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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

May 18, 2024 at 7:40am

#1071313

What's the Opposite of Eureka?

Now, here's a kid who's going to be subject to government scrutiny for the next few years.

13-year-old has eureka moment with science project that suggests Archimedes’ invention was plausible

After which they'll probably recruit him.

Often called the father of mathematics, Archimedes was one of the most famous inventors in ancient Greece, with some of his ideas and principles still in use today.

While there is no doubt that Archimedes made important contributions to mathematics, calling him "the father of mathematics" is rather insulting to earlier mathematicians, not to mention horrifically Eurocentric.

But one fabled device has left scientists speculating on its existence for hundreds of years — the death ray. Now, a middle schooler may have some answers.

Hey, when I was that age, I was fascinated by death rays, too. But this was a simpler time, and as far as I know, I wasn't subject to government surveillance for my hobbies.

Brenden Sener, 13, of London, Ontario, has won two gold medals and a London Public Library award for his minuscule version of the contraption — a supposed war weapon made up of a large array of mirrors designed to focus and aim sunlight on a target, such as a ship, and cause combustion — according to a paper published in the January issue of the Canadian Science Fair Journal.

Also, calling it a "death ray" is probably sensationalism. Most sources I've seen use "heat ray," but I think even that is misleading. Regardless; the point is, people have argued over whether Archie could have actually constructed the weapon using Greek technology of the time, or if perhaps it was speculation (similar to da Vinci's later speculation about flying machines or whatever). Hell, René Descartes dismissed the idea.

There is no archaeological evidence that the contraption existed, as Sener noted in his paper, but many have tried to recreate the mechanism to see if the ancient invention could be feasible.

Absence of evidence isn't evidence of absence, of course. Oh, and no one, as far as I know, is saying the idea is unworkable; only that it might not have been feasible using tech available in the 3rd century BCE.

At the same time, evidence that it could have been built and used isn't the same thing as evidence that it was built and used.

The article describes his setup, and then:

Writing in the paper, Sener said he found these results to be “quite remarkable as it suggests that light is going in all directions and that the shape of the concave mirror focuses the light waves onto a single point.”

Well... that's a bit disappointing. Was CNN clickbaiting us with that headline? While this is certainly what I'd call a good middle school science fair project, it's not like we didn't already know that focusing light rays intensifies the resulting temperature. Hell, all this is, is the reflection version of using a magnifying glass to burn ants.

While the experiment doesn’t offer “anything significantly new to the scientific literature … his findings were a nice confirmation of the first law of thermodynamics,” which states energy or heat can be transferred, Ho said.

Blink. Blink.

Look, I'm not trying to diminish the kid's accomplishment. Hell, I couldn't ever come up with an idea for a science project at that age. It's not that I wasn't interested; it's that I wasn't creative enough. Still not. But it proves nothing about Archie's heat ray.

2 Like • Comment

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