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Saturday, Dec. 21, 2024

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Complex Numbers

by Waltz Invictus

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:

Annette

about 10 hours ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

June 6, 2024 at 9:51am

#1072234

Elevator to Heaven

From Wired, some panic about a thing that might not even happen.

What Happens If a Space Elevator Breaks
These structures are a sci-fi solution to the problem of getting objects into orbit without a rocket—but you don’t want to be under one if the cable snaps.

Yes, they're a staple of science fiction, but early concepts for them were thought up way back in the 19th century, before even controlled powered atmospheric flight and way before achievement of space travel.

They're also called Tsiolkovsky towers after the Russian who apparently first conceptualized them. According to Wiki,

other names include "space bridge, star ladder, and orbital lift." Personally, I find all those names descriptive but boring. No, I think it should be called a space lift. Because it rhymes with "face lift," and I find that amusing. Everything should be named in accordance with what I find amusing.

In the first episode of the Foundation series on Apple TV, we see a terrorist try to destroy the space elevator used by the Galactic Empire. This seems like a great chance to talk about the physics of space elevators and to consider what would happen if one exploded.

Not even the prospect of a Foundation series is enough to get me to pay any attention to Apple TV. But the idea, as I said, isn't new, nor is thinking about the security issues surrounding them. If you think about it, the idea of a tower connecting Earth to space will inherently offend a large portion of the population, who will inevitably call it the Tower of Babel, decide that it's against God's will, and actively try to blow it up.

This is why we can't have nice things.

Well, actually, we can't have a space lift because, so far, no one's been able to come up with a material that with the appropriate requirements, or address numerous other issues including powering the thing or shielding any passengers from space radiation. As far as I know.

Anyway, the article mentions that, sort of, but starts out by explaining, in great detail, how a space lift would be an improvement over rockets. This takes up most of the article, and I'm not quoting that part. Only after that does it get into what the headline promised.

In the first episode of Foundation, some people decide to set off explosives that separate the space elevator’s top station from the rest of the cable. The cable falls to the surface of the planet and does some real damage down there.

Again, not the first time this has been considered. I don't remember a scene like that from the Foundation books (by Asimov, whose entire output I devoured as a teen), but it's been a very long time. I do remember Kim Stanley Robinson addressing the issue in his Mars series.

The (over-simplistic, which the author acknowledges) video model in the article aligns with what I recall of Robinson's description.

So not only is building a space elevator very difficult, but you really don’t want the cable to snap and fall.

At this point, though, it's firmly in the realm of speculation, both in science fiction and actual science. The problem may be so tough that we'll actually develop antigravity first, which would negate the need for a space lift. Which is why you don't see many space lifts in Star Trek (budget considerations notwithstanding).

Of course, all of that assumes that a small remnant of humanity doesn't get plunged back into subsistence living before either happens, which I'm not prepared to rule out.

5 Like • Comment

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