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Tuesday, Dec. 3, 2024

1:49pm 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:

Elisa: Snowman Stik

about 4 hours ago
In response to "Coasting Along"

"always approaching an answer, never quite getting there. But learning more and more along the way."

If only I could put this on a bumper sticker.

1 Like

Wordsmitty ✍️

Dec 1, 2024 at 12:18pm
In response to "Revisited: "Useless""

At least we can still play Duke Nukem

among other classics.

2 Like

Elisa: Snowman Stik

Dec 1, 2024 at 9:10am
In response to "Revisited: "Useless""

I bet the toilet paper site made people a bit envious/wistful a few years ago

2 Like

Dave Ryan

Dec 1, 2024 at 8:56am
In response to "Revisited: "Useless""

There's an add-on for the major browsers called Ruffle

that is a flash emulator. The bubble site is still poppin'!

3 Like

tj-Merry Mischief Maker

Nov 29, 2024 at 4:36pm
In response to "Shroom with a View"

The use of psychedelics leads to a higher{i/} life form? Sorry, I couldn't resist the pun.

Elisa: Snowman Stik

Nov 29, 2024 at 9:47am
In response to "Shroom with a View"

Originally proposed by ethnobotanist Terence McKenna in his 1992 book Food of the Gods, this provocative idea has recently resurged in popular discourse, thanks in large part to its discussion on Joe Rogan’s widely followed podcast.

Well, now I'm even less inclined to believe it.

Side note: I think we need to more publicly discuss the unintended consequences of Joe Rogan's podcast. It's played a huge (and not always ideal) role in the development of men. I worry that ignoring Rogan's impacts has made them worse.

1 Like

tj-Merry Mischief Maker

Nov 28, 2024 at 12:40pm
In response to "Trolley Pop"

Doing this type of test using mice instead of people is not going to yield the same results. I base this statement on my experience shopping for a few things yesterday and would have loved to be able to "throw the switch" on many of the rude, crude, and socially unacceptable people in the store. But to harm those cute, furry, and innocent mice? I think not.

Sure, mice can be a problem, and we do have to deal with them from time to time, but even in this scenario, I use a live trap and transport the little critters safely to the residence of the above mentioned morons... (in truth I transport them to abandoned buildings)

3 Like

Wordsmitty ✍️

Nov 28, 2024 at 12:27pm
In response to "Trolley Pop"

Are these the same mice that were turned white in that other experiment a few entries back? I would think they may have suffered enough. Or maybe waiting to see if they get shocked would be how they were stressed to turn white. A two-for-one experiment! Would it make a difference if the mice were white or gray? Are there mice in the trolley? , , ,

3 Like

Kåre เลียม Enga

Nov 28, 2024 at 11:05am
In response to "Trolley Pop"

What comes to mind? Any kōan. They aren't necessarily "solvable" either.

2 Like

tj-Merry Mischief Maker

Nov 27, 2024 at 6:28pm
In response to "Inevitable Two"

What about death by Taco Bell?

49-year-old Diane Durre was killed by a falling Taco Bell sign that was knocked over by strong winds. He husband was also injured but survived.

1 Like

November 10, 2024 at 9:43am

#1079759

Revisited: "Worst Year Ever"

No, the title isn't political commentary. My random selection of past entries yielded this bit from the end of 2018: "Worst Year Ever"

The (very short) entry is basically a few comments on a link to an article from Science.org,

which is still available and claims that the year 536 C.E. was "the worst [year] to be alive."

My commentary back then was pretty much focused on praising the interdisciplinary science that produced this result. But now, six years on, I might have a few more things to say about the article itself.

Ask medieval historian Michael McCormick what year was the worst to be alive, and he's got an answer: "536."

"Worst" is obviously a matter of opinion. It's also dependent on the opinion-holder's experience and knowledge. Ask people what the worst movie ever made is, and you'll get a bunch of different answers, but none of them are definitive because I guarantee you none of them have seen every single movie ever made, and one person's "worst" may be another's "yeah, it was pretty bad."

In this case, we've got a guy whose area of focus seems to be medieval Europe, so his answer is understandably Eurocentric.

A mysterious fog plunged Europe, the Middle East, and parts of Asia into darkness, day and night—for 18 months.

See? Nothing about North America, which had a decent population at the time, or anything in the Southern Hemisphere. It might have been a shitty time in those places, but maybe not the worst year to be alive. Especially for the native Americans or Australians.

Temperatures in the summer of 536 fell 1.5°C to 2.5°C, initiating the coldest decade in the past 2300 years.

Hey, guys, I think I've figured out how to stop global warming. If we can't make a volcano go boom, there's always the similar effects of nuclear winter.

Historians have long known that the middle of the sixth century was a dark hour in what used to be called the Dark Ages, but the source of the mysterious clouds has long been a puzzle.

Spoiler: volcanic eruptions in Iceland.

Probably. I mean, it's science, so results can have varying confidence levels, and I haven't seen any updated articles since then. Still, my main point remains: when different disciplines cross-reference each other, you get better science.

2 Like • Comment

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