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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

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 28, 2024 at 9:35am

#1067075

What're Y'all Doin'?

I'm aware that language changes over time. But some things are just always wrong. For example, "alot" is not, never has been, and never will be a word, as in "I have alot of problems with spelling." One does not "loose" one's keys if they're misplaced; one can only "lose" them. "It's" is never possessive, and is always a contraction of "it is." But, being Southern, this one especially annoys me:

What's The Difference Between Y'all And Ya'll?
There's only one correct way to spell it, y'all.

The South is known for its laundry list of unique, quirky, cultural sayings, like "Bless your heart," "Too big for his britches," and "Well, I s'wanee," to name a few.

Okay, I've never heard that last one until now. I don't know everything, but damn if I'm not working on it.

But the best-known word in the Southern vernacular is probably our most-loved pronoun: y'all.

And make no mistake, it is absolutely a word. Modern English lacks a universally-agreed-upon second person plural, and the other candidates, with the possible exception of the very British "you lot," just don't work outside their regions.

The only proper way to spell the contraction of "you" and "all" is "y'all."

And that should be the final word on the subject, but I guarantee you, sometime soon, I'll see someone's typed it as "ya'll" and rage will boil up once again.

The article goes into why. Basically, an apostrophe serves two major purposes in English: possessives (for words that are NOT pronouns such as "it"), and to replace missing letters. There are a few edge cases, but they mostly involve borrowed words from other languages. "Y'all" is obviously not possessive, so the apostrophe replaces missing letters. The missing letters are "ou." As in "you all" contracts to "y'all."

I did say the apostrophe is not used for pronoun possessives, but here, "y'all" is an exception. If you're writing about something that belongs to y'all, it's "y'all's," as in "Where's [where is] y'all's [belonging or relating to all of you] tater tots?" (Never mind that it should be "Where are your tater tots?"; you gotta cut people a bit of slack.) For context, one might ask a helpful grocery store employee this question, usually while standing right next to the freezer containing the tater tots.

Though, to be fair, Wikipedia

asserts: "The possessive form of y'all has not been standardized; numerous forms can be found, including y'alls, y'all's, y'alls's, you all's, your all's, and all of y'all's."

Unlike French, German, and Spanish languages, the English language does not have a designed second-person plural pronoun.

I think they mean "designated," because English was far from "designed." But yes, it does. It's "y'all." Anyway, the French second-person plural doubles as the formal second-person singular, and you have to figure out the difference from context.

What we desperately need is another second-person plural. Right now, if I said, "We are going to a party tonight," it's ambiguous whether "we" refers to "I and you" or "I and my closest friends, of which you are not one." Call it first-person plural inclusive and first-person plural exclusive. I suggest "ze" for the latter, but no one cares.

While we're on the subject of poor spelling, what the hell is up with "Opps!"? Look. I've never, ever heard someone exclaim "opps," which, by that spelling, would be like in "drops." No, I've only ever heard "Oops," though the oo there can be pronounced either like book or like boob.

Speaking of boobs, I've been seeing more and more people writing something like "a women" as in "There was a women waiting for the store to open." No. There is no such thing as "a women." There's a woman, or there's several women.

Look, I'm not saying I never make mistakes. That would be a mistake. And by Waltz's Second Law of the Internet, because this post discusses spelling mistakes, it probably contains an inadvertent spelling mistake. But come on... at least try.

5 Like • Comment • View 2 comments

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