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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:

Lazy Writer est 4/24/2008

about 19 hours ago
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

about 22 hours ago
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

a day ago
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
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

Apr 25, 2024 at 3:09am
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

Apr 25, 2024 at 2:58am
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

August 15, 2019 at 12:03am

#964231

What's Good for the Propaganda

https://www.fastcompany.com/90304574/the-secret-history-of-midcentury-modern-des...

At the intersection of art and functionality lies "design."

I have to admit, most of it is opaque to me. I have no artistic talent, and only a very rudimentary aesthetic sense, so I tend to choose products for their functionality rather than their looks.

Or do I?

It's quite possible that I make unconscious choices based on what something looks like. That would make me a target, not a conscious consumer.

Good design is largely unnoticeable - I do know that. In my field, this concept relied on hiding stuff rather than making it look a certain way. The "looks" part was the domain of architects and landscape architects; all I had to do was make sure things like storm drains were buried. And while a road is largely visible, no one notices anything about the road unless, like me, they design the things, or if something's dysfunctional about it.

Buildings, they notice.

And sometimes I notice things too. Cartoon mascots, for breakfast cereal and the like, are almost always depicted with their mouths open. I don't know the reason for this; I'm guessing it makes people want to put the product into their own mouths. Also, large swaths of "green" or environmentally friendly design - as well as products marketed as "healthy" - possess an aesthetic that says something like "Here is something that is good for you and/or the environment. We're making it ugly so you can feel like you're doing penance for past overconsumption or enjoyment."

That last tide seems to be turning, now, thanks to Elon Musk making electric cars that people might actually not be embarrassed to be seen in, as opposed to the pug-ugly "Smart Car."

That's a subjective observation, of course; there's no One True Aesthetic, or else nothing would ever change.

So, back to the article's premise: design as propaganda.

I never really gave that much thought, although in retrospect I probably should have. We know that grocery stores, for example, do extensive research into human psychology to help them determine a layout that extracts the maximum profit from a shopper. Casinos, too, rely heavily on psychology; my first experience with one was that you had to walk through a gauntlet of flashing and beeping slot machines just to get to registration (this is not as common as it used to be). And just the other day, a friend of mine got lost in an Ikea store; she couldn't find the exit. I told her, "the trick is to buy something, and then the exit magically appears." And behold, she bought something, and the exit magically appeared. (Her attempts to put said something together later led to her having to go back to the Ikea to return it, after which she texted me: "Never. Again.")

Point is, these places don't hire someone like me to do their layout; I'd be trying for the most efficient layout from the point of view of a shopper, just like I used to design roads that were as straight as possible given constraints of terrain and other externalities. No, they employ people who think of design from the viewpoint of maximizing profit.

There's nothing wrong with that, intrinsically. A business exists to make profit. But I think it's important to know that these things are working on you on some level. Go grocery shopping with a list and stick to the list, and you're not swayed by prominent displays of, say, Oreos. Avoid slot machines (generally good advice anyway). And for the sake of everything that's right and pure in the world, stay the hell away from Ikea.

Likely, other people have considered this way more than I have. I don't usually think about it, which makes me a sucker. But I'm going to work on it.

1 Like • Comment • View 5 comments

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