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Sunday, Jun. 30, 2024

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Complex Numbers

by Robert Waltz

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:

Kåre Enga in Montana

a day ago
In response to "Je Voyagerai"

I once was allergic to going on a cruise. But... I should... just for the experience. I've gotten out of my comfort zone for experience.

With the crush of tourists these days any travel should include how much you want to put up with "other people's vacation" as opposed to your own.

1 Like

Lazy Writer est 4/24/2008

a day ago
In response to "Je Voyagerai"

Happy traveling..be safe.

Elisa: Middle Aged Stik

a day ago
In response to "It Ain't Wrong"

Ain’t apparently begins as amn’t, a contraction for am not, which you can still hear in Ireland and Scotland today

I mean, an abundant number of Scotch and Irish immigrants ended up in the American South, so this tracks.

While a lot of people consider ain’t improper, it’s a very regular and legitimate part of many forms of English, including in Black English (AAVE). Be mindful that judging someone’s use of ain’t as “wrong” can be a very socially loaded act, to say the least.

For some reason, this reminds of one of the reasons I stopped reading Ask A Manager. A bunch of people were getting real uppity about the use of the phrase "baby daddy". Unsurprisingly, many of these people appeared white. One Black person in the comments finally had enough and threw down with this remark:

"I gotta say, as a black woman it grates to have phrases that come out of AAVE be appropriated, assigned negative connotation (likely because they come from black culture), then discarded with prejudice. If you’re using the phrase to conjure up stereotypical imagery, I can get on board with putting an end to that. But there are plenty of people for whom baby daddy or baby mama are not pejorative at all, just descriptors of the relationship in their dialect, and correcting them to “Father of my child” is just another case of denigrating minority speech patterns and legitimate AAVE grammatical constructions and upholding “white is right” standards."

(For more context, check out this link

1 Like

🌕 HuntersMoon

Jun 28, 2024 at 10:54am
In response to "It Ain't Wrong"

Ain't you on a roll today...

3 Like

Adherennium Dr of Phoolishness

Jun 27, 2024 at 11:53am
In response to "Wave Rider"

Horrifying fact, I once painted a reproduction of the Hokusai wave on our bathroom wall. Eventually of course it was painted over, but I like to fantasise that in some distant future it will be archaeologically excavated and held up as an example of early cultural appropriation, (badly executed too.)

1 Like

Annette

Jun 26, 2024 at 8:16pm
In response to "The Oz Hypothesis"

The nekked wimmin look like something that I might have drawn in first grade.

1 Like

Aiva Raine

Jun 25, 2024 at 10:16pm
In response to "Can't Spell Success without Sucs"

Ok- this made me truly LOL- "sipping a gin and tonic made with low-paid laborer tears"

Thank you. Totally agree with the rest of your article.

Money doesn't solve all problems but it sure as hell eliminates many and makes it easier to go places or buy things that can create some happiness. IE- a property somewhere quiet and peaceful and a trailer with which to chill on said property.

Rich people are typically clueless assholes.

1 Like

Anni Pon

Jun 25, 2024 at 9:30am
In response to "Can't Spell Success without Sucs"

I've never heard anyone say, "That guy is so successful, but he doesn't really make much money." Or anything similar. Sure, you can have a positive impact on the world without making lots of money, but people won't call it success.

2 Like

Annette

Jun 23, 2024 at 1:28pm
In response to "Revisited: "Experience""

This is how I coped:

1 Like

Elisa: Middle Aged Stik

Jun 23, 2024 at 9:51am
In response to "Revisited: "Experience""

Not gonna lie I kinda miss Zoom parties, at least for this community since people on WDC are so spread out. Meeting in person is pretty tricky and/or expensive. It's certainly more socializing than I've been doing regularly since, oh, 2022 or so.

As for server migration, well, I work in the IT world. I've been through that. And honestly, server migration is a bit nerve wracking, as some stuff can go missing. It's still more manageable than a complete redesign. Complete redesigns are awful. You can test in different environments that the public can't see till kingdom come, but things always go wrong when the public version is rolled out. A local grocery store recently redid their website, and the old site held thousands of recipes. When the new site was unveiled, none of those recipes made it over. I ended up reaching out on Messenger and was able to get a copy of a recipe I use somewhat often, but I'm kind of annoyed that the text recipes are currently MIA because somehow that data didn't transfer with the site rebuild. Absolute madness.

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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