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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

a day 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

a day 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

a day 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

Apr 24, 2024 at 4:26pm
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

Apr 23, 2024 at 6:51pm
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?

September 14, 2020 at 12:03am

#993295

The Inner Fright

Waking up to find it was all just a dream is the cheapest ever way to end a story.

PROMPT September 14th

You just woke up to discover you had dozed off in your 3rd grade class... how would you react realizing your entire life since then was just a dream?

I mean, I guess it worked for Lewis Carroll. But it's not the kind of thing the rest of us can get away with.

I have trouble sleeping when I know I have an alarm set. I've been known to sleep right through alarms. I'm not on a regular work schedule, so I no longer wake up at the same time every weekday, and that compounds the issue. If I have, say, a doctor appointment at 9:30 then I have the alarm set for 8:00 or whatever, even if I go to bed at midnight (way too early for me), when it goes off, I get up and slog to the shower. Along the way, I notice something: the light is dim, or some of the clutter on my nightstand is missing. That's when I realize I'm dreaming. To prove to myself that it's a dream, I will myself to rise up through the ceiling. Once I do that, I wake up for real and check the time. Whew - only 6 am. Still plenty of time to catch some more Zs before I have to wake up. I wake up again, and it's 9:45. Oh shit, I've missed the appointment! Wait... no. It's dark. I'm still dreaming. Levitate. Yep, dreaming. Then the alarm goes off, and there's someone in the room with me who's not a cat. Sigh. Dreaming.

Finally I wake up and it's 7:55, and I haven't gotten any decent sleep and I can't levitate so I know I'm not dreaming. Five minutes isn't anywhere near enough, so I get up and take a shower -- during which the alarm goes off because like an idiot I forgot to turn the blasted thing off.

I say "alarm" but I just use my phone these days.

The point of all of this is to relate that the whole "butterfly dreaming I'm a man" conundrum never made sense to me. Even if my mind starts out thinking a dream is reality, eventually there's some discontinuity that makes me realize I'm dreaming. Rarely, I can use that to my advantage and have a lucid dream, like my own personal holodeck. Usually, I just wake up, or at least I think I do.

Reality is persistent. That's how we know it's reality.

So if I woke up one day from a nap in a classroom and I'm eight years old, my first reaction would probably be that this is just another nightmare, and pretty soon I'll wake up for real, safely NOT in Miss Martin's classroom.

Miss Martin was one of those bachelor teachers of the old mold, with the pointy glasses and seventeen cats at home. Think Dolores Umbridge, but in green instead of pink. Possibly she was gay, but more likely she spent her adult life teaching assholes like Kid Me and decided that having children was not for her. Her like will never be seen again in our time, and that's a shame, but I have no good memories of that school year.

This whole thing kind of reminds me of the great ST:TNG episode "The Inner Light." In it, Picard falls into a deep coma on the bridge, and wakes up to find he's living a life on a pastoral planet. He lives the rest of a very long life on that planet, with a wife and kids, and the show expertly compresses something like fifty Earth years into less than an hour of runtime. I mean, really, if you watch no other Trek, that one's worth it by itself. Point is, spoiler alert, he finally wakes up back on the Enterprise and he's in his whatever decade Picard was supposed to be on TNG. Forties, I'd guess. But he's retained all the memories of this other life, even though it was, for all intents and purposes, a dream. The exact mechanics of this involves hand-waving some alien technology, which is kind of a specialty of Trek, but the salient character point here is that to him, it was not a dream.

And so I would hope it would be for me in the purely hypothetical situation outlined in the prompt above: that I would have memories of this life, know what was coming. I mean, in the episode it turned out that everything he experienced in his mind were based on things that happened long ago, but the parallels remain. That is, assuming that this new reality turned out to be persistent and not, in fact, a nightmare.

Consequently, as soon as Apple became publicly traded, I'd dump every last meager dollar fourteen-year-old me had into it.

And then with my luck, it would go bankrupt in that timeline.

13 Like • Comment • View 7 comments

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