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Monday, May. 6, 2024

4:56am EDT

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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:

🌕 HuntersMoon

about 20 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 11, 2021 at 12:01am

#1008209

Brain Trust

Today in You're Doing It Wrong, "Thinking:"

Your Brain Doesn't Work the Way You Think It Does
A conversation with neuroscientist Lisa Feldman Barrett on the counterintuitive ways your mind processes reality—and why understanding that might help you feel a little less anxious.

This is one of those articles that is basically a book promotion, but to reiterate: This is a writing site, and I'm not going to rag on anyone for promoting their book, here or elsewhere. And honestly, this one looks like it might be interesting.

People tend to feel like we’re reacting to what’s actually happening in the world. But what’s really happening is that your brain is drawing on your deep backlog of experience and memory, constructing what it believes to be your reality, cross-referencing it with incoming sense data from your heart, lungs, metabolism, immune system, as well as the surrounding world, and adjusting as needed. In other words, in a process that even Dr. Barrett admits “defies common sense,” you’re almost always acting on the predictions that your brain is making about what’s going to happen next, not reacting to experience as it unfolds.

Or as I like to put it: we think we have free will, but that's an illusion; we don't so much make choices as rationalize our choices after the fact.

“Predictions transform flashes of light into the objects you see. They turn changes in air pressure into recognizable sounds, and traces of chemicals into smells and tastes. Predictions let you read the squiggles on this page and understand them as letters and words and ideas,” Barrett writes. “They’re also the reason why it feels unsatisfying when a sentence is missing its final.”

Oh, she's smart and funny? I think I'm in love.

Anyway, my own brain is (metaphorically) running on fumes right now, so I don't have a lot more to say. The article proceeds in interview Q&A form, and both Qs and As are interesting and insightful. But one quote by Barrett stands out for me:

Your brain is making guesses about what is going to happen next, so it knows how to act next to keep you alive and well. It’s continuously drawing on your past experiences to create your present. The really cool thing about this? It's really hard for people to change their past. However, by changing your present, you are cultivating a different future. By changing what you do and say, and feel, you are seeding your brain to predict differently in the future.

This, of course, has implications for psychology and probably even philosophy. I think I suspected this on some level, because this is why I don't stop trying to learn new things. Thus:

The actions and the experiences that your brain makes today become your brain's predictions for tomorrow. So making an effort to cultivate new experiences and learn new things today is an investment in who you will be tomorrow. Some people have control over many things in their lives, and some people have less control because of their life circumstances, but everyone can control something.

So it's worth a read; the article isn't all that long. And for once, I'm actually tempted to buy the book. Or, to put it another way, I've been conditioned to accept advertisements disguised as journalism, and when said ads spark my confirmation bias, my brain wants me to buy the book so I can learn more.

7 Like • Comment • View 6 comments

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