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Sunday, Dec. 22, 2024

11:39am EST

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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 24 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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2 Like

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

September 15, 2024 at 10:44am

#1076824

Revisited: "Gotta be Aliens"

In rooting through the archives at random, I pulled out this entry from early 2020: "Gotta be Aliens"

The linked article,

from aeon, is still available as of this post.

The entry was, apparently, one of my earlier attempts to criticize popular coverage of the sciences involved in the search for extraterrestrial life.

Today, I'm going to talk about aliens again.

I checked, and I'd had ET or ET-adjacent entries at least twice before in that month, but it certainly hadn't taken over my blog.

If these topics seem random, that's because they are, in part.

I don't choose articles at random to put into my queue. I add to it when I come across (or someone sends me) something I find interesting or might have something to quibble or laugh about. It's the order in which I draw from the queue which is random.

In this particular case, the linked article plays off the question in its headline: how would we recognise an alien if we saw one?

One of the reasons I do this retrospectives is to see if things have changed, either in the world or with my own opinion. As far as the latter goes, I don't think I've changed my mind, and I'm pretty sure I've done several other blog entries supporting my view that complex life is probably rare in the galaxy.

In the world, things change all the time. One part that didn't age well was the part about someone saying that what would convince them that aliens were out there would be a photograph.

I said:

I'm not sure that would convince me. After all, photographs can be faked, and the technology needed to fake them is widespread and always getting cheaper.

Since then, we have of course seen an explosion in what's commonly called AI, making it way easier and cheaper to fake a photograph of an alien (or anything). Because discovery of any sort of life elsewhere than on Earth would be such a Big Deal, there would need to be multiple kinds of robust evidence for such a discovery to be accepted.

The rest? Like I said, I haven't changed my opinions on the subject.

3 Like • Comment

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