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Saturday, Nov. 16, 2024

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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:

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

June 14, 2022 at 12:03am

#1033806

The First But Not the Last

I last linked an article from The Atlantic just a couple of days ago. This one, from the same source, is its polar opposite. I can't snark on it.

The Holocaust Started With My Great-Uncle’s Murder
Arthur Kahn is believed to be the first Jewish person killed by the Nazis. I’ve known the story of his death as long as I can remember, but I wanted to learn the story of his life.

Perhaps you feel you've been hearing too much about this lately. Personally, I recently saw a bunch of articles about Anne Frank because the anniversary of her birth was on June 12, the same day I ragged on the happiness article. She'd be 93 now. Not an impossible age. Millions of deaths are a statistic; one is a tragedy.

But, considering that there are still people around who want to exterminate other people for being "other," I for one am not going to let it slide.

"Hey Waltz, what about all the other genocides in history? Why don't we talk about them in the same way?"

Good question. They all suck. The reasons we keep going back to 1930s Germany when we talk about genocides are 1) They were, arguably, the most advanced civilization on the planet at the time, and yet they still committed barbaric atrocities, and 2) there are still people around who want to exterminate other people for being "other," so we have to remember this shit so that history doesn't repeat itself. Which it looks like it's about to.

As for the article I just linked, well, I don't have anything I want to quote from it. You can read it. You might encounter a paywall, especially if you also read the one I linked on Sunday, but there's a way around that (I'll email it to you if you don't know). It's another story of an individual, not a statistic -- someone who, as the title suggests, might have been the first victim of Nazi genocide.

I've heard there were about 10,999,999 more after him. Oh, sure, you've heard the "six million" number quoted. Those were known Jews. The other five million shouldn't be forgotten, either: people of African origin, Romani, homosexuals, political prisoners, those who opposed the Third Reich, etc.

When I was in high school, I was the only Jewish kid in the class when we read the Frank diary, so most people walked on eggshells around me (those that didn't were going to bully me anyway, and took this opportunity to unleash their bigotry). No need for that, though. One time I pointed out the 11 million statistic, and I remember someone being amazed that I would care about the non-Jewish victims.

As if I should only care when I or someone in my subgroup is affected. Caring only about your own community is the problem.

That said, there's a big difference between hating someone for things they have no control over, such as race, and hating them for things they do, like being assholes (fascists, e.g.). There aren't "two sides" here; there's people who just want to live their lives; and then there's people who want to exterminate them for being "other." I don't care whether that "other" is Black, Jewish, Mexican, Muslim, Asian, Christian, atheist, gay, trans, or whatever. Of course, I could make the argument that you can't help being an asshole, because we don't really have free will. But assholes have been known to become non-assholes, whereas you don't stop being your race.

Anyway. Enough depressing shit. I'll write more comedy later. I just felt this was too important to not put in the blog rotation.

3 Like • Comment • View 1 comment

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