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Monday, May. 6, 2024

7:40am EDT

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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

about 23 hours ago
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

a day ago
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

June 1, 2021 at 12:02am

#1011075

Kids These Days

Welcome to June. My inner optimist says it'll be different than May; my inner pessimist fears that he's right.

Let's start this month with an entry for "Journalistic Intentions"

[18+]. There's still time to join in the fun there if you want.

CHOP Kids First

My state, Virginia, is often cited as having the largest percentage of vanity license plates in the US.

Honestly, I don't care one way or the other. Some of them can be amusing. Others have indecipherable meanings. But real creativity can come in when one combines vanity plates with special commemorative plates. And Virginia has a lot of them, too.

For example, my optometrist, who went to UVA, got UVA tags. These consist of a giant orange V logo on the left side, which gave her the opportunity to add ISION as her personalized tag, so when read in full, it says VISION. Cute. On brand. Glad to have someone that creative taking care of my eyeballs. On the other end, I hope whoever got AGINA

on one of those is a gynecologist.

Other commemorative plates are more controversial. Every time I see the one based on the Gadsden flag

(99% of the time, these are on oversized pickup trucks), I assume the driver is a raging asshole and give him (99% of the time it's a "him") a wide berth and a short "thank you" for advertising his assholery. That's what I like about freedom of speech; it lets me know who it would be a waste of time and energy to listen to. "Dont Tread On Me" is translated, by me at least, as "Tread on THEM," where "them" is any sort of minority.

Another problem one is the "Choose life" logo. Okay, it wouldn't be problematic if our state government also issued "pro-choice" plates, but they don't. Come on, Virginia, you're a blue state now; get with the program.

The above should not be construed as an invitation to get into an argument about abortion or politics.

But the one VA specialty plate series I have hated above all others is the one that reads, in some sort of multicolored crayon font, "Kids First."

My reasons for raging about such a thing are complex; basically, I don't agree with "kids first." We have too much emphasis on kids as it is. We're not supposed to be adults living in a kids' world; they're supposed to be kids living in an adult world, and preparing for it. And too many people use "for the children" as a shield to mask their own Puritanical dislikes.

So, when I saw this plate,

I about tore a muscle laughing

I honestly can't remember if I saw it first on the road, or on the internet. I suspect the latter; there are over 7 million registered vehicles in Virginia, and besides, if I'd seen it on the road, I would have wrecked from laughing so hard.

Like most states, we're pretty picky about questionable tags. You can't get "FUCK," for example, or racially-charged terms. There are procedures in place to stop those before they ever get stamped. Somehow, though, this one got through.

At least, it did until some Puritanical wet-nose decided that "Eat The Kids First" was a sexual reference, and got the tag retroactively canceled.

You have to have a certain sort of mind to believe that it's a sexual reference. I don't have that sort of mind. I envisioned a zombie apocalypse, not a massive orgy of statutory rape. The thought never ever crossed my mind, and I have an exceptionally dirty one. In retrospect, I'm not sure that a joke about cannibalism was any better. Still, it was, obviously, a joke.

But it crossed someone's filthy, disgusting mind, and so there came to be just a little less humor on the road. Not in the world, though; as you can see from the link above, the plate is immortalized in pictures on the internet. And from what I've seen, similar ones have slipped through the cracks in other states, too.

It might be tempting to point out that I expressed a dislike of other kinds of specialty plates, so isn't it hypocritical of me to rail against someone else's objection to one? Well... consider that I have never tried to get any kind of license plate canceled, and maybe you can see that there's a difference. We don't have the right to not be offended. I'm perfectly capable of hating something without getting all activist about it. In fact, it's a core theme of my personality.

Which is not to say that I willingly support businesses run by people with what I consider the wrong politics. I just don't expect legislation to back me up on my boycotts. But that's another topic.

And it looks like the business that provided the above prompt probably got similar backlash. I risked getting put on a List by typing "CHOP kids first" into Google, and one of the results starts out: "At the CHOP Primary Care practice (formerly Kids First) in West Chester, PA, we believe that every child should have a medical home..."

Fortunately, Kid Sex Change

is apparently still in business, for those of us who have to giggle at such things. Word spacing, people. It exists for a reason. Use it! Or don't, and risk the juvenile attention of the internet.

6 Like • Comment • View 3 comments

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