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Wednesday, May. 8, 2024

6:21pm 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:

Lazy Writer est 4/24/2008

about 3 hours ago
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

about 7 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.

March 31, 2024 at 8:32am

#1067220

Revisited: "Heartbreak"

You know what today is, right? Oh, sure, it's April Fools' Eve, of course, but being Sunday, it's time to revisit an older entry. This one was from five years ago, and follows my usual comment-on-an-article format: "Heartbreak"

The BBC article

is still up, as of today. Remarkable, considering how many episodes of early Doctor Who the BBC destroyed to make room for newer things. Maybe they learned their lesson.

To summarize, there was some evidence that a particular heart condition is at least partially caused by stress or strong emotion.

Me: The more I learn, the more I think that the commonly stated dichotomy between mind and body is bogus.

I would probably phrase this differently, now. Also, throughout my entry, I seem to have used "mind" and "brain" interchangeably, which I think I'd be more careful to avoid, these days.

My understanding of the internal workings of a person or other animal is rudimentary, but from what I've heard, the brain is a physical, identifiable organ located mostly in one's head. It does lots of stuff, including stuff we don't understand, but it seems to be responsible for, among other things, telling your feet to walk and your chest to occasionally fill with air. The "mind," however, is a far more nebulous concept. I seem to recall doing another entry about that at some point in the not-so-distant past; it involved René Descartes, who asserted that because you can't put a set of spatial coordinates (Descartes invented coordinates) on the mind, but you can on the brain, that there's no way that one can act upon the other. Might as well link it, too, for reference: "Mind, the Gap"

In addition to walking and breathing, the brain is sometimes fairly good at thinking. More in some people than in others, but "thinking" is a legitimate activity, even if it doesn't look like much of an activity to other people. But many people think (pun intended) that it's the mind doing the thinking. Once you're done thinking, often, you do some physical activity. For example, writing what you just thought. We draw that separation between "thinking" and "doing" because we love categorizing things, like cats and dogs being different species, or Pluto not being a full-fledged planet after all.

Point being, a lot of the seeming contradictions of mind/body dualism, such as in the last entry I linked, go right out the window when you consider that the mind is a product of the body. It's probably more complicated than just being conjured up by your brain, but the brain is a body part too. Descartes' assertion that the mind cannot influence the body is, therefore, wrong. Brilliant guy, but in this case, he was working from a shaky premise.

Anyway. The original entry, from up top, ends with the literal video version of Total Eclipse of the Heart, and I'm pleased (state of mind and body) to see that the video is still in existence. I have a whole entry on that song (the actual song, not the parody) coming up at some point; it's in my queue and will pop up at random.

3 Like • Comment

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