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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

about 7 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 7 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 7 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

about 17 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?

October 18, 2021 at 12:03am

#1019575

Speling Iz Dificult

Ever wonder why spelling is so damn hard?

Typos, tricks and misprints
Why is English spelling so weird and unpredictable? Don’t blame the mix of languages; look to quirks of timing and technology

Yeah, I don't know about that, a bunch of stolen words from other languages has to take at least part of the blame.

Part of the problem is that English spelling looks deceptively similar to other languages that use the same alphabet but in a much more consistent way. You can spend an afternoon familiarising yourself with the pronunciation rules of Italian, Spanish, German, Swedish, Hungarian, Lithuanian, Polish and many others, and credibly read out a text in that language, even if you don’t understand it. Your pronunciation might be terrible, and the pace, stress and rhythm would be completely off, and no one would mistake you for a native speaker – but you could do it. Even French, notorious for the spelling challenges it presents learners, is consistent enough to meet the bar. There are lots of silent letters, but they’re in predictable places. French has plenty of rules, and exceptions to those rules, but they can all be listed on a reasonable number of pages.

Sure, but consider the French translation of "birds:" oiseaux. Not one single solitary goddamned letter in that word is pronounced the way it ought to be pronounced.

The answer to the weirdness of English has to do with the timing of technology. The rise of printing caught English at a moment when the norms linking spoken and written language were up for grabs, and so could be hijacked by diverse forces and imperatives that didn’t coordinate with each other, or cohere, or even have any distinct goals at all. If the printing press had arrived earlier in the life of English, or later, after some of the upheaval had settled, things might have ended up differently.

Okay. This author is a linguist so I'm inclined to give more weight to what they're saying than, for example, what I'm thinking.

I don't have much more to say about the article, but it's a fascinating brief history of written English.

I will say this, though: At some point, the spelling/pronunciation link becomes a shibboleth. I think people use it to identify in-groups. For example, in my area, there's a road with the name Rio Road. We use it to spot tourists. "Yeah, I hear (business) is on Ree-oh Road." Oh, they must be from out of town; the proper pronunciation is Rye-oh. Or there's a nearby town named Staunton. You hear someone pronounce it "stawn-ton" and you know they ain't from around here and need to be watched carefully and maybe lynched.

Probably the worst offender in the orthography world, though, is the geoduck.

You see a word like that, and you think: oh, it must be gee-oh-duck. And it's probably a bird, right? An... earth bird? Well, obviously you're an ignorant rube and unworthy of respect because you didn't know it's pronounced "gooeyduck" and it's actually an enormous mollusk. How in the inconsistent hell do you get "gooey" from "geo?" I mean, seriously, goddamn, STOP IT.

So my contention is a language's inconsistencies are mostly there to fool outsiders to the language. It's like a secret code between club members: there to distinguish the cool people from the out-of-touch. You can also identify nerds with it: people who read more than they ought to tend to pronounce words they way they sound in their heads. For example, I know someone who, upon seeing a picturesque scene, always called it "picture-skew." Because that's a perfectly legitimate reading of the pronunciation of all those letters.

Now, I'm not one of the long line of idiots who try (and certainly fail) to "reform" English spelling to something more consistent. Such efforts were always doomed to failure, because, as I noted, it's a private club and you can't get in until you familiarize yourself with, at least, 90% of the silly rules, and even then, we'll still mark you as an outsider because you'll certainly have an accent. But dammit, I'm tempted.

Merit Badge Mini-Contest!

What's your favorite example of a word that ought not to be spelled like it is? Comment here before midnight tonight WDC time (Monday night) and you might get a Merit Badge on Tuesday.

3 Like • Comment • View 5 comments

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