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Monday, Jan. 27, 2025

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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 wanderlust-words-in-motion

about 16 hours ago
In response to "Revisited: "Unwritten, Expanded""

I seldom use emojis in texts and spell out words, use correct (I think) punctuation; it is, after all, still writing. But, just recently I was shown a paper written by her fifth-grade daughter for English. The entire story was written in "text-language" complete with emojis (a lot even took the place of words) on a computer and printed out. The child was very proud of the B+ she had gotten on the assignment!

1 Like

Jayne

about 22 hours ago
In response to "Revisited: "Unwritten, Expanded""

As someone who does not have, and will not have, TikTok: isn't that vertical by default? Does that skew the overall tolerance for vertical video? (among the masses, not for you 😂)

Stik: I'd agree those get a pass. I've had to do it in an emergency, and you really don't think about turning your phone, especially if you don't shoot a lot of video.

2 Like

Elisa: Snowman Stik

about 22 hours ago
In response to "Revisited: "Unwritten, Expanded""

"If I see a vertical video, I ignore it."

Does this apply to videos that call out harmful/discriminatory behavior? I'm willing to give those videos a pass if they're vertical.

2 Like

tj wanderlust-words-in-motion

a day ago
In response to "Let It Lie"

I cannot say honesty is always the best policy, I write fiction for Pete's sake, or whoever else reads and enjoys it. However, in questions such as, "Does this dress make my butt look big?"

I can honestly answer with, "No." After all, it's not the dress. As for the question, "Is there a Santa Claus?"

"Hell Yeah, I saw him at the mall."

2 Like

Adherennium - Maybe Writing?

a day ago
In response to "Let It Lie"

I remember telling my youngest that Santa didn't exist. He thought for a moment then said "Does that mean you and Mom bought all those presents? Cool!" But then my youngest is one cool dude.

4 Like

🌖 HuntersMoon

a day ago
In response to "Let It Lie"

Reminds me of an old joke:

What do you call a kid who doesn’t believe in Santa? A rebel without a Claus.

3 Like

tj wanderlust-words-in-motion

Jan 24, 2025 at 4:30pm
In response to "Watch Out"

I'm reminded of my Grandma who would only have a radio in the kitchen which she unplugged when not in use, because she was convinced it was eavesdropping on conversations. She also had a big, thick, homemade quilt she covered the TV with, so no one could watch activities in the living room.

She was already on to something!

2 Like

Graham B.

Jan 24, 2025 at 1:23pm
In response to "Watch Out"

George Orwell wrote books about guys like Larry Ellison.

2 Like

Sum1's Home

Jan 24, 2025 at 11:50am
In response to "Watch Out"

Your statement about being watched is spot on. I'm privy to a bit of knowledge I can't share, but after that mass-killing in the Fort Lauderdale airport baggage claim, cameras were added. Not just ordinary surveillance cameras either. These cameras would monitor a designated area, the computer it fed would 'know' the scene based on provided data. If a bag, piece of baggage, or almost anything was in one place (and unattended) for too long, an alarm would sound. Where? I am not sure, but I would think it would be at a monitored station/computer, much like a dispatcher working in a radio system.

That was quite a few years ago, camera's and monitoring software have been greatly improved. Here's an example of what could happen. Let's say a camera is monitoring a parking lot, sweeping back and forth slowly. It sees your car pulling in as it sweeps. No big deal.... Yet. On it's next pass, the computer it feeds expects to see your car in a parking spot. If not, an alarm might be raised. Furthermore, it may have caught you getting out of the car in one of it's passes, and now expects to find you approaching an entrance. It can zoom in automatically and capture your license plate. It can do the same to your facial features. So yeah, we're being watched almost all the time. Why do I say almost? Those things are expensive, they are not deployed everywhere. When they are, or once they are, we'll be living in the times of the novel 1984. BUT.... you are still safe in your home, unless Alexa or Siri is listening to you, and your computer camera is operating on the sly, or your home interior surveillance system has been hacked.

2 Like

Jayne

Jan 24, 2025 at 10:55am
In response to "Watch Out"

Yes, loonies have a loon on them.

Toonies? Polar bear. Just one.

2 Like

January 26, 2025 at 9:08am

#1082815

Revisited: "Unwritten, Expanded"

My weekly roll of the dice landed, this time, on an entry the significance of which I could not have known at the time: "Unwritten, Expanded"

Written on December 14, 2019, it's just over five years old.

I'm back! Actually been back a while, but it's taken me this long to recover enough from my trip to concentrate on a blog entry.

The entry was my first in over a week. The significance is that it was the last time I wrote anything like that, because it's the entry that began my current >5 year daily blogging streak. It was also only ten days after the subject of my last "Revisited" post. Random numbers do things we don't expect, like clustering.

As for the actual subject of the entry, of course it's a riff on an article, one which still exists

. The article is about trends; as I said, this was over five years ago, before covfefe, and before Twitter became Xitter (pronounced "shitter"), so it's likely everything in it is out of date.

Article headline: 'Use at least one Emoji per text'

Me: I, and the people I text with regularly (a select few), use emojis sparingly, if at all. We also use complete words, spelled correctly (absent the inevitable occasional typo), and proper punctuation.

There have been arguments about whether one should use periods at the end of a text message. My answer: Yes, absolutely, if you're texting a complete sentence. Younger folks say it makes you seem "curt" or whatever. You know what's curt? Fucking emojis. Younger folks aren't always right, and they don't get to make rules. That's the job of us oldsters.

And here's a rule I made that I'd like to see enforced: no more vertically-oriented video. Ever. If I see a vertical video, I ignore it. I don't care if it's a warning about an incoming tsunami or something cute your cat did. (One exception is rocket launches, where it makes sense. Another is video of a CEO jumping out of a skyscraper.)

Me: If someone has my phone number, I expect they might call at some point. That's okay. As long as they don't expect me to answer, especially if they're not on my contact list. Any unidentified number is a health insurance telemarketer, as far as I'm concerned.

I'm sure I mentioned this somewhere, but there was a period when I was getting dozens of calls per day from telemarketers. Maybe I put my phone number somewhere I shouldn't, but don't blame the victim (me). That's reduced now to maybe once a week, but I still get scam calls of different sorts 2-3 times a day, on average. Consequently, I don't answer my phone unless I know the number or am expecting a call from, like, a doctor or whatever.

Me: So... wait... we're supposed to, on the one hand, condense our texts into emojis and "u" for "you" and acronyms such as IDK or LOL or whatevs, but you're going to get pissed because someone typed "K" for "OK?"

That wasn't the only "rule" I found to be stupid and inconsistent.

The entry continues, with me mostly getting more and more agitated about these arbitrary and changeable "rules," but I don't have any further comments on what I wrote back then. I'll just add one of my own about punctuation in text messages:

Except in truly extreme circumstances, one ? or ! (not "and;" "or") is more than sufficient. Also, if you end each of your texts with ... I will end up ignoring you. I actually don't care if you end a text with a period/full stop or not, but don't give me shit about it when I do.

So, in conclusion, the rules might have changed since then—I neither know nor care—but one thing hasn't: my lack of patience with arbitrary "rules." Except, of course, the ones I make up.

6 Like • Comment • View 3 comments

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