Complex Numbers (Book)

Blog Calendar

◄ February ► 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
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

February 17, 2022 at 7:37am

#1026872

Over the Rainbow

Last day of being away from home... until next week.

Even Rainbows Have a Dark Side
Humans were once united by the belief that you should never, ever point at one.

I find that extremely difficult to believe. Not because it's a silly superstition, but the idea that "humans were once united by" anything.

Both had learned as children that if you broke the taboo, your finger would become bent like a rainbow.

Right, and if you keep making faces, your face will freeze like that; if you crack your knuckles you'll get arthritis (to be fair, you might, but not from cracking); and if you watch too much porn, you'll go blind.

*looks at medical bill for cataract surgery*

...okay, so that last one might be true.

The first hint that he was on to something bigger, something truly boggling, came from a report of a prohibition on pointing to rainbows in India. “It did not take long for the shock to set in,” he wrote. The report suggested “the rainbow taboo”—as he would come to call the phenomenon—was not confined to Southeast Asia.

Oh, it's in Southeast Asia and India? Wow, it must be all over the world.

He would soon amass evidence for the rainbow taboo—in some form or another—in 124 cultures. The prohibition turned up in North America, among the Atsugewi of northern California and the Lakota of the northern plains; in remote parts of Australia and isolated islands in Melanesia; among the Nyabwa of Ivory Coast and the Kaiwá of Brazil.

Okay, okay, jeez, I get the point. You make one joke...

The belief was not found in every culture, according to Blust’s search, but it was present globally, across all inhabited regions.

See? I told you we weren't united.

Less commonly—such as in parts of New Guinea and Australia—the ill effects would befall your mother.

When I was a kid and my mother made me do something I didn't like, or scolded me for doing something I did like, I'd deliberately stomp on the cracks in the sidewalk.

I was an asshole kid.

This, by the way, took significant effort and patience on my part, because where I spent my childhood there were no sidewalks for miles, so I had to wait until someone let me ride with them into town. If it was my mom, I'd leap onto a crack, look back at her, jump to another one, look back, stomp, look... getting more and more disappointed each time (never mind that if I'd been successful, no one would have been able to drive me back home).

As her back never broke, I lost all faith in kid lore. But later, when I learned about how concrete (such as that in sidewalks) works, I discovered that as concrete cures, it develops microfractures throughout its matrix. You can't see them (hence, "micro") but if you're walking on a sidewalk you cannot avoid stepping on dozens of cracks with each and every pace.

The relative lack of mother's back breakage in the world should be enough to put people off such taboos, but apparently not.

A final recurring idea was that, should you accidentally point to a rainbow, there were remedies. You could wet the offending digit; or put it into a bodily cavity like your mouth, anus, or belly button; or, according to the Javanese version of the taboo, plunge it into a pile of buffalo dung.

Or any of the above, in random order?

Anyway. No, the article isn't about fact-checking the taboo; it's about the very interesting widespread nature of the belief and speculation about the reasons for it. And while even that didn't unite humanity as one shining, glorious people singing under the rainbow, it's a fascinating glimpse into peoples' beliefs.

5 Like • Comment • View 5 comments

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