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Saturday, Jun. 1, 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:

Elisa the Bunny Stik

May 29, 2024 at 9:02am
In response to "Ordinary Average Guy"

I think we need to be careful about saying there's no difference in socializing between online and off. I saw the following in response to a comment about discussions of gender online and the stances taken by LGBTQ community members that are chronically online:

"Truth. I had to stop looking for queer spaces online because it was full of this and angry exclusion discourse. I found some queer spaces offline and it reminded me that most people are normal and chill."

This is a topic I will likely be visiting in my journal in July. I figured I'd at least get this response in here first as a warm-up.

1 Like

Elisa the Bunny Stik

May 28, 2024 at 1:46pm
In response to "Long in the Tooth"

I feel I was too busy as a teen to screw around in convenience stores. On the rare occasion I wasn't at school or working, I tended to hang out by myself. If I hung out with friends, it was usually at someone's house (rarely mine).

Elisa the Bunny Stik

May 27, 2024 at 11:42am
In response to "Olive It And More"

Every once in a while, someone will misread the order slip and give me green peppers, which are an abomination, instead of green olives.

They truly are an abomination. If you're going to put peppers on a pizza, make sure it's anything but those little soggy cardboard slice things. Hell, even poblanos would be a major upgrade.

1 Like

Elisa the Bunny Stik

May 27, 2024 at 11:38am
In response to "Coming Up the Pike"

Man, people on Fandom Secrets would be aghast at how much you like Strange New Worlds. Personally, I haven't seen much of it. However, I did watch an episode at the gym once and found it enjoyable. It gave me that fascinated feeling I had when watching The Next Generation as a kid.

1 Like

Elisa the Bunny Stik

May 27, 2024 at 11:13am
In response to "Burgundy"

I will admit that I'm not much of a wine drinker. I've had reds and whites but tend to prefer reds. Then again, when it comes to booze, I tend to prefer things that are more intense in flavor. White wines...tend not to be that way for me.

2 Like

Elisa the Bunny Stik

May 27, 2024 at 10:38am
In response to "Distrust the Process"

That being said, I do think that people going out of their way to demonize ultra-processed foods are causing just as many issues as lobbyists are. These folks' actions exacerbate eating disorders and nervous thinking around food insecurity in equal measure. I wish the conversation around this set of actions was louder.

3 Like

Elycia Lee ☮

May 27, 2024 at 10:31am
In response to "Distrust the Process"

To me, as long food is 100% natural, then it is healthy. Pretty much like fruits, veggies and rice. I know people have thoughts about whether rice is good or not, but it is natural food so... I shall go with that.

2 Like

Kåre Enga in Montana

May 25, 2024 at 3:13pm
In response to "Plan Solo"

I'm more introverted than extroverted, but my only apprehension involves language and cultural barriers.

I'm bi- or ambi- but... always annoying. I waver between wanting to be left alone and not wanting to be alone.

I make my adjustments as necessary.

But LANGUAGE and CULTURE: true barriers that can cause problems for some and angst for me. I love strangers but find it frustrating when I can't connect.

For Belgium: make those plans soon. Today's connectivity means booking lodging in advance. In the old days it was show-up-and-ask-if-they-have-a-room. Still possible but not recommended unless cost is not an issue.

I prefer staying in hostels but rarely join in 'events'. I have gone out with fellow travelers however.

Kåre Enga in Montana

May 25, 2024 at 2:58pm
In response to "Banned Camp"

I remember when the movie "Brokeback Mountain" received "F"s from folks who basically commented that they would never NEVER watch such filth. Even those who liked or enjoyed it missed the main theme of poverty (financial, cultural, individual...). Personally, I preferred the short story to the movie. Both made a point that America didn't/doesn't want to face: choice and lack of choice.

That said, if someone were to ban my poetry I could probably live off of the notoriety.

Burning at the stake though seems a more likely outcome.

2 Like

🌕 HuntersMoon

May 25, 2024 at 11:32am
In response to "Banned Camp"

"Any book worth banning is a book worth reading." Isaac Asimov

2 Like

January 6, 2024 at 9:27am

#1061966

At Last

Last year, I featured several articles about planets. Over time, I hit every one... except this one, which has been languishing in obscurity due to the inherent randomness of life. Well, not life, but my system. Anyway, here it is, published way back in September of 2019:

A Love Letter to the Last Planet
Neptune really deserves more attention, if you ask me.

Oh, it deserves more attention, does it? Well, I can't disagree, but it's not like we can just stroll over there.

You see, I fell in love with Neptune as a kid, back when I was in the second grade.

Dude, I like astronomy too, but he's too old for you.

We all had to read about a planet and tell a few sentences about why we liked it. I got assigned Neptune.

What if you turned out not to like it? Huh? Did the teacher ever think of that? "Jupiter's pretty, but its radiation would kill anyone within a million miles." "Everyone's fascinated by Mars, but there's nothing there." Or, you know, phrased the way a second-grader would.

And what if the teacher made them draw the planet? I mean, most planets are pretty easy. Circle. Appropriate color. Lots of black background. But whoever got Saturn would be in trouble.

Anyway.

In August of 1989, when Voyager 2 started sending back the first clear pictures of Neptune and its moons, the mysteries began giving way to marvels. Neptune is a world of giant methane storms and strange rings.

Coincidentally, I read an article recently which noted that the Voyager 2 pictures were false-color, giving Neptune a much deeper blue than it would actually appear to have in the unlikely event that there was a human hanging out nearby. Ah, here it is.

Looks way more like that other planet, the one I won't name.

So, then the article goes into some of the things we know about Neptune, and they are indeed Amazing Science Facts (well, to the extent that anything we know can be).

Something else even more wondrous happens in those deep layers of superionic ice. Carbon atoms get squeezed out of the methane molecules mixed in with the water, creating clumps of crystallized carbon. You probably know crystallized carbon by its more common name, diamond. According to laboratory simulations, the diamonds inside Neptune could have grown to be a meter wide. They are denser than the surrounding ices, so they sink downward toward the planet’s core.

That’s right: Inside Neptune, it is raining meter-wide diamonds.

Somewhere out there, according to some astronomers, is at least one entire planet made of diamond. I don't know, maybe it was like Neptune, but got too close to a star and its lighter materials blew away. Point being, diamonds aren't as rare on Earth as they try to convince us they are; and Out There, they're probably even less rare.

A diamond deserves a ring, and Neptune has several of them — five of them, in fact. Unlike Saturn’s rings, these are thin, dark structures around the planet, too dim to be observed clearly from Earth.

I also recently saw a JWST image of... you know, that other ice giant, which also has rings. Spectacular image.

That telescope was meant to peer into the farthest reaches of the universe, and yet they pointed it at what's, comparatively speaking, right next door.

Look, I'm purposely avoiding the puns, here. Just pretend I've already made the one you're thinking of.

So yeah, my adult self agrees with my 8-year-old self that Neptune is a fascinating place. Voyager 2 gave us only a taste of what it’s really all about. And Neptune is just the prototype of a whole class of Neptune-size planets that appear to be common around other stars.

When Voyager 2 did its thing, we had no evidence for planets around other stars. I mean, sure, we figured they had to be there, but no direct evidence. Now, we've found thousands.

In general, the more we know, the more we understand. Sure, there are probably higher priorities than a mission to Neptune. But that doesn't mean we shouldn't do it.

4 Like • Comment • View 1 comment

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