Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ October ► 2022
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

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Tuesday, May. 7, 2024

9:55am EDT

Members: 908

Guests: 695

Total Online: 1,603

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

May 5, 2024 at 8:50am
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

May 4, 2024 at 5:42pm
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

October 18, 2022 at 12:01am

#1039361

The Once and Future Viking

In today's "we were wrong all along" news...

Goodbye to the Vikings
The term ‘Viking’ as it is commonly used is misleading, warping our perception of the Middle Ages. It should be retired.

That yipping noise you just heard was the collective barking of Minnesota sportsball fans.

There was no such thing as a ‘Viking’ in the medieval period. Use of the term emerged in the 19th century. The word wicing occurred in Old English and víkingr in Old Icelandic, but were used very differently, to mean something like ‘pirate’.

Which explains much about a certain cruise line and its pricing structure.

In Old Icelandic víkingr could be applied to any pirate regardless of where they came from or when, or what language they spoke; they might be Estonians or Saracens, for example. It is also noteworthy that it is almost never used to describe the people who we today call ‘Vikings’. Many of the men labelled ‘Vikings’ in textbooks and popular histories were warriors led by kings on military expeditions with clear political objectives, such as the Great Heathen Army that fought Alfred the Great or the Norwegian force that accompanied Harald Hardrada to his death at Stamford Bridge in 1066. Calling such people ‘Vikings’ would be like calling 18th century British, French or Dutch naval officers ‘pirates’ simply because they wore vaguely similar hats and sailed vaguely similar ships to Blackbeard.

Have you seen what 18th century British, French, and Dutch naval officers got up to? That's not far off the mark.

The final development, the ‘ethnicisation’ of the word that allows the use of terms such as ‘Viking farms’, ‘Viking towns’ and ‘Viking women and children’, is much more recent and has gradually crept up since the Second World War. This is insidious; by linking military prowess and savagery to an entire ethnic group, it encourages its appropriation by racial supremacists.

Right, because when I think of military prowess and savagery, I think of Scandinavians and not a certain Mongolian.

On the other hand, my ex-wife is of Norwegian descent, so I get the savagery part.

The issue with the term is not merely semantic. This conception of ‘the Vikings’ seriously distorts our understanding of European history. We have tended to group almost all Scandinavian activity between the 790s and the mid-11th century together under the ‘Viking’ label, creating a distinct ‘Viking Age’ and an imagined ‘Viking’ culture and identity. The evidence, however, does not support this analysis.

The article goes on, of course, to explain said evidence, not all of which I'm going to repeat here.

Irish, English and Frankish chronicles generally refer to Scandinavian aggressors as ‘heathens’ and this, rather than any ethnic identity, seems to have been what struck the victims of these attacks as significant. The 793 raid on Lindisfarne, often said to herald the ‘Viking Age’, is described in the Anglo-Saxon Chronicle thus: ‘The ravages of heathen men miserably destroyed God’s church on Lindisfarne with plunder and slaughter.’

Hey, Lindisfarne again (from a couple of entries ago).

The construct of the ‘Vikings’ conflates and blurs the distinction between eighth- and 12th-century pirates. Tenth-century kings based in Dublin and Christian rulers such as Cnut, all of whom lived in very different societies, had different belief systems and political and economic objectives. Each of these contexts needs to be dealt with on its own terms and not within a 19th-century construct that has more than a hint of racist essentialism to it.

It's also, insofar as I can infer from this article, religious exceptionalism.

3 Like • Comment

© 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/10-18-2022