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Saturday, Nov. 23, 2024

10:11pm 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:

tj-turkey-jobble-jobble-hard-J

about 3 hours ago
In response to "Pursuit"

My grandmother used to say, "Pursuing happiness is like a dog chasing it's own tail."

2 Like

🌕 HuntersMoon

about 10 hours ago
In response to "Pursuit"

Happiness is reading your ramblings daily. True happiness is posting a snarky response.

3 Like

Robert Waltz

Nov 20, 2024 at 2:54pm
In response to "Powers of Three"

🌕 HuntersMoon

- that's pretty much what quantum computing is, from what I've read.

2 Like

Brandiwyn🎶

Nov 20, 2024 at 2:32pm
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

Nov 20, 2024 at 1:20pm
In response to "Powers of Three"

With binary, it's either on or off. Wouldn't ternary introduce Schodenger's Cat? On, off, or both?

2 Like

Turkey DrumStik

Nov 19, 2024 at 7:43pm
In response to "Paramount Purpose"

I suspect old web filter attempts

would have combusted when confronted with this article.

1 Like

tj-turkey-jobble-jobble-hard-J

Nov 19, 2024 at 4:04pm
In response to "Losing Weight Is Easy"

Some of them break out in hives if you ask them to add 10% to something.

Yesterday I purchased an item that cost $6.42 after tax was affixed by the register. I handed the cashier a ten dollar bill and watched as she placed it in the cash register, which like most now days, showed her how much change to return. She had to try three times to count out the proper amount, and as I was leaving commented to the bagger, "Why do people have to pay with cash, don't they know how hard it makes my job?"

I didn't say anything, but was trying desperately not to break out in hysterical laughter.

1 Like

🌕 HuntersMoon

Nov 19, 2024 at 9:28am
In response to "Paramount Purpose"

At your age, Bob, take heart in the fact that it can be restored...

2 Like

Wordsmitty ✍️

Nov 18, 2024 at 12:34pm
In response to "Losing Weight Is Easy"

This brings up the old question of whether your weight changes when you inhale a helium balloon to make your voice higher.

Maybe this has to do with the difference of a mug of beer vs a tankard of ale.

The universe has so many weighty/massive questions.

3 Like

Brandiwyn🎶

Nov 18, 2024 at 11:27am
In response to "That's the Spirit"

Maybe you’d go with “Thunder” because that one’s so terrible that only divine intervention can explain its success. Wow. Missed opportunity, here. How could you let this go without a shoutout to mighty Thor, son of the Allfather, wielder of Mjolnir, He with the Long Forehead? (Said in the voice of the Soup Nazi): "No Valhalla for YOU!"

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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