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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:

Wordsmitty ✍️

about 16 hours ago
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

about 19 hours ago
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

a day ago
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

a day ago
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 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).

January 15, 2021 at 12:05am

#1002138

All In A Dream

PROMPT January 15th

Write about dreaming. Do they ever mean anything, or are they all meaningless? Why are they sometimes scary, emotional, silly, or prophetic? Have you had a memorable dream recently?

At the risk of slipping on a stray philosophy peel, "meaning" is highly subjective, and dreams can only have the meaning we ascribe to them.

Long-time readers might know that I've discussed dreaming in here before. I got interested in the science of it (which is called oneirology) in trying to understand episodes of sleep paralysis.

Truth is, science can't tell us much, especially when it comes to subjective experiences. This or that part of the brain being used, certain chemicals expressed or suppressed, links to REM sleep, the technical aspects of how long a dream state lasts; those sorts of things can be studied.

My personal favorite hypothesis has to do with dreams serving to consolidate and file away memories, as well as being a means of emotional practice. Often dreams seem to be related to waking events, which makes the most sense because your brain doesn't stop working when you're asleep; it just does different stuff.

As for meaning, though... well, it's my considered opinion that "dream interpretation" books are, at best, crap; and at worst, utter bullshit. They do serve the purpose of making the authors' dreams come true, sometimes, so at least there's that. Yes, symbolism and metaphor are powerful things, but they tend to have very personal meanings. Like, if I saw a turkey vulture in a dream, it would mean something very different and far more positive than if someone else saw one in their dream. For instance. That is, if it meant anything at all, which I'd wonder about.

Nevertheless, thinking about these things can open up new connections in one's mind, and that's usually a good thing, especially for writers or artists. For instance, I've woken up before and realized that, in a dream, I made a pun. Yes, that's right... I pun even in my sleep. Lately, I've sometimes been dreaming in very simple French, which I take to mean that the lessons are starting to sink in.

So... "Why are they sometimes..."

Scary: Like I said up there, I think dreams can serve as emotional practice. Perhaps there's some evolutionary benefit to practicing responses to environmental threats; I don't know, because I despise evolutionary psychology hypotheses. In any event, I think maybe sometimes the body just needs to practice pumping out certain neurotransmitters. Does this serve to enhance or moderate one's anxiety? Eh. I don't know. To me, the only scary dreams are the ones where sleep paralysis is involved. That shit sucks.

Emotional: Processing the day's emotions, and preparing for possible future emotions? Makes as much sense to me as anything.

Silly: Humor and absurdity are essential parts of human life.

Prophetic: Couple of things going on here. First of all, we dream almost every night, and we have the cognitive ability to predict things that might happen in the future; consequently, it's not shocking that some of this predictive processing would go on even at night. And, second, even if that weren't happening, it would be far more odd if no dream were ever predictive in some way. I mean, I've been known to have dreams of nuclear bombs going off all across the horizon, and I really, really hope that those aren't prophetic. But I've also had dreams in which I got stuck in traffic behind, say, a blue Ford truck and behold, in the next few days I got stuck in traffic behind a blue Ford truck. Given how many blue Ford trucks there are and how often I (used to) drive, such a dream had a near 100% certainty of coming true at some point -- especially when we tend to remember the ones that come true way more than the ones that don't.

I don't really remember my dreams the way I used to. Mostly just brief impressions. Oddly, lately, a lot of these have involved me being completely aware of my surroundings -- but also being completely blind. Like, in the dream, other senses substitute for sight. Fear, prediction, or just my mind being silly? Who knows? I'm not going to worry about it, though, and the dreams are kind of interesting.

One thing I know with almost complete certainty, though: there's nothing supernatural involved. Just your brain firing away, doing what it does, maybe storing memories, maybe rebooting, maybe trying to make sense of the world or, contrariwise, reminding us that there is no sense and why not just embrace the absurdity?

And sometimes you get story ideas out of it, so enjoy it!

12 Like • Comment • View 8 comments

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