Complex Numbers (Book)

Blog Calendar

◄ December ► 2022
S	M	T	W	T	F	S
				1	2	3
4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 2 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 4 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

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.

8 Like • Comment • View 5 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.