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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

about 17 hours ago
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

about 21 hours ago
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

a day ago
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

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

July 29, 2020 at 12:01am

#989410

Humanity's Last Invention

As a lifelong consumer (and sometime writer) of science fiction, and having lived through the last half-century, I can attest that technology can certainly make one's life better, for various definitions of "better," but as with a monkey's paw or a genie's wishes, everything comes at a cost.

PROMPT July 29th

Write about an invention or technology that you wish existed that would make your life better.

This prompt came in at the same time as my friend was texting me her idea that they should remake some of the original episodes of Star Trek, with a new cast and better budgets. And she wasn't even stoned. So of course we're going to talk about Star Trek today.

The first thing that came to mind, of course, was the holodeck (holosuite in DS9 because it wasn't set on a starship). That would certainly make life better in so many ways, but as someone (Dave Barry, maybe?) pointed out, the holodeck would be humankind's last invention.

There are a lot of inventions speculated about in the various incarnations of the show. Some of them have even been realized in some form (at one point, William Shatner's character in Boston Legal opened a flip phone and it made a communicator chirp). Others probably can't be, at least not in the foreseeable future. All of them have their benefits... as well as their downsides. I'm going to go the overachiever route and talk about not just one, but many of them today. And hell, maybe this will be the first draft of my next Fantasy newsletter editorial because I'm lazy and out of ideas. I mean, come on, I was so starved for inspiration that I talked about tea in this week's newsletter. Tea. Earl Grey. Hot.

So let's start with tea. Specifically, let's talk about how Picard was able to get his tea just the way he liked it in his ready room. The replicator is, like, a 3D printer on steroids. Upside: Using transporter technology (which I'll discuss in a bit), it can craft almost any arrangement of matter. Want a sandwich? Order it at the replicator. Want a thick, juicy steak? Order it at the replicator (no cows were harmed in the making of this episode). Want some Romulan ale? Ooops, sorry, that's not going to happen. Downside: some people actually enjoy cooking and preparing food, not to mention yet another profession lost to tech.

Speaking of the transporter, this idea was introduced as a cost and time saving measure so they wouldn't have to show planet landings and such all the time, but it's become just as intrinsic to Trek as warp drive. Your atoms are scrambled, converted to energy, and then reconstituted at some other point. There's an ongoing philosophical debate as to whether this in fact kills and resurrects you. Upside: near-instant travel. Downside: Transporter accidents are usually gruesome and fatal. But then again, so are many plane crashes.

While we're talking about warp drive, I mean, come on, how would that not make life better? As with the transporter, though, there's little chance it'll happen anytime soon. Upside: explore strange new worlds, seek out new life, etc. Downside: Klingons.

Then there's artificial gravity. Oddly, every other system on a starship could be fried, and the gravity still works. Okay, not that oddly, because it's still just a TV show produced on a planet. Point is, though, if you can create gravity at will, you can also negate it and use the tech to dampen acceleration, so... Upside: easy transportation, loft stuff into orbit; also, not suffering bone loss and other effects known to occur in microgravity. Downside: Well, who knows how much power such a thing would have to use? And it would suck for it to glitch out while you're accelerating at 20 Gs.

Another thing of great personal benefit would be the Universal Translator. Whatever language they're speaking, it becomes English, like magic! It even makes their lips move in English. Technology, I'm telling you! Upside: Understand everyone who doesn't speak in metaphor (watch the TNG episode Darmok if you don't know what I'm talking about). Downside: There are a lot of benefits to actually doing the work to learn a different language, including a better understanding of the culture. Besides, I'm not even sure such a tech would even be possible; there are just too many complexities to language.

Want to make life better? Invent the phaser. Upside: stun setting eliminates threats without those messy ethical issues. Downside: you know we'd abuse the fuck out of it just like cops are abusing pepper spray now.

Going back to drinks for a minute, there's synthehol, which is the obvious portmanteau of "synthetic" and "alcohol." Upside: Drink all the scotch you want without getting drunk! Downside: Drink all the scotch you want without getting drunk.

Want to know everything about a particular, say, rock? Then you need a tricorder. This handheld device can analyze the molecular and crystalline structure of, well, pretty much everything. Upside: know what everything is. Downside: where's the joy of discovery?

And so we finally come to the holodeck, the ultimate Virtual Reality experience. Upside: Any scenario you can imagine, it can create, much like the replicator but for more than just food. Rest on a beach. Go camping in the mountains. Experience the pleasure domes of Risa. All without leaving Deck 38 or whatever. Downside: spend the rest of your now-shortened life getting foot massages from Uhura. "Nichols or Saldana?" "Pourquoi pas les deux?"

But you can't tell me it wouldn't be worth it.

7 Like • Comment • View 10 comments

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