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Friday, Apr. 26, 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

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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

a day 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

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?

December 4, 2020 at 12:01am

#999616

Barbaric

Well, this is an interesting combination. Let's see how it turns out, shall we?

"30-Day Blogging Challenge ON HIATUS" [13+]:
4. Waiting for the Barbarians Day!
Ok, tell us what you're up to and how you are preparing.

"JAFBG" [XGC]:
What was the worst gift you ever received and what was that person even thinking when gifting it to you?

A while back, when I was still married, there was some fad going on around the holidays involving group gift swaps. For all I know it's still going on, but I wouldn't know because even before the pandemic I rarely hung out with people around the holidays, except for my friends in California, and they had the great good sense not to participate in this activity.

I don't remember what it's called. Gift stealing? Something like that. Some of you probably know and can remind me in the comments. But as I recall, it goes something like this: Each person brings a themed gift, usually with a price cap. Like, maybe the theme is "red" or "fish" or "barbarians."

This particular gift swap was hosted by my then-in-laws. (Hey, can I claim credit for "then-in-laws?" I don't think I've seen it anywhere.) Since we all lived in Virginia, the theme for this one was "Made in Virginia," and the price cap was like $25 or something like that. Like I said, I don't remember too many details, including what I or my wife brought. No, ham wasn't involved. There might have been Virginia wine; I honestly can't recall.

So, like, all our names go into a Santa hat on little slips of paper, and one name comes out. That person picks a gift and unwraps it. Okay, great so far. Next random person can either pick a new, wrapped gift from the pile, or steal the first person's gift, which means the first person has to pick another wrapped gift. Third person can then pick a new gift or steal one of the first two. And so on. I think that when all the gifts are gone, the first person gets to swap with any of the now-unwrapped presents, because they didn't get a chance to steal before this.

Anyway, what I recall about this is that I started out with something really nice that I don't remember, and ended up with a giant can of Virginia peanuts.

I fucking hate peanuts. I mean, I hate them with an all-consuming fiery passion (for some reason, though, I like peanut butter; go figure.) If I were an asshole -- okay, if I were a bigger asshole, like the kind of barbarian who claims their annoying little yippy mutt is a service animal so they can bring them into restaurants, or the like -- I'd claim I was allergic to peanuts just so no one would break them out when I'm around. But I'm not allergic; it's just that my level of abhorrence goes off the scale. I avoid trail mixes with peanuts. I can't stand Snickers bars. Peanuts suck. Not only do I hate peanuts, but I loathe peanut breath more than is probably reasonable. If someone around me is eating peanuts, I'll go open a can of surströmming, pop a sewer manhole, or clean a cat's litter box just so I can smell something more pleasant than their exhalations.

(I do make one exception: Thai or Vietnamese food with peanut sauce. I don't know why, but they work for me in those cuisines. I justify this by classing it in my head as "peanut butter.")

Now, as far as I can recall, I never told my then-in-laws that. My wife knew, of course, and maybe she told them; I don't know. And like I said, I don't even remember the nice gift I started out with. But what has stuck with me all these years is the smug smirk on my shithead stepfather-in-law's face as he handed me this giant can of nasty legumes.

And even after all of that, I'm at a loss to find an artistic segué into the barbarian prompt. I mean, I could say something like "anyone who forcibly swaps me a can of hideous peanuts for pretty much anything can only be described as a barbarian," but that really does barbarians a disservice. At least most cultures commonly referred to as "barbarians" had their own code of honor, and this guy had no honor.

See, history was written not only by the victors but by people with the ability to write, and write in such a way that their writings stuck around a while. If your writing system consists of charcoal marks on tree barks, it's not going to last. If it's chiseled in stone or it's done with ink on parchment, well, then you get to define history, and so the people you don't like can get slapped with the "barbarian" label.

But people are people, and most of them have cultures that work for them, even if those cultures are not understood by the ones who call themselves "civilized." The most obvious examples are the Nordic people, who had a strong culture, but were feared by the more city-dwelling cultures as barbarians. To be fair, they did invade a lot. But just because you don't like someone doesn't mean they follow a failed culture; just a different one. Like... Europeans who settled the Americas considered the natives to be savages or barbarians, but from the native point of view, the invaders would have been the barbarians.

Except that some of these same American natives were the ones cultivating peanuts, so they obviously weren't completely blameless.

Point is, everyone's a barbarian to someone. Keep that in mind next time you're tempted to think some other culture is inferior in some way.

Oh, and Waiting For The Barbarians Day

commemorates a novel written in 1980, which sounds awfully pretentiously literary but I can't be arsed to delve into it further; also, according to my surely-infallible source, it's observed on November, not December, 4. December 4 is, among other things, National Cookie Day.

(I'm sure MirandaCookies COLLEGE SOON

will be happy to know this.) Just don't put any gods-be-damned peanuts in mine, thanks.

10 Like • Comment • View 7 comments

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