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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 9 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 9 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 9 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 19 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?

February 8, 2021 at 12:02am

#1003941

Let It Roll

Entry #2 of 8 for "Journalistic Intentions"

[18+]

Let It Roll

Back in college, I had occasion to visit the Drama Department every once in a while, mostly in my capacity as newspaper photographer. This department was in what was then a relatively new building, with more contemporary fixtures than in many of the other University buildings. One such fixture was the toilet paper dispensers in the restroom stalls.

Now, there wasn't a lot of graffiti at the school in general. Oh, there was some, to be sure; the scribblings in the Philosophy Department, much older than Drama, were particularly incisive, and I had great laughs at the occasional math pun in the Engineering department (which is where I took most of my shits). But in this particular case, someone had seen that the toilet paper dispensers had a lever with words on it that read: "PRESS DOWN FOR NEW ROLL." Predictably, but still amusingly because this was, in fact, the Drama School, this person had altered the last L to become an E.

Anyone who's been following along should know that I like to learn about language, and play with it. "Roll" and "role," as you might imagine, are... absolutely of the same origin.

Surprised? I was, when I discovered this.

Turns out that, at least according to Dictionary.com, the word "role" split off from "roll" somewhere in Old French, where an actor's part was referred to, in what I suppose is a case of metonymy, from the roll of paper upon which the actor's lines were written.

I absolutely love this sort of thing; it gives me insight into the way peoples' minds work through the lens of language development.

I should also note that it appears that the French word "roue," which translates as "wheel," comes from the same source as well. Not entirely sure of this one, though.

The "role" origin also seems to tie into one of the other definitions of "roll," as in "roll call." Oddly enough, though, the word "scroll" doesn't seem to be related, at least not as far back as they can trace it -- though it should be, describing as it does a roll of paper, parchment, vellum, whatever. No, "scroll" comes from, of all things, "escrow," which itself was an alteration of an older word "scrow," which apparently meant... roll.

Essentially, "roll" is traced from Latin and "scroll" is Germanic in origin -- though both language families, naturally, stemmed from the same source, even further back: Proto-Indo-European, or PIE. This is, of course, what we call it now; no one seems to know what this original language was called or even, with any level of certainty, what its words or structure were.

A while back, I did a blog entry about the invention of the wheel. After much searching, I finally found it. Here: "As the Turn Worlds (or whatever)"

. And in that entry, I refer to another entry from a couple weeks prior, here: "Lox Pie"

. Now, based on what I found out in writing those entries, it seems that people smarter than I am have figured out where the PIE-speakers probably originated from, and that the reason that particular language spread so far and wide was because those bastards invented the wheel, slapped those suckers on a cart, and hooked the resulting contraption to horses. This made the people in that culture incredibly mobile for the time. I mean, anyone with a horse would have been more mobile (Genghis Khan comes to mind), but if you want to take your stuff with you, you need a cart, too. Preferably one behind the horse, rather than in front of it.

So, essentially, the PIEs rolled all over Europe and parts of Asia, bringing their language with them -- a language which then fractured, merged with other languages in different areas, adapted to its speakers' varying needs and environment, and then -- thousands of years later -- maybe started coming together again, in a vastly different form, as English borrows heavily from so many different other languages.

All of which is to say that there's more than half a dozen songs called "Let It Roll," and I haven't even heard some of them, and those that I have, I don't particularly like, so this entry's about roll and not rock.

8 Like • Comment • View 2 comments

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