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Saturday, Apr. 27, 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:

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
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

Apr 25, 2024 at 3:09am
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

Apr 25, 2024 at 2:58am
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?

March 17, 2024 at 9:27am

#1066413

Revisited: "Power"

When I do these Sunday retrospectives, I can usually find a lot of things in common with the guy who wrote the earlier blog entry. The further back in time I go, the less I find in common, but such is life.

This personal update, though, from February of 2008, is tough for me to relate to, and difficult to re-read: "Power"

The wind has been crazy here, today. It started sometime during the night, whistling between the houses and threatening to spin my attic vents right off.

While I still live in the same house, I've replaced the roof since then, and goodbye old-fashioned spinning attic vents.

When I woke up, at around the crack of noon, it was still going on.

I'm always a late to bed, late to rise person, but, with age, my ability to sleep until noon has vanished.

I figured I'd grab some breakfastlunch and go write this week's Comedy newsletter.

Well, I'm still writing Comedy newsletter editorials, at least. I'm not sure if this is a good thing or a bad thing.

That, of course, is when the power went out.

I've since purchased and had installed a whole-house generator, an automatic start one hooked up to the city gas line. While I justified it to myself and others with my medical devices and a basement sump pump that tends to be most necessary at the times when the weather's lousy enough to cut the power, the real reason is so I never lack internet access.

I'm sure the neighbors appreciate the blast of a nat-gas engine cranking up and running like a combination leaf blower / lawnmower every time we lose electricity, but if anyone ever said anything to me, I'd absolutely claim medical necessity.

Now, I don't have my truck this weekend. A friend of mine is using it to move.

I don't drive pickups anymore, either. And that's one of the reasons why: someone inevitably asks to borrow it or, worse, me.

My wife was out in her car, so I was stuck.

No longer married, either.

I worked some crosswords for a while, but then started feeling antsy about getting the newsletter in.

I miss old-style paper crossword puzzles. Probably they still make them, but there's plenty to do on the internet.

So I called my wife to drive me to my office.

Nor do I have an office. Or a business. Or a job. (My choice.)

I booted up my computer, checked some email, started looking for items to include in the newsletter (funny things about romance, mostly - it's the Singles Awareness Day issue of the Comedy newsletter), and the power went out.

Well, I continue to rag on Valentine's Day most years in the Comedy NLs. Again, good or bad thing? I don't know. With my memory the way it is, I'm sure it gets repetitive.

Before we went home, though, we visited the hospital, where my dad's still being treated for his UTI.

Dad would go on to pass on the following month. Not of the UTI.

When the doctor called back, she said, "I don't know too much about that patient. UTI. Tested positive for influenza. Going to have to keep him at least a couple more days. Did they make you wear a mask in the room?"

As a reminder, this was 2008, long before masks became a political statement and were merely an effective means of helping to prevent disease transmission.

"Oh, and there's some question about whether we can send him back to assisited living or if he'll have to be moved to a nursing facility."

Wow, a rare misspelling. Eh, it happens. And I'm certainly not going to edit out that wart at this late date. Anyway, as I recall, they eventually moved him back to the assisted living facility (which specialized in Alzheimer's care).

He didn't die of the flu, either. Which would have been an irony I would not have appreciated. See, he had been born in New Orleans in 1917. A year later, his mother, quite a young woman at the time, dropped dead. The family never told me more details than that; when I was a kid, I just accepted that dying is what grandparents do.

It wasn't until much later in life that it dawned on me: New Orleans. 1918. Death of a young person. Oh... right. Spanish Flu.

Not going to leave you in suspense. Official cause of his death was "complications from Alzheimer's."

But I got home and did the Comedy newsletter anyway. Sometimes you just have to be funny, even if there's nothing left to laugh at.

And that philosophy, folks, seems to be the one thing about me that does not change.

There's a kind of power in that.

2 Like • Comment • View 1 comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
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