Complex Numbers (Book)

Blog Calendar

◄ March ► 2020
S	M	T	W	T	F	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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:

Elycia Lee ☮

about 5 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

2 Like

Wordsmitty ✍️

about 18 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

about 21 hours ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

about 23 hours ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

March 2, 2020 at 12:04am

#976765

No Clause for Celebration

My career was in urban/suburban planning, design and development -- so stories like this one are like candy to me.

https://www.thedailybeast.com/celebration-florida-how-disneys-community-of-tomor...

Celebration, Florida: How Disney’s ‘Community of Tomorrow’ Became a Total Nightmare
In 2004, Disney sold the downtown of utopian Celebration, Florida, to a private equity firm. Residents say it took their money and let the city rot around them.

The highly municipal-coded hamlet, built in 1995 to look like 1955, was billed as an antidote to the chain-ridden sprawl of suburban America. In Celebration, there were no fast-casual franchises, no hulking commercial trucks, no visual reminders of poverty. Every lawn was cut to code; every fence was freshly painted.

This is what we come up with for "utopia?" Count me the hell out.

Eventually, Kelly started selling Celebration real estate herself. “I wanted people to get it,” she said. “I didn’t want people coming to Celebration, particularly at that time, and going, ‘Oh this is cute.’ This is not cute. This is a fucking miracle.”

I don't think Disney would approve of your language, young lady.

But in 2016, when Kelly started a blog about Celebration called Cookie Kelly Blog, she wanted readers to get something else. Things in town had changed. The cracks in Celebration’s utopian façade had been evident for years: there were major segregation issues; the school, which didn’t assign homework, grades, or even books, was losing students by the dozens; the recession had bankrupted local businesses and pushed homes to foreclosure; and in one brutal week of 2010, the town experienced its first murder, followed by a police shootout with another man who barricaded himself in a house for 14 hours and shot himself in the head.

Okay, all of that is a bit much even for those of us who live for schadenfreude.

A third, the mother of three small girls, said her building often swayed beneath her feet. “Why?” she said. “Because the building leaked since 2008. The water has disintegrated the building, causing mold. The termites have come and gone. There’s nothing left for them to eat.“

Ah, the sweet, delicious tang of metaphor.

The intentional community was an experiment in New Urbanism, a neo-traditional planning movement that sought a return to early American small town life by designing compact, walkable cities with diverse housing options, mixed local businesses, and abundant public space.

I can say from experience that if you want both "compact, walkable cities" and "abundant public space," you might as well wish for fairy dust and a flying pony while you're at it, for all the good it'll do you. The two are incompatible, like Skittles and M&Ms.

Everything about Celebration telegraphed cozy familiarity. Brochures depicted a quasi-fantastical realm of home-cooked meals, traditional family values, and G-rated movies.

"The mind is its own place and in itself, can make a Heaven of Hell, a Hell of Heaven." -John Milton

When Disney first laid out his plan for Experimental Prototype Community of Tomorrow, he painted it as a model of American capitalism. “EPCOT will always be a showcase to the world,” Disney said, “for the ingenuity and imagination of American free enterprise.” In a sense, it always has been—a corporate-built town constructed too quickly and too cheaply, sold off to unsuspecting owners under the guise of utopia while nurturing the same social issues that exist everywhere else.

And now, in 2020, the "ingenuity and imagination of American free enterprise" mostly displays itself as private equity firms parasitically sucking the lifeblood out of corporations, giving nothing in return. The system is working as designed -- for the private equity firms.

3 Like • Comment • View 3 comments

© Copyright 2024 Waltz en France (UN: cathartes02 at Writing.Com). All rights reserved.
Waltz en France has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.