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Thursday, Apr. 25, 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:

Aiva Raine

about 9 hours 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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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?

Aennaytte: Free & Wild in GoT

a day ago
In response to "Going to the Dogs"

I have never been to New York, but it seems that my assessment years ago that Berlin, Germany and New York have some similarities. Both cities are known for being inhabited by rude people. And both places, as I now found out, are dog obsessed. And they have high rents.
Berliners though, have a habit of letting their dogs run off leash. Maybe New York is a little better than Berlin in that regard.

1 Like

Robert Waltz

Apr 21, 2024 at 1:48pm
In response to "Revisited: "Hack This""

Wordsmitty ✍️, far be it from me to speculate on the motivations of space aliens, but why in Xenu's name would they do such a thing to the universe?

1 Like

Wordsmitty ✍️

Apr 21, 2024 at 1:39pm
In response to "Revisited: "Hack This""

I thought humans got bigger brains because extraterrestrials affected our evolution, and we eat processed chicken and eggs.

1 Like

February 5, 2021 at 12:02am

#1003671

Savvy This

Kids these days with their slang...

14 Colonial-Era Slang Terms to Work Into Modern Conversation

Curious, I looked up the word origin for "slang."

Dictionary.com: "mid 18th century: of unknown origin."

M-W: "origin unknown " ... "The first known use of slang was in 1756"

My money's on it being a contraction, s'lang, short for something like "side language" or "short language" or something beginning with the letter s. But until we invent time travel (which won't happen), we'll probably never know.

The point is, this article is about American colonial-era slang, which oddly enough coincides with the same period when the word "slang" appears to have been coined -- but the word itself is probably older, because these things tended to be used in conversation before they were written down (as opposed to today, when we get most of our argot from the internet). And the concept of slang, the use of informal words and phrases in everyday conversation, is surely older than the word used to describe it, and might even be as old as language.

An argument could be made that language depends upon slang to evolve... but I'm not qualified to make or defend such an argument. It's just something to think about.

Anyway, back to the linked article, which is about a year old but what difference does it make?

But the Colonial Period—which stretched from roughly 1607 to 1776, starting when America was just a group of colonies on the east side of the continent and ending with the Revolutionary War and the signing of the Declaration of Independence—was a fascinating but complicated time in which settlers from England forged a proud new identity. These new settlers brought the English language with them when they came, and whenever English finds a new home, it often takes on a new life.

Or as I like to put it, the British invented it, and we perfected it.

1. Kedge

What It Meant: Doing well

I'm feeling pretty kedge today, so this entry isn't going to be too depressing.

Don't worry; I'm not going to list all of them. Just go to the article to see more.

6. Fishy

What It Meant: Drunk

Possibly no one invented more ways to say “drunk” than colonial Americans. Benjamin Franklin alone compiled 200 ways to say it.

Ben Franklin: Still my favorite Founding Father. Sorry, Alex. We always need more synonyms for "drunk." In college, we called it getting cabbaged. Hell, it's a lot like the situation with reproductive organs: one can adapt a wide variety of words for the purpose. "I got writ last night." "After an evening of getting completely astronomical, he almost regretted it the next morning."

Bonus points if the word you adapt for this purpose is in an obscure foreign language. "I'm going to get completely danchu tonight."

Okay, Mandarin is the polar opposite of "obscure." Still. (According to the googles, "danchu" means "to fade out," as in the end of a scene in a movie, or to fade from memory. What? It's appropriate for describing getting plastered.)

9. Savvy, Savey, or Sabby

What It Meant: To know or understand

While we still use this word to mean something like “literate” (computer-savvy), in Colonial times, it was actually used more like the way Jack Sparrow uses it. So you might say, “I don’t want to come to work anymore, savvy that?” According to Merriam-Webster, it’s derived from sabe, which means “he knows” in Portuguese.

I can't be arsed to trace it all the way back, but another source lists Spanish as the origin for this word. There's a similar verb in French, "savoir," "to know," which in at least one of its conjugations is "savez" which is pronounced a little bit like "savvy" only with the emPHAsis on the other sylLAble. I can only assume that what with all of these Romance languages using a similar verb that it came from Latin, because I've forgotten most of the Latin I ever knew.

Anyway, I knew the word long before Pirates of the Caribbean came out. I guess you could say I was savvy.

14. Circumbendibus

What It Meant: Roundabout

Of all the ways to describe something unnecessarily roundabout— like someone telling a rambling story or taking a weird road when driving somewhere—this word, which dates to 1681, might be the most delightful.

I absolutely need to work this into my vocabulary, since a lot of these blog entries are circumbendibus.

Now it's time to get fishy.

9 Like • Comment • View 10 comments

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