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Wednesday, Nov. 6, 2024

4:37am EST

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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:

Aiva Raine

about 14 hours ago
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

about 14 hours ago
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

JayNaNoOhNo

about 15 hours ago
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 Like

tj-turkey-jobble-jobble-hard-J

a day ago
In response to "It's Hard Not To Scare"

Smarter mice? Just what we need!

1 Like

Wordsmitty ✍️

a day ago
In response to "It's Hard Not To Scare"

"Friendly neighborhood spider-goat." Isn't Marvel working on that for release in '26. - "Yes, it's cute, MJ, but you shouldn't ..."

2 Like

tj-turkey-jobble-jobble-hard-J

Nov 3, 2024 at 3:52pm
In response to "Revisied: "Inevitable""

I can think of far more absurd ways to die, but most of them involve alcohol and maybe prostitutes... This statement reminded me of the passing of a friends grandfather; he died of a heart attack while intoxicated and with a prostitute, Viagra also aided in his heart failure.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:46am
In response to "She Said Spatchcock"

You can spatchcock, or butterfly, any bird.

That bit might only be funny if you're familiar with British slang.

It's really a pity that the British national team's mascot is a lion and not a rooster. Ironically, that's the French national team's mascot, which did make for a pretty good joke during the Olympics.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:31am
In response to "Cave In"

tj-turkey-jobble-jobble-hard-J

-Yeah, those instigators from Illinois and Texas would really degrade the standards of Hell.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:30am
In response to "Revisied: "Inevitable""

Though I clicked on it to check, I no longer follow that site and want nothing to do with them, which is why we haven't had any LitHub links in over a year.

Well, now my curiosity is piqued. What happened on this front?

2 Like

🌕 HuntersMoon

Nov 3, 2024 at 8:37am
In response to "Revisied: "Inevitable""

Let's get real. Once you're dead, you really don't care do you...

2 Like

October 1, 2022 at 12:02am

#1038403

Muddy Talks

I'm participating in "Journalistic Intentions"

[18+] again this month, so some of my entries will be prompts from that activity.

This is one of them—as usual, selected at random.

Locks, dams, and the future of the Mississippi

When I was in Minneapolis in the summer of 2021, I got to see some of these locks and dams up close. I wrote, briefly, about it at the time: "Dam It"

So apparently, based on the link above, there's talk about removing some of them. Not the ones I toured, but downstream from there.

You might think that, being a civil engineer whose whole thing was hydrology, I'd have an opinion on it. After all, I have opinions on plenty of things that I know far less about. But you'd be wrong. Well... I do actually have an opinion, which is "they should do what's expected to have the best overall outcome." Which is why we have people do studies for this sort of thing.

If I thought about it long enough, I'd probably come to the conclusion that this should probably be my opinion on everything else, too. But no, then life would be no fun, and worse, I'd have nothing to blog about.

Besides, rivers are complicated. They build dams for reasons: flood control, erosion prevention, power, recreational purposes; usually some combination of these things. There's always a trade-off too, like when the dam blocks fish spawning or whatever, or the resulting lake drowns a community.

Left to its own devices, a river will shift over time. Not just geological time, but often in one human lifetime. You can see the effects if you look closely at a map of the rest of the Mississippi: horseshoe bends where the river once flowed, and down the center of which a state line was surveyed, have gotten cut off, leaving, for example, a bit of Tennessee on the Arkansas side of where the river is now. Several bits, actually. Some of that might have been due to Army Corps projects, but probably there was also some non-human-caused shifting over the years. If you wanna see, look up Memphis on Google Maps and then scroll north.

And I'm not saying this is bad, or good; it just is. We modify rivers for our own purposes, and for a long time we didn't think much about the consequences. Now that they're modified, though, there are consequences to unmodifying them, as well.

Even further downstream, in Louisiana, the primary Mississippi discharge has been trying to shift over to the Atchafalaya river (no, I can't pronounce it, either). If it weren't for levees and locks and whatnot—engineering projects—it probably would have switched channels by now. From what I understand, it used to switch back and forth every thousand or two years. As one channel silts up, water flows to the other, and vice-versa.

This, of course, would leave New Orleans dry (if not high), so there are economic reasons not to allow it. But there are probably good solid ecological reasons to do so. But we're a part of the ecology, too, part of nature, and we have to make decisions based on incomplete information.

I'm just glad it's not my job.

1 Like • Comment • View 1 comment

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