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Complex Numbers

by Waltz Invictus

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:

Annette

about 10 hours ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

June 17, 2024 at 7:47am

#1072773

I Want It To Work, But...

Today's article, from SciAm, is an ad. Though it's for a book, which I've repeatedly insisted is appropriate here (much as movie previews are appropriate ads before movies), I just wanted to state that up front.

Can Scientific Thinking Save the World?
A physicist, a philosopher and a psychologist are working together to bring better, smarter decision-making to the masses

As I've also repeated, my default answer to any binary headline question is "no."

I mean, I'd like it to be "yes," but the world stubbornly refuses to conform to my wishes.

Spurred by what they saw as a perilously rising tide of irrationality, misinformation and sociopolitical polarization, they teamed up in 2011 to create a multidisciplinary course at the University of California, Berkeley, with the modest goal of teaching undergraduate students how to think—more specifically, how to think like a scientist.

Seeing that now, 13 years later, that particular (red) tide keeps rising, I'd say the world stubbornly refuses to conform to their wishes, too.

Now the three researchers are bringing their message to the masses with a new book, Third Millennium Thinking: Creating Sense in a World of Nonsense.

Like I said: ad.

And their timing is impeccable: Our world seems to have only become more uncertain and complex since their course began, with cognitive biases and information overload all too easily clouding debates over high-stakes issues such as climate change, global pandemics, and the development and regulation of artificial intelligence.

Perhaps they're just pissing into the ocean.

Scientific American spoke with Perlmutter, Campbell and MacCoun about their work—and whether it’s wishful thinking to believe logic and evidence can save the world.

The rest of the adarticle is in interview format. I find it interesting, which shouldn't be surprising, given that the disciplines in question are ones I've discussed here on numerous occasions. But no point in rehashing points.

Instead, since the subhead up there cries out for it, I'll attempt to make up a joke:

A physicist, a philosopher and a psychologist walk into a bar. Bartender says, "What'll it be?"

The physicist says, "The answer depends on the level of our knowledge of all the prior states of the system."

The philosopher says, "The future is unknowable; we just have to wait to find out."

The psychologist says, "I'll have a beer. These two chucklefucks want wine."

...I didn't say it would be a good joke.

5 Like • Comment • View 4 comments

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