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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:

Kåre Enga in Udon Thani

about 13 hours ago
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

about 13 hours ago
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

about 13 hours ago
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

about 23 hours ago
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

a day ago
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

August 1, 2020 at 12:02am

#989626

Remember, Remember

Apparently, today's premiere virtual travel blog challenge is about camping in Antarctica. Clearly, this month's challenge is SO not for me.

Instead, why don't we talk about memory?

https://www.mentalfloss.com/article/585887/mandela-effect-examples

10 Examples of the Mandela Effect

Would you believe us if we told you the most famous line of 1980’s Star Wars sequel, The Empire Strikes Back, was never uttered? Darth Vader doesn’t reveal his paternity to Luke Skywalker by saying, “Luke, I am your father.” He actually says, “No, I am your father.” The line is but one instance of what blogger Fiona Broome dubbed the “Mandela Effect” a decade ago, after she learned that a number of people shared her erroneous belief that human rights activist Nelson Mandela had perished in prison in the 1980s.

Also, McCoy never once said, "He's dead, Jim" in the original Star Trek.

The Mandela Effect is basically just false memory writ large. It happens to all of us -- perhaps some more than others. But these particular accounts are more than just one person's false memory; they're shared by many people.

This is not the same as lying. This is something that people actually remember, but they remember it incorrectly.

With apologies to conspiracy theorists, the idea of a shared false memory isn’t proof of alternate realities.

Yeah, I wanted to quote that here because it really isn't proof of alternate realities. We have no proof of alternate realities.

1. The Monopoly Man’s Monocle

For decades, Rich Uncle Pennybags (or Mr. Monopoly) has been the de facto mascot for Monopoly, the Parker Brothers (now Hasbro) game that somehow made real estate exciting.

And also somehow ended numerous relationships.

2. Jiffy Peanut Butter

If you looked forward to your school lunch break because your parent or guardian packed a Jiffy peanut butter sandwich, your childhood may be a lie.

I don't think I ever thought there was a "Jiffy." I distinctly remember the very effective line from the Jif commercial when I was a kid: "Choosy mothers choose Jif." Of course, that memory could have been falsified also. I could probably find one of those old commercials on YouTube to check it, but I can't be arsed.

I'mma skip a few here, but I think you get the idea. Or you could, you know, click on the link and read the article.

9. Risky Business

Remember Tom Cruise dancing in his underwear, a dress shirt, and Ray-Bans while home alone in 1983’s Risky Business? Your brain got most of it right.

I never really gave that much thought. I mean, sure, it's a memorable scene, but... shades or no shades? Never even thought about it until I saw this article.

I spent most of last week rewatching all of the Mission:Impossible movies. If you'd told me after Risky Business that I'd be a fan of a rebooted M:I with Tom Cruise in it, I'd have laughed.

Should these processes that lead to false memories be considered flaws? Not exactly. Current theories in psychology are exploring the idea that our ability to cull details from past experiences to create theoretical concepts is actually part of a survival mechanism.

Let's just say I'm skeptical. Not everything has an evolutionary explanation. Some things are just kind of hangers-on, neither beneficial nor detrimental. It's clear that memory itself has survival value, but obviously it's got its flaws. It is often better to remember something poorly than to not remember it at all -- but when it comes to something as useless as movie quotes or whether or not a game mascot has a monocle, I'd expect it to be irrelevant to the course of evolution, which after all is only a process by which species either continue or not.

Still, we know that memories are suspect. This has important consequences. A few decades ago, there was a massive moral panic about Satanic abuse at day care centers. It was all over the nascent internet, as I recall (which may not mean much). Turned out to be false memories; no evidence of ritual abuse was ever uncovered apart from the faulty reminiscences of supposed victims, which were induced by some shrink or something. And yet, during this panic, several people lost jobs and reputation, at the very least, and may even have gone to prison over it. I don't remember.

And yet, if someone tells you a story that turns out to not be true, maybe don't immediately jump to the conclusion that they're lying. Memory isn't a video tape; it's more of a cobbled-together hologram of chaos. (Hologram of Chaos can be the name of my Journey cover band.) So it's likely that it is the truth as they remember it; they just have no idea they're remembering it wrong.

And at the same time, none of us can fully trust our own memories.

This can be a scary thought, I know, but I've learned to come to terms with it. At least I think I have.

The only instance of false memory that I can think of offhand is that sometimes I'll remember a quote from a book or movie, and the next time I read the book or see the movie, it'll turn out I was wrong about it. But I'm pretty damn sure a lot of my memories are wrong, conflated with other memories, or otherwise suspect.

How about you? Have you experienced the Mandela Effect or discovered any false memories?

4 Like • Comment • View 3 comments

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