Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ November ► 2018
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
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Wednesday, May. 1, 2024

4:00am EDT

Members: 737

Guests: 929

Total Online: 1,666

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:

GeminiGem of House Lannister

a day ago
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
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

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

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

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
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 going to Montana

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 going to Montana

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 going to Montana

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

November 15, 2018 at 12:58am

#945587

R.E.M. Minders

I've written here before about my lovely experiences with sleep paralysis and its accompanying nightmares. But those are relatively rare; like most people, the majority of my somnolent experiences are just dreams.

When you think about it, dreams are weird. I don't just mean that the dreams themselves are weird, but also that the concept is strange.

As I understand it, we don't really know why we dream. Or sleep, for that matter. What evolutionary advantage is there to be unconscious for a third of the day? Or even more, if you happen to be a feline. The benefits to survival must outweigh the risks of being caught napping by a predator or a tax collector.

Sleep does seem to play a role in processing and organizing experiences, turning them into memories, and it's probable that dreams are key to that - a time for the brain to integrate the latest inputs into one's consciousness, or to discard the unimportant bits. Like a defrag routine for a storage medium, maybe, though it's not really accurate to compare organic processes with electronic ones.

Those of a more mystical bent might interpret dreams as messages. Perhaps it's a time for the subconscious to alert us to something important. I know that there have been many times I've gone to sleep after banging my head against a problem, for instance a spreadsheet solution that has eluded me, and woken up with the key to working it out. This is, I suppose, why sometimes you're urged to "sleep on it" when something's bugging you. But I've also woken up with ideas that turn out to be dead ends - though even failures are useful if you can learn from them.

I have to wonder, though, what role lucid dreaming might play in this kind of explanation for dreams, though. Lucid dreams, as I understand them, combine the knowledge that one is dreaming with the ability to control the dream. And just typing that sentence is enough to send me down the rabbit hole of a discussion about free will, which is not something I'm prepared to go into here just yet. For the sake of argument, let's say that one is in control when one believesone is in control.

For myself, I feel like I have some degree of control most of the time once I realize I'm in a dream. Usually when that happens I verify the hypothesis that I'm dreaming by willing myself to levitate. Since I can't levitate in real life, if I find myself starting to leave the floor or ground or whatever, I know I'm dreaming (of course, there are flying dreams that I don't initiate, but that takes the "will" out of the situation).

As for what I do then - well, let's just say this blog doesn't have a high enough content rating, and leave it at that.

I think it was Dave Barry who said something to the effect of "The holodeck [from Star Trek: The Next Generation] will be humanity's last invention." In their purest form, lucid dreams are like being in a holodeck simulation. Not only do I see and hear, but I have also engaged my other senses. The surroundings seem real. If you have control over not only yourself but your realistic surroundings, why would you ever go back to a world where random crap can happen to you, you have bills to pay, and the car needs new tires? I suppose some would, but not me. I'm always disappointed when I wake up from a lucid dream. Not that my life is horrible - far from it - but the dreams are just more interesting.

5 Like • Comment • View 6 comments

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

Printed from https://www.writing.com/main/profile/blog/cathartes02/day/11-15-2018