Complex Numbers (Book)

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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.

http://www.ddewey.net/mandelbrot/

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December 22, 2022 at 12:02am

#1042019

It's Trying to Kill You

It's widely known that everything in Australia is trying to kill you.

Mapping the Many Monsters of Aboriginal Australian Lore
A “terrifying pantheon” of ogres, sorcerers, and malevolent mermaids reflects a diversity in geography and environment.

This includes, apparently, the cryptids.

The rumors about the deadliness of Australian flora and fauna are mostly exaggerated to keep people from the US from going to Oz and polluting their landscape with their presence.

But these monsters of folklore are seriously messed up.

In the Australian Central and Western Deserts there are roaming ogres, bogeymen (and bogeywomen), cannibal babies, giant baby-guzzlers, sorcerers, spinifex, and feather-slippered spirit beings able to dispatch victims with a single fatal garrote. There are lustful old men who, wishing to satiate their unbridled sexual appetites, relentlessly pursue beautiful, nubile young girls through the night sky and on land, and other monstrous beings, too.

I had to Google "spinifex." I'm not any more enlightened than I was before I Googled it.

Arnhem Land, in Australia’s north, is the abode of malevolent shades and vampire-like wind and shooting star spirit beings. There are also murderous, humanoid fish-maidens who live in deep waterholes and rockholes, biding their time to rise up, then grab and drown unsuspecting human children or adults who stray close to the water’s edge. Certain sorcerers gleefully dismember their victims limb by limb, and there are other monstrous entities as well, living parallel lives to the human beings residing in the same places.

All of these things make the D&D Monster Manual seem like a collection of friendly stuffed animals.

The trope of metamorphosis is evident in the real-life stories and media representations in Australia’s dominant culture: Consider the image of the kindly old gentleman next door or the devoted, caring parish priest who shocks everyone by metamorphosing into a child-molester, creepy, predatory, though ever-charming.

Okay, that last bit definitely comes from reality.

All cultures, it seems, have fairytales and narratives that express a high degree of aggression towards young children. There are many reasons for this, but ultimately it reflects the special vulnerability of the very young with respect to adults and the exterior world.

Probably the best reason is to keep the little brats from misbehaving too much.

All of these figures materialize fear, bringing it to the surface. At the psychological level, the stories about these entities are a means of coping with terror. To this I would add that such monstrous beings also attest to some of the least palatable aspects of human behavior, to the nastiest and most vicious of our human capabilities.

As scary as mythological beasts are, they've got nothing on the worst a human can do.

Importantly, in Aboriginal Australia, these figures and their attendant narratives provide a valuable source of knowledge about the hazards of specific places and environments. Most important of all is their social function in terms of engendering fear and caution in young children, commensurate with the very real environmental perils that they inevitably encounter.

Because even if the reports of the deadliness of Australian wildlife are, indeed, exaggerated, that doesn't mean that some things aren't out to kill you.

The anthropologist Ute Eickelkamp has written persuasively about mamu from a largely psychoanalytic perspective, but also argues in a 2004 article that Western and Central Desert “adults commonly use the threat of demonic attacks [by mamu] to control the behavior of children.”

Just in case you were thinking that I was joking up there.

There was no doubt in my mind that such narratives are first and foremost about social control with respect to the specific dangers of the desert where, in the summer months, people can die horribly tormented deaths from thirst within a matter of hours.

Getting lost in the desert is a very abstract way to perish. Makes sense that we'd construct supernatural beings to give it a more personal terror.

The article goes into (sometimes quite gory) detail about several of these monsters, and I found it a fascinating read. But as you know, the whole of cryptid folklore, from ancient to modern, interests me, because it says a lot about who we are, what we fear, and how we deal with what we fear. So of course I had to share.

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