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Sunday, Feb. 2, 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 5 hours ago
In response to "Revisited: "Friend""

I had an employee that requested some time off the week leading up to December 21, 2012 to be with his family. They had prepped and prepared for over a year and wanted to be together, in shelter, for the end of the world. On December 22 he came into work looking like he had not slept all night, head hung low, and not a word to say about the rest of us still hanging around. In March, he and his family all moved to Florida, probably to start prepping for the next end of the world.

1 Like

Elisa, Stik of Clubs

about 6 hours ago
In response to "Revisited: "Friend""

🌖 HuntersMoon

, that emoticon use is top notch! I have feelings like that on a regular basis.

2 Like

🌖 HuntersMoon

about 6 hours ago
In response to "Revisited: "Friend""

@ Elisa, Stik of Clubs - Cognitive Distortions: It seems to apply equally to our current Pumpkin Prophet.

3 Like

Elisa, Stik of Clubs

about 6 hours ago
In response to "Revisited: "Friend""

for a country that claims to love freedom and individuality, some of us are remarkably susceptible to following prophets of the End Times.

I wonder how much of that stems from a large portion of the population not being aware of how cognitive distortions work. (Luckily there are some advances

in making that kind of learning a bit easier.)

3 Like

tj wanderlust-words-in-motion

about 23 hours ago
In response to "This Is the Whey"

Years back there was a dairy farm just outside of Anoka Minnesota that specialized in old-world cheeses; I loved that place. It's too bad we don't have craft cheeseries like we do craft breweries.

1 Like

tj wanderlust-words-in-motion

a day ago
In response to "Unscheduled"

I would have to add fear to this as well: "Only by making us feel guilty can they sell us stuff to assuage that guilt."

I agree, everyone has their own "productive time" and sleeping patterns change, growing up I was an early riser no matter what time I went to bed; it worked great. Then, for whatever reason, I started sleeping later and was more productive in the evenings and into the night. Now, it's somewhere in between.

1 Like

Wordsmitty ✍️

Jan 31, 2025 at 12:37pm
In response to "Unscheduled"

My mom would recite in the morning: "Here is dawning another new day, whilst thou let it slip useless away?" Thinking back, even if I got up and went to school, sometimes it still was a useless day.

3 Like

Elisa, Stik of Clubs

Jan 31, 2025 at 9:33am
In response to "Unscheduled"

"Only by making us feel guilty can they sell us stuff to assuage that guilt."

This might change thanks to the underconsimption(core) trend/movement that's currently circulating on social media. This trend may start with getting people to use what they've already purchased, but along the way it can help people rethink a wide variety of spending habits.

3 Like

Ichabod Crane

Jan 30, 2025 at 3:24pm
In response to "An Eye For a Lie"

Thats just smaller windows.

2 Like

tj wanderlust-words-in-motion

Jan 30, 2025 at 3:23pm
In response to "An Eye For a Lie"

I've heard it said that the eyes are the window to the soul, except for those people with those beady little eyes...

3 Like

February 2, 2025 at 9:58am

#1083161

Revisited: "Friend"

Well, it's Groundhog Day. Again. It's also Sunday, so we get to dredge up something from the murky depths of the past.

Before I spin the wheels of the timeship today, a brief personal update. You remember how I promised myself I would drink every day in January, because the concept of Dry January deeply offends me? Well, remarkably, I did it. I actually followed through on a (sort-of) resolution, and managed to down at least one serving of alcoholic beverage every single day. Sometimes this meant taking a shot before midnight and then another one just after, but that's still "every day."

It was harder than you might think, knowing me. I really don't drink every day, usually. Still, I feel boosted, poised, confident, because I actually did something I said I was going to do, powering through despite naysayers and my inner critic.

I'll never be able to do that again. Fulfill a commitment, I mean. I'm absolutely drinking again, after I take a couple days off.

Anyway, getting back to the past now. In September of 2021, I featured a Cracked article about an interesting historical figure: "Friend"

The article it references is still available.

I haven't been sharing much from that source recently—certainly less than I used to—because it seems to have become more about promoting various TV shows than providing interesting articles. Whatever; it's bounced back from crap before. Like the elevator industry, it has its ups and downs.

As for the article itself, if "nonbinary doomsday prophet" doesn't hook you, nothing will.

I really wouldn't change much about what I said back then. The only thing that jumps out is when I wrote "No, no relation." That made perfect sense to me at the time, but I can see where it might have been confusing. I was referring to the name Jemima, and joking about the person being no relation to Aunt Jemima.

So I'll just comment on one quote from the article that I left out back then:

This good news was that the world would soon end. Which might sound like bad news to some people, but times were tough in the 18th century, before Bluetooth and deodorant, and many were happy to hear Jesus was about to destroy everything and spirit us away.

It has, of course, been a perennial American tradition for some doomsday prophet to come out of nowhere testifying for the end of days or whatever. It's happened again and again. Sometimes, it even happens outside of the US, but as with hamburgers and Black Friday, we do it more and better than anyone else.

And they keep getting followers for it. I'm sure lots of doomsday prophets have popped up and, for lack of charisma or maybe just being introverted, didn't get the cultists they needed to become famous. But again and again, we've been subjected to end-of-the-world prophecies, with some prophets even declaring the exact date and time of the Rapture (or whatever), which, as I understand things, should be grounds for God to zap them with a lightning bolt.

Or is that Zeus? I forget.

Anyway, the point is, for a country that claims to love freedom and individuality, some of us are remarkably susceptible to following prophets of the End Times. And not just the religious kind, either. Nothing like a good scientific doomsday story, like the imminent Yellowstone Supervolcano (not actually imminent), the certain destruction of the biosphere by climate change (not going to be sudden), or maybe the impending supernova of Betelgeuse (won't have a damaging effect).

But, face it, it's mostly the religious kind that gather minions and cause problems for everyone else. But sometimes we get great stories out of it.

3 Like • Comment • View 4 comments

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