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

Tuesday, Apr. 30, 2024

6:08pm EDT

Members: 1,092

Guests: 1,188

Total Online: 2,280

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 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

November 16, 2018 at 12:53am

#945662

Sure Thing

It's hard to be certain of almost anything.

I say "almost" because there is one thing we can all be absolutely certain of: "I exist." Not me, I, but every one of us I, each to their own mind.

Now, you can play games with that, saying that "I" is an illusion, but it's difficult to argue with Descartes: I'm pink; therefore, I'm spam. Er, I mean, I think; therefore, I am. It doesn't matter if we're meat suits, actors on a stage, avatars in a simulation, or disembodied brains trying out this thing called material existence; we simply are. Well, I am. I'm not so sure about the rest of you lot.

In life, we all like to make statements with certainty, and find things we feel we can be absolutely sure of. Apart from my own existence, though, I'd put a degree of certainty on everything. Like, I'm sitting here looking at a kitten. Does the kitten exist, or is she a figment of my imagination? The scratches on my arm and the fact that I see her tell me she probably exists. Like, 10^-50 uncertainty, and I'd call that as certain as I can get about anything. I'll call this the kitten level of certainty - basically, indisputable proof.

Now, I understand that you've never seen this kitten (you should; she's incredibly cute), so your level of certainty that this kitten exists is - and should be - much lower. You only have my word on it, and I could be deluded or lyingcreating a fictional story to support a point. Her name is Katushka, and she actually belongs to my housemate, if it can be said that a cat belongs to anyone at all.

Does Afghanistan exist? I once met a person who said he was from Afghanistan. I've met a few people who claim to have been there and returned. I've seen it outlined on a map. I've heard reporters talking about it. It's usually first on the list of countries on dropdown menus on the internet. But I've never been there, myself, so I'd only give it a 10^-10 probability of nonexistence. After all, the only thing a map proves (to kitten levels of certainty) is that the map itself exists.

On the other end of the spectrum, if you were to ask me if my mother were alive, I'd have to give that a near-zero probability - the polar opposite of kitten level certainty. I mean, I watched her die, there's a death certificate, I saw her body in the coffin, and I was there when they lowered it into the ground. But memory could be playing tricks on me.

So if anyone were to ask me if I'm certain of - I don't know - the existence of the sun, the best I'll be able to do is kitten level certainty - and that's during the day if I'm outside. At night, it becomes slightly less certain.

I've been burned too many times by saying I'm certain about some fact or other, only to find out later that I misremembered or was misled. So I've learned - much to the annoyance of non-pedants everywhere - never to be 100% certain of anything.

This might become a problem if I'm ever in court. "Mr. Waltz, are you absolutely certain you saw someone drive off in your car?" "Well, I'm 99.999999999999% sure, but I suppose it could have driven off on its own, or maybe someone slipped me some acid." "So, you're not 100% certain."

So when I see something like "Only 66% of 18-24 year olds in the US are certain the Earth is round," it doesn't surprise me much (assuming that's even an actual statistic and not something made up out of thin air). But it worries me. Not because it implies that 34% of 18-24 year olds aren't completely certain the world is round (that statement says nothing about the level of certainty of the other 34%; it could range from "I believe the Earth is flat" to "I'm almost completely sure the Earth is round") - but because 66% of them are so absolutely sure of themselves that they don't stop to think that absolute certainty is (almost) absolutely impossible. I've never personally seen the curvature of the Earth, but I have seen ships disappear over the horizon, and I've looked at plenty of evidence, and heard statements from scientists and astronauts - so I'm going to give this one Afghanistan levels of certainty. In addition, "round" has a squishy definition when it comes to a planet. Obviously the Earth isn't perfectly round; it has ocean trenches and mountains, and an equatorial bulge - plus, if you consider the atmosphere to be part of Earth, its boundary isn't clearly defined.

Consequently, if you asked me "Are you certain the Earth is round?" well... I might answer "no" just to be pedantic about it.

6 Like • Comment • View 5 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/11-16-2018