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Thursday, May. 9, 2024

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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:

Lazy Writer est 4/24/2008

about 14 hours ago
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

about 18 hours ago
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 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.

October 19, 2019 at 12:08am

#968099

Birthed in Beer

https://www.theguardian.com/technology/2016/jul/15/how-the-internet-was-invented...

How the internet was invented

In 40 years, the internet has morphed from a military communication network into a vast global cyberspace. And it all started in a California beer garden

You will note the prominent feature of the subhead is the phrase "in a California beer garden." Remember a while back I posted on the link between bars and invention?

In the kingdom of apps and unicorns, Rossotti’s is a rarity. This beer garden in the heart of Silicon Valley has been standing on the same spot since 1852. It isn’t disruptive; it doesn’t scale. But for more than 150 years, it has done one thing and done it well: it has given Californians a good place to get drunk.

And it hasn't achieved National Historic Monument status because...?

It doesn’t seem a likely spot for a major act of innovation. But 40 years ago this August, a small team of scientists set up a computer terminal at one of its picnic tables and conducted an extraordinary experiment. Over plastic cups of beer, they proved that a strange idea called the internet could work.

As far as proof of concept demonstrations go, I've seen worse.

If you had walked into Rossotti’s beer garden on 27 August 1976, you would have seen the following: seven men and one woman at a table, hovering around a computer terminal, the woman typing.

Typical 1970s scenario. It's always the woman typing. That's what they're for, don't you know?

The fact that we think of the internet as a world of its own, as a place we can be “in” or “on” – this too is the legacy of Don Nielson and his fellow scientists. By binding different networks together so seamlessly, they made the internet feel like a single space. Strictly speaking, this is an illusion. The internet is composed of many, many networks: when I go to Google’s website, my data must traverse 11 different routers before it arrives. But the internet is a master weaver: it conceals its stitches extremely well. We’re left with the sensation of a boundless, borderless digital universe – cyberspace, as we used to call it. Forty years ago, this universe first flickered into existence in the foothills outside of Palo Alto, and has been expanding ever since.

And so the internet, like civilization itself, owes its existence to beer.

Okay, so I had to do a search on Rossotti's. Turns out it was recently restyled.

https://www.paloaltoonline.com/news/2019/10/10/the-best-version-of-rossottis-tha...

Zott's may have new floors, clean bathrooms, free WiFi and artisan wood-fired pizza, but the spirit of the place largely lives on.

Heh. Free WiFi. And so we come full circle.

2 Like • Comment • View 2 comments

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