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Saturday, Jun. 1, 2024

12:57pm EDT

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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 17, 2024 at 9:45am

#1062540

In Decision

Here's a pretty recent one from Cracked. Mostly just because I felt like sharing it.

4 Times Corporations Invested in the Exact Wrong Thing

The title is maybe a bit misleading, but close enough.

Making decisions has to be one of my absolute least favorite things to do. That’s why I try to avoid it at all costs.

Would it help to know that your decision is already made, but you just haven't caught up to that moment in time yet?

And the more decisions matter, the more they suck. Picking a cereal to start your day with is a decision, but given the general futility of life, who really cares? Realizing halfway through a bowl of Cap’n Crunch that you really would have preferred Froot Loops is just another thin cut delivered by the blade of life.

I avoid this by not having cereal in the house.

It’s when you’re faced with decisions that really influence the future of your life or business that you get to experience the full cocktail of stress and anxiety.

Hence the relevance to the article's content. Though sometimes the wrong decision turns out to be not deciding at all.

4. Sony Backing Betamax

Given that plenty of people under 30 probably don’t even remember VHS tapes, I’m going to wager that Betamax rings even less bells. It’s an old, cursed technology, that barely made the cut for my 33-year-old brain, much less Zoomers’.

We really need to teach history better.

Anyway, yeah, so Sony backed the losing technology. They're still around, though, unlike the next fool:

3. Borders Gives Amazon Its Business

The biggest mistakes they made? First was not investing in or offering e-books, and the second was outsourcing all their online book sales to a little company called Amazon.

Yeah, I'm gonna call that one of the worst mistakes of all time.

2. Kodak Doesn’t Go Digital

This one's pretty well-known.

In 1975, a Kodak engineer named Steve Sasson invented an early digital camera that could record images electronically onto tape and display them on a TV screen. He showed it to executives, who gave it a resounding thumbs down, because it would ruin their ability to sell film, a big part of their business.

So someone else went to market with it, and the tech steadily improved, ruining their ability to sell film. If only they could have seen the writing on the wall. (Okay, that might be an obscure reference.)

1. JCPenney Respects Its Customers’ Intelligence

I'd have titled this "JCPenney Overestimates Its Customers' Intelligence." I mentioned the 1/3-pound burger fiasco a few days ago in here, and that people were so abysmally ignorant that they thought it was a worse deal than a quarter-pounder because, clearly, 3 is less than 4. Well, this is similar.

It turns out that they do not want a $40 waffle maker, they want a $40 waffle maker they can tell people was worth $80, and if they don’t get it, they will figuratively burn your store to the ground. Sales dropped 20 percent, and one ex-customer with a real peach of a brain explained, “If I don’t get a special discount, it’s not worth the trip.”

No, I'm not calling YOU stupid. Anyone who reads this blog is automatically smart, attractive, and talented, if only by association. But goddamn, the vast amorphous bulk of consumers are idiots to the core.

Anyway, I'd add one more to this list: Sears. They built a sales empire on mail-order, sending catalogs to the farthest reaches of the US and Canada, and probably beyond, I don't know. At one point, they were mail-ordering houses. I'm not kidding. They got so huge that they built and occupied what was then the tallest building in the world.

And then the internet came along, and they didn't keep up.

There are probably lots more, of course. Most decisions are going to turn out to be bad ones, or at least neutral, which is why people like me and this article's author avoid making them whenever possible. Which is also going to be a bad decision, but whatever, at least then it's not my fault.

8 Like • Comment • View 1 comment

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