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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?

March 1, 2021 at 12:03am

#1005530

Cry Wolf

Finally, the despicable month of February is over. To celebrate, I thought I'd do another Merit Badge giveaway; see below. But first a word about a word.

Never Say Wolf
How taboo language turned the wolf into a monster.

The article is fairly long, but intriguing to me because I've been fascinated by taboo words for a very long time.

The howl of the wolf, and the fear that accompanies it, sounds across millennia. Comparing the mythologies of cultures that descended from ancient European tribes, wolves loomed large in their minds. There are myths of heroes brought up by wolves, of great wolves who will devour the sun, of wolves guarding the underworld, and of warriors taken over by the spirit of wolves.

If you've ever seen a wolf -- or, on a cold winter night, heard one in the distance -- you can understand this.

Speakers had to find ways of referring to wolves without naming them. The word for wolf becomes taboo: It shouldn’t be said. Instead, the magic of summoning through a name can be tricked. By changing the sound of the word, by using another word, perhaps borrowed from another language, or by using a descriptive phrase rather than the word itself, speakers could talk of wolves, but avoid the dangerous word itself.

This article focuses on wolves, but there were similar taboos for other feared animals, notably the bear. If you can stomach another article about linguistic taboo, here's the story

of the words used to describe ursines.

What fascinates me, though, is that it's not just the feared that become linguistic taboo. The sacred and the profane both get the same treatment. Notably, the original Hebrew pronunciation of the word for "God" has been lost to time. At the same time, we're always coming up with new ways to say curse words to get around peoples' sensibilities (such as "Holy forking shirtballs" made famous by the hilarious series "The Good Place.")

Another example from modern times is the word "retarded." It's taboo in many circles now, but I have no problem using it. I understand that the word was coined as a value-neutral way of describing someone who's mentally challenged, or "slow," hence the Latin-root "retarded." Before we had "retarded," there were three words with precise definitions: idiot, cretin, and moron. I forget which is which now, but each one of those words were assigned to people who tested at certain points of the below-average IQ scale. Then, being assholes, people started tossing those words around with great abandon, using them to simply describe someone they didn't like. "That guy's an idiot." "She's a moron." That sort of thing. "Retarded" was meant to replace those words, but of course, being assholes, we started using it to describe people and situations we didn't like.

Once that fell out of favor for that reason, they started using the word "special" as in "special education," the idea being, I suppose, that you take a word with positive connotations and maybe people will stop being assholes to the mentally challenged. And so, of course, now you can't call someone "special" without implying, deliberately or otherwise, that they're a moron.

My prediction is that there is no word or phrase that we can come up with to describe that condition which will not eventually become stigmatized.

And, of course, there's the word that cannot be uttered, the one that was used to dehumanize an entire group of people.

I, personally, came up with certain taboos myself. For instance, I almost never name the seventh planet, you know, the one orbiting between the orbits of Saturn and Neptune. This is because assholes just can't help making stupid puns about it, regardless of how it's pronounced (you have a choice between "Yer Anus" and "Urine Us," unless you want to get all Ancient Greek and pronounce it Our-Ahn-oos, at which point no one will know what the hell you're talking about).

Anyway. Point is, "wolf" is a case study for taboo word modification. You have a word, everyone knows it, but you don't want to bring down evil spirits (or public outcry, in modern times) so you use a different word. That one becomes the default word, but you don't want to bring down evil spirits, so you change the word again. And so on until some hypothetical future time when people stop being assholes. Or superstitious.

Merit Badge Mini-Contest!

I thought about asking for other examples of taboo words, but then I remembered that this blog is rated 18+ so most of the fun ones are off limits -- another variant of taboo against certain language. And you can do that in the comments if you want, if you can think of one that won't break the rating. Or you can talk about wolves or bears or planets or whatever. But as it is a) no longer February and b) at some point over the last few days, this blog ticked past 100,000 views (a pleasant milestone and I appreciate the support), as long as you comment below, today, you have a chance. The comment should have *some* relevance (that is, just posting something like "I hope I win" won't count), and I'll pick a relevant comment at random and give the person a MB tomorrow.

As always, the deadline is midnight WDC time tonight, at the end of Monday March 1. And I'll do this again, so you'll always have another shot at it.

2 Like • Comment • View 4 comments

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