Complex Numbers (Book)

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Complex Numbers

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/

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Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 8 hours ago
In response to "Sensational"

They say carrots can improve your eye sight, but it's been proven that drinking alcoholic beverages can make you see double.

After stating this, I find myself wondering why hasn't anyone tried fermenting and distilling carrots and marketing it as a vision tonic?

2 Like

🌖 HuntersMoon

about 13 hours ago
In response to "Sensational"

OK, look around you and observe (where possible) the reality of the newly revealed "facts." It's pretty clear that "Smartphones make you a hell of a lot of folks stupid."

2 Like

Elisa: Snowman Stik

about 14 hours ago
In response to "Sensational"

Thank you for reminding me to check on Retraction Watch.

https://retractionwatch.com/

3 Like

tj-Merry Mischief Maker

a day ago
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

a day ago
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

🌖 HuntersMoon

a day ago
In response to "Gray Matters"

I've always believed "better gray than gone away..."

2 Like

tj-Merry Mischief Maker

Dec 25, 2024 at 3:02pm
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

Dec 24, 2024 at 5:16pm
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

tj-Merry Mischief Maker

Dec 23, 2024 at 4:55pm
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

🐕GeminiGem🎁

Dec 23, 2024 at 12:56pm
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

April 30, 2024 at 9:51am

#1070196

Mad as Hell

Sometimes I have to be reminded of stuff, because apparently I have a problem with object permanence once an item drops off my Favorites sidebar. In particular, "JAFBG"

[XGC] is still around, under new management, and there have been prompts to tackle since the beginning of the year.

As usual, I picked one at random:

How useful do you think anger can be?

Well, I'm not a psych-talker person, nor are emotions something I know much about. I can barely identify them in myself, let alone in others.

That said, it seems to me that anger is, at base, a manifestation of the well-known "fight or flight" response to a threat. That makes it related to fear, in my book (which I won't write because, like I said, not an expert). The "flight" part probably doesn't involve anger, but the "fight" part does. I hear that, in those cases, anger can be fairly useful to focus one's hostility into action... so long as it doesn't escalate into blind rage, which leads to random flailing around and, eventually, defeat.

I used language related to physical conflict there, but this also applies to the mental realm, like when government passes a law you don't agree with, and anger leads you to mobilize.

"I'm as mad as hell, and I'm not going to take this anymore!"

The quote there is from a 70s movie, Network. I don't recall ever seeing the film, but the line is iconic, with or without the context provided by the story. So of course, I looked it up on Wikipedia,

because it's not like I have to avoid spoilers for a movie that came out before Star Wars.

Which, if you take a look at the link there, provides a nice segué into the other half of the equation. Above, I touched on how useful anger might be to the person feeling it. But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation.

An angry person doesn't think rationally. This is almost by definition: "mad" is a synonym for "angry," but it's also a synonym for "fucking nuts." If you don't want people thinking rationally, if you want them to react with their limbic system instead of their neocortex, as it were... get 'em angry. Convince them, through emotional language, that their social position, their way of life, their very lives are in imminent danger, and you'll sell more torches and pitchforks.

I always thought it would be fun to put a Torch and Pitchfork store into an RPG campaign, to provide helpful tools for the occasional riot. The proprietor would be bored most of the time, so, occasionally, they'd drum up some business by manufacturing some sort of outrage. "The King wants to increase taxes so he can gold-plate his throne! Meanwhile, honest merchants are struggling! Are we going to let that stand?"

Might be a little too close to reality for a fantasy role-playing game, though.

So, to answer the prompt, anger can be very useful... in the people you're trying to influence. Way more useful there, as an agent of chaos, than it can be for an individual reacting to an actual threat.

So, if a headline spurs you to anger... take a step back. While suppressing anger is probably bad (or so I've heard), it may be possible to calm down enough to let some rational thought take over. If I'm right about the fight-or-flight thing, which I can't guarantee, anger is a kind of burst emotion; I imagine a whole cascade of neurotransmitters firing indiscriminately, urging us to action. And that burst can't really be sustained, any more than more pleasant emotions can.

Anger is a useful tool for the people in charge. It's way more useful for the rest of us to recognize when we're being manipulated, and sidestep that.

In my unprofessional opinion.

4 Like • Comment • View 1 comment

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