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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 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 21, 2021 at 12:07am

#1008886

Mind Matters

Well, I haven't mentioned this subject in a while. The article is from 2018, but I just found it recently.

Could consciousness all come down to the way things vibrate?

I think the last time I ragged on panpsychism was about a year ago. This article has the added benefit of the word "vibrate" in the headline, which makes me want to make vibrator jokes. But those would be too easy, so I'll try to restrain myself.

Why is my awareness here, while yours is over there? Why is the universe split in two for each of us, into a subject and an infinity of objects? How is each of us our own center of experience, receiving information about the rest of the world out there? Why are some things conscious and others apparently not? Is a rat conscious? A gnat? A bacterium?

"Infinity?" [citation needed]

Over the last decade, my colleague, University of California, Santa Barbara psychology professor Jonathan Schooler and I have developed what we call a “resonance theory of consciousness.” We suggest that resonance – another word for synchronized vibrations – is at the heart of not only human consciousness but also animal consciousness and of physical reality more generally. It sounds like something the hippies might have dreamed up – it’s all vibrations, man! – but stick with me.

Because if there's any place where such a hypothesis could emerge, it would be Santa Barbara.

Based on the observed behavior of the entities that surround us, from electrons to atoms to molecules, to bacteria to mice, bats, rats, and on, we suggest that all things may be viewed as at least a little conscious. This sounds strange at first blush, but “panpsychism” – the view that all matter has some associated consciousness – is an increasingly accepted position with respect to the nature of consciousness.

I've laid out my problem with panpsychism before. In brief: where's the evidence, for or against? Is it falsifiable? Can we do experiments on it? Because otherwise it's just an idea. Maybe it's a good idea - I mean, can it really hurt to consider all things as related? But to me it has one great flaw, which is that if you claim that every atom has some kind of consciousness, you dilute any definition of consciousness. Like when you call time an illusion, you change the definition of "illusion."

Still, the article is worth reading, because who knows? Maybe they're onto something (as opposed to on something, which is the usual state necessary to claim "It's all ONE, dude.") From a purely physical standpoint, it's clear that there's a deep connection between all life, and for that matter, all matter. What's not clear to me is that consciousness, which from the standpoint of parsimony might be better described as an emergent property of an individual's neural connections, also comes from some sort of lower-level consciousness.

It's a lot to think about, and it's not like I can come up with a more compelling idea. So I keep reading on the subject, and thus, sharing what I find.

After all, that's what group consciousness is all about, yes?

2 Like • Comment

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