Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ April ► 2021
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

Sunday, May. 5, 2024

10:57pm EDT

Members: 953

Guests: 2,343

Total Online: 3,296

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:

🌕 HuntersMoon

about 14 hours ago
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

a day ago
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
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

April 16, 2021 at 12:03am

#1008600

Healthy, Wealthy, and Wise

Today's article talks about something I've harped on before -- the unreliability of food science studies and reporting.

Here’s Why It’s So Impossible to Get Reliable Diet Advice From the News
What’s good for you seems to change every week. Maybe we should stop blaming the media and look at the studies underneath the stories, too.

And maybe we should stop blaming ourselves and being so damn neurotic about these things.

It is easy, especially as someone who is on the research side of things most of the time, to fault the media for sensational coverage of individual studies that fails to consider the broader context. And certainly there is a healthy dose of that all around us (for example, why write a headline like “Do Tomatoes Cause Heart Attacks?” when the answer is “no”?).

Uh, I know that was a rhetorical question, but the answer is "for clicks." It's best to assume that the answer to any headline in the form of a question is "No."

I would argue the main problem is that the studies that underlie this reporting are themselves subject to significant bias.

I've been saying this for years. If you've been following along, you're probably sick of hearing me go on about it.

Take coffee as an example. On the one hand, coffee drinkers are more educated on average, and they exercise more.

How do you know that? A study? But didn't you just say that studies are biased? And of course coffee drinkers want to think they're smarter, but if they're so smart, how did they get addicted to caffeine? I should commission a study that shows how guys with long hair who wear Birkenstocks and Hawaiian shirts are far, far sexier than average.

I set out to analyze—using a top-notch data set and standard analysis techniques—a simple question: “Which foods make you thin?”

None. None foods make you thin. Lack of food makes you thin. Duh.

In the data, eating quinoa is associated with a whopping 4.2 point reduction in BMI, whereas eating breakfast sandwiches is associated with more than a 2 point BMI increase.

So if you eat a quinoa breakfast sandwich, it balances out.

There are other issues with quinoa, cultural ones. But this isn't a post about American cultural imperialism.

The article goes on to describe kind of a study of studies, with lots of bar graphs and explanation. It's worth at least glancing through if you're interested in this sort of thing.

But if not, here's the bottom line: Educated rich people are healthier than ignorant poor ones. (Educated people who wear Birkenstocks and Hawaiian shirts are also way more attractive.)

Or something like that. Honestly, she loses me about halfway through, but that's probably because I have a bit of a mind fog right now. No, I haven't been drinking; I got my second Trump Mumps shot yesterday and, while I'm generally feeling pretty good, my brain's kinda wonky.

In any case, it's pretty well established that eating vegetables is better for your health than eating candy bars. I don't think any of us need a study to know that, but since candy bars taste way better than any vegetable, it helps to be reminded from time to time.

4 Like • Comment • View 3 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/4-16-2021