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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 16 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 16 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 16 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

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 13, 2020 at 12:01am

#1000143

I Scream

"30-Day Blogging Challenge ON HIATUS" [13+]:
13. National Ice Cream Day
What are your favorite flavors, weirdest flavor you've ever tried, or a flavor you would NEVER try!

"JAFBG" [XGC]:
Do you think the holiday cheer is genuine or do you think most people are just acting fake around this time of year?

Well. I'm still choosing JAFBG prompts at random here. I was kinda hoping to land on this one to go with today's 30DBC prompt.

See, my favorite ice cream flavor is...

Vanilla.

Now, I know what you're thinking. "But Waltz, vanilla is the most boring flavor!" If you think that, then you haven't had real vanilla. Only fake vanilla.

See why it's appropriate now?

Look, I'll be the first to admit that I have a weird palette. I can't stand coffee, for example -- though if it's combined with other stuff, like when they put it in beer, especially a stout or a porter, sometimes it works for me. And my taste buds are surely affected by the cigars I smoke - which, also, are a result of having a weird palette; unlike many people, I truly enjoy the taste of tobacco.

I've spent years working on identifying flavor overtones in beverages such as wine, beer, whiskey and tequila. I don't always succeed. When it comes to beer, though, I'm also an outlier: I don't appreciate the same kinds of beer as the majority of other beer snobs. One really popular style, for example, is IPA -- and after having conducted a number of beer tastings, I can identify the thing that puts me off in IPAs: the presence of Cascade hops.

Cascade hops tend to impart an astringent citrus flavor to the beer they inhabit. To me, they taste like grapefruit. And I dislike grapefruit. Oh, I've eaten it, even drank grapefruit juice on purpose, but it's never been something I sought out. That is, until I started taking a statin, at which point, for the first time in my life, I craved grapefruit juice, simply because it was forbidden to me.

Well, that was a few years ago, and I'm over it now. So if you give me a beer with Cascade hops, well, I'll still drink it -- it is, after all, beer, and since you're giving it to me, it's free beer, which is the best kind of beer. Though, to quote Marvin from Hitchhiker's: "I won't enjoy it."

But it's been a trend in beer for many years, and apparently Cascade is one of the cheapest varieties of hops, so a lot of brewers use it. I'm not one to follow trends blindly, though. There are things I like, things I don't, and things (like tomatoes) that I can take or leave, and none of that is dependent on what other people like. In other words, I don't care to fake it for the sake of conformity. There are, as an aside, a few IPAs that use other kinds of hops, and those I don't mind so much.

And thus it is that I proclaim: I like vanilla ice cream. Not that I eat a lot of ice cream these days, but that's all the more reason not to eat the stuff I like less. I'm also a fan of chocolate ice cream, which is far more widely enjoyed, I think -- but the best chocolate has vanilla overtones as well.

At the same time, I can't say I've ever had a flavor of ice cream that I didn't like, to some extent, which is actually more than I can say for beer. Still, I don't think I'd like coffee ice cream. I would totally try it, though, because how do I know if I don't try?

But again, there's real vanilla, which is delicious, and there's the synthetic crap that is probably what gives vanilla its bad reputation. Either way... it is not "plain". Not by a long shot. Real vanilla has a subtle, ephemeral flavor that fills the mouth and coats the tongue, while the fake stuff tastes, to me anyway, like medicine.

Still, I can't say whether other people are pretending to like these things that I don't like, or if they actually enjoy them. I've had some coffee drinkers swear that it's like ambrosia to them, while others have mentioned that they don't really like the taste; they just drink it because it's convenient, ubiquitous, and caffeinated. I can respect that, too; it's just that I use tea and Crack Zero for my wakey-wakey juice.

Which is another thing. To me Crack Zero tastes just like Crack, only a bit less cloying. Other people have had the stuff and despise it.

Incidentally, if there is a worse commercial soft drink out there than Vanilla Crack Zero, I have never encountered it. That stuff is absolutely horrible. I'd say it tastes like ass, only that would be an insult to ass.

I think they use fake vanilla.

Point is, I'm honest with myself and others about my tastes, and I don't do things just because they're faddish - though I've participated in fads that suit me; I don't usually shun something just because it's popular. Which is why I can't really comment on the "holiday cheer" prompt. I'm sure there's a lot of fakery out there, but even if so, I get the feeling that it's a "fake it til you make it" kind of fakery, like the idea that if you engage all the muscles in your face to force a smile, the effort alone can be enough to make you happy.

And if you need that to keep going through the dreary pre-solstice period? Please, go right ahead. Just don't call me Scrooge or Grinch for not following along.

Or do. Whatever. I always have to stop the original Grinch animation before the point where his heart grows. What even is that, anyway? That happened to me once and I ended up in the hospital for it.

There's a certain kind of honesty in fakery, anyway. I know a lot of people complain about other people being "fake," but to me, they're making an effort, and that takes some level of commitment. Like, if you're naturally grumpy but you act all cheery just to get along with people? I'm okay with that. Outright dishonesty can piss me off, but if you're trying to get along, well, that means that you care enough to try.

I'll end with a short anecdote. On one of my cross-country trips in the Before Time, I ended up in Aurora, Colorado. Colorado in general is well-known for its diverse beer ecology; there are many excellent breweries there, though I have no idea how many of them have survived this fucking year. Anyway, this one brewery I hit right around sunset, and there weren't a lot of people around, so I got to talking to the bartender, as is my habit. He quickly pegged me as a beer guy and gave me a bit of their secret stash, which on that day was a stout made with vanilla, chocolate, and cinnamon.

I took one sip of that, and my eyes went wide in appreciation. I turned to the bartender and said, "This needs ice cream."

Any flavor would have worked. But alas -- I had to drink the stuff on its own.

7 Like • Comment • View 3 comments

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