. And it's nice to know the GR, anyway. If only to remember that it's a quick and easy approximate conversion from km to miles and vice versa.
Other thinkers were deeply skeptical: David Hume, the 18th-century philosopher, considered the search for formulas to be absurd, because the perception of beauty was purely subjective, residing in individuals, not in the fabric of the universe. “To seek the real beauty, or real deformity,” he said, “is as fruitless an enquiry, as to pretend to ascertain the real sweet or real bitter.”
Hume obviously lived before there was really good beer.
In the 1960s, the psychologist Robert Zajonc conducted a series of experiments where he showed subjects nonsense words, random shapes, and Chinese-like characters and asked them which they preferred. In study after study, people reliably gravitated toward the words and shapes they’d seen the most. Their preference was for familiarity.
I'm sure that, as with most studies of that sort, they completely ignored the minority preference for novelty.
The evolutionary explanation for the mere-exposure effect would be simple: If you recognized an animal or plant, that meant it hadn’t killed you, at least not yet.
Sigh. At the risk of repeating myself to exhaustion, evo-psych explanations are speculative at best.
But the preference for familiarity has clear limits. People get tired of even their favorite songs and movies. They develop deep skepticism about overfamiliar buzzwords. In mere-exposure studies, the preference for familiar stimuli is attenuated or negated entirely when the participants realize they’re being repeatedly exposed to the same thing. For that reason, the power of familiarity seems to be strongest when a person isn’t expecting it.
This, however, also makes sense.
Several years ago, Paul Hekkert, a professor of industrial design and psychology at Delft University of Technology, in the Netherlands, received a grant to develop a theory of aesthetics and taste. On the one hand, Hekkert told me, humans seek familiarity, because it makes them feel safe. On the other hand, people are charged by the thrill of a challenge, powered by a pioneer lust.
Meh. Challenges are exhausting. That's why I prefer being in a relationship to pursuing one.
Raymond Loewy’s aesthetic was proudly populist. “One should design for the advantage of the largest mass of people,” he said.
And once again, that leaves out outliers like me.
Let me give you an example. I used to buy Oreos fairly often. Don't judge. But then Nabisco started putting out different flavor Oreos. Some of them were obvious trolls, like Candy Corn Oreos (abomination) and Swedish Fish Oreos (crime against nature). But they also made a Dark Chocolate Oreos. Those were delicious. So delicious, in fact, that when they pulled them because they weren't popular enough, I quit buying any kind of Oreos. So instead of reaching a wider audience, they lost one: me.
Could Loewy’s MAYA theory double as cultural criticism? A common complaint about modern pop culture is that it has devolved into an orgy of familiarity.
Sure, people complain about that. But then when a truly new movie (for example) comes out, no one goes to see it. So there's no incentive to try new stuff there.
The hit-making formula in Hollywood today seems to be built on infinitely recurring, self-sustaining loops of familiarity, like the Marvel comic universe, which thrives by interweaving movie franchises and TV spin-offs.
You shut your whore mouth. Those are (mostly) awesome.
One of Loewy’s final assignments as an industrial designer was to add an element of familiarity to a truly novel invention: NASA’s first space station.
Can't get more novel than the first space station, I suppose. But this led me to wonder who designed the iconic NASA logo.
Huh. It was an artist working for NASA. 
See? There's hope for that liberal arts degree yet. |
© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
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