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Complex Numbers

by Waltz Invictus

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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:

Annette

about 10 hours ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

June 12, 2024 at 11:01am

#1072557

Phrase Shift

I tend to be skeptical about the sort of thing featured in this article from Mental Floss, because there's a lot of fauxtymology out there, and I've called out a bunch of it in here before ("tip," for example, which most definitely did not start out as an acronym for "to insure promptness" but that crap keeps getting repeated as truth). So I'll just note, by way of disclaimer, that I can't guarantee that all of these are true.

The Racist Origins of 7 Common Phrases
From ‘cakewalk’ to ‘no can do,’ the origins of these common idioms and sayings are surprisingly dark.

Even the most nonsensical idioms in the English language originated somewhere.

I could get pedantic about it and note that the true "origin" stretches all the way back to whatever proto-language our distant ancestors used to hunt antelopes or whatever, but I think I can stick to the intent of the article, here.

While these common phrases are rarely used in their original contexts today, knowing their racist origins casts them in a different light.

Let's also point out that meanings and connotations change over time, like how the swastika was once a symbol of peace and harmony and now... it's not. It can go the other way, too, from bad to innocuous or good. If someone calls you "nice," that doesn't mean they think you're foolish. Necessarily.

1. Tipping Point

No, this isn't directly related to the gratuity kind of tipping.

In the 1950s, as white people abandoned urban areas for the suburbs in huge numbers, journalists began using the phrase tipping point in relation to the percentage of non-white neighbors it took to trigger this reaction in white city residents.

I'm still not sure if that's racist in itself, or just calling out racism. Given that it was the 1950s, it could go either way.

Tipping point wasn’t coined in the 1950s (it first appeared in print in the 19th century), but it did enter everyday speech during the decade thanks to this topic.

So it's not really an origin. And if you use "tipping point" in relation to, say, climate change, that doesn't make you racist, either.

It's a fairly common and descriptive term in other areas of science, too. Like, maybe, the stress at which steel stops acting elastically and starts to deform permanently.

2. Long Time, No See

In contrast, this one is clearly and deliberately racist.

According to the Oxford English Dictionary, this type of isolating construction would have been unusual for the indigenous languages of North America. Rather, it originated as a way for white writers to mock Native American speech, and that of non-native English speakers from other places like China. By the 1920s, it had become an ordinary part of the American vernacular.

Other sources emphasize the Chinese immigrant stereotype over the Native American one.

3. Mumbo Jumbo

In the Mandinka language, the word Maamajomboo described a masked dancer who participated in ceremonies.

Hardly the first, or last, word or phrase mangled from another language, though other sources peg it as "uncertain origin." While it does reflect a disdain for African language on the part of colonials, if you want to get technical about it like I did way up there, all our words have African origins.

4. Sold Down the River

Before the phrase sold down the river meant betrayal, it originated as a literal slave-trading practice.

So, yeah, not great, and there's more about it here.

A roughly equivalent expression of betrayal is "thrown under a bus," which, given the implied violence, I'm not sure is much better.

5. No Can Do

Similar to long time, no see, no can do originated as a jab at non-native English speakers.

This one was more explicitly mocking Chinese-Americans.

6. Indian Giver

Merriam-Webster defines an Indian giver as “a person who gives something to another and then takes it back.”

I think even Kid Me recognized that this phrase was culturally inappropriate. It's pretty damn obvious from the "Indian" part of the name, which didn't refer to Asian Indians.

7. Cakewalk

In the antebellum South, some enslaved Black Americans spent Sundays dressing up and performing dances in the spirit of mocking the white upper classes. The enslavers didn’t know they were the butt of the joke, and even encouraged these performances and rewarded the best dancers with cake, hence the name.

As this one was about getting one over on the oppressors, I'm not sure it's such a bad thing.

Anyway, I've tried to avoid using the obvious ones. As writers, I think it's important to know the tools (words and phrases) we're working with, and make more deliberate decisions about them. Hence my sharing of this list. Besides, a lot of them are cliché anyway.

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