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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:

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

September 20, 2020 at 12:02am

#993759

Patterns

Yay! MadLibs!

PROMPT September 20th

Complete this sentence:

The next time I ___________, I will __________.

The temptation is there to plug in random verbs, so I found a random verb generator and cranked it up.

The next time I settle, I will whisper.

The next time I put, I will hope.

The next time I revise, I will award.

The next time I teach, I will travel.

The next time I interpret, I will assist.

Hm. Maybe if there were an option to limit to intransitive verbs. But, you know, I don't build these things; I just wreck 'em.

So I also tried a sentence generator, pulling entire verb phrases out of the randomly generated sentence. For example, my first result was: "She had a difficult time owning up to her own crazy self." Plug in the phrases and:

The next time I have a difficult time, I will own up to my own crazy self.

This is fun, if maybe a little too on the nose. Let's try more:

The next time I should have been a time and a place, I will be it.

The next time I crash on the shore, I will be a lovely sight.

The next time I play with Legos, I will be at camp.

Okay, so not all of them work. Still fun, though.

Oooh, found another one where you can specify more parts of speech.

The next time I abhor Hades, I will disengage mousse. (I changed the verb tenses, but that's about it)

The next time I immobilize medication, I will cache vise.

Nah... maybe not.

The links I used are here:

https://randomwordgenerator.com/sentence.php

http://watchout4snakes.com/wo4snakes/random/randomphrase

Be careful with that second one. I don't fully trust it. There's also one I found that didn't quite do what I was looking for, but someone might be able to do something with it:

https://www.michaelfogleman.com/phrases/

Anyway, yeah, some of these are nonsense, but nonsense can be fun. Hell, poems -- entire novels -- have been written with nonsense, and people drool all over them looking for meaning (I'm talking about YOU, Ulysses.) Because that's what we do... we look for patterns. Usually this serves us well, especially if we're being stalked by a lioness. Sometimes it leads to impressive accomplishments. Other times, it's just cool -- people looked up at the stars and decided they made little connect-the-dots sketches, and named them, and so we have the constellations.

And then, sometimes, things get weird, like with pareidolia -- seeing a face in a mesa on Mars, or Jesus on a piece of toast. But then, that's also how we get a "man" (or in some cultures, a rabbit) in the moon.

According to Wiki (look, I can't be arsed to check every reference, especially when I'm just playing like I am today), Pareidolia

"can be considered a subcategory of apophenia

. So of course I had to be reminded what apophenia was, and at that entry I found this:

Apophenia... is the tendency to mistakenly perceive connections and meaning between unrelated things.

And this:

In contrast to an epiphany, an apophany (i.e., an instance of apophenia) does not provide insight into the nature of reality nor its interconnectedness, but is a "process of repetitively and monotonously experiencing abnormal meanings in the entire surrounding experiential field". Such meanings are entirely self-referential, solipsistic, and paranoid—"being observed, spoken about, the object of eavesdropping, followed by strangers".

As that article explains, taken to an extreme, it's a disorder or an indication of a disorder. And it can certainly lead to fallacies. But... that's what I do as a writer: I find or imagine connections between disparate things. Hell, a metaphor can be considered an apophany by this definition.

Metaphors are what humans do. It's what we're good at. Like... when airplanes were invented, we called their fixed appendages "wings," even though they're not exactly the same as the flappy wings of the birds which inspired them.

It's important to not take these connections too far, to mistake symbol for referent. This sort of thing is, however, what creativity in writing is all about - at least to me. And I mean, hell, isn't a realistic painting just a case of intentional pareidolia? Take La Gioconda, for example, better known as Mona Lisa -- da Vinci intended it to represent a woman's face, and that's what we see. We don't actually see a person, of course, just a bunch of paint splotches, but our minds are tricked into seeing some long-dead Italian.

Randomness can lead to imagined connections, and imagined connections are the heart of creativity. So...

The next time I write a story or poem, I will be more conscious of apophenia.

9 Like • Comment • View 8 comments

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