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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 15 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

June 3, 2024 at 8:51am

#1072084

One for Sorrow, Two for Joy...

It's fairly well known that corvids are hardly birdbrains, but this recent article from SciAm delves into further evidence, while also punning on one of my favorite bands.

Crows Rival Human Toddlers in Counting Skills
Counting crows proclaim “caw, caw, caw, caw” when staring at the number four

The rock group Counting Crows were onto something when they chose their band name. Crows can indeed count, according to research published this week in Science.

That's not why they picked the name, but by Waltz's Law, never let facts get in the way of a good joke. Or a bad one. Especially a bad one.

But, you know, that's just, like, a pinion, man.

Okay, okay, puns out of the way for now, there's some interesting stuff here.

The results show that crows have counting capacities near those of human toddlers who are beginning to develop a knack for numbers, says lead study author Diana Liao, a postdoctoral researcher in neurobiology at the University of Tübingen in Germany.

So, no, they're not about to take over the world or build rockets to Mars.

“We think this is the first time this has been shown for any animal species,” she adds.

I know there's been research done in this area, but I can't be arsed to search for examples countering what the researcher says here. Yes, there have been claims that horses, e.g., can count, but those usually turned out to be hoaxes or misunderstandings.

They presented the birds with randomly ordered cues, four of which were visual—colored Arabic numbers that appeared on a touch screen—and four of which were auditory, including a short guitar chord and a drumroll.

Please, please tell me they sampled the latter from Counting Crows albums. Well, in my headcanon, they absolutely did.

Onur Güntürkün, a biopsychologist at Ruhr University Bochum in Germany, who was not involved in the research, says the new paper is “excellent”—even if the findings are “not unexpected” given all that scientists already know about crows and many other species’ intelligence.

Like I said: we know they're smart. They also apparently have a long memory. There are plenty of stories about people who pissed crows off, only to find themselves harassed by black-winged birds for the rest of their lives, indicating that not only does the pissed-off crow take revenge, but gets all their corvid buddies and offspring to punish the offender. People associate elephants with never forgetting, but elephants ain't got nothin' on crows.

On the flip side, do something nice for a crow, and they could become your army of darkness. I've thought about doing this by leaving shiny things out for them to collect, but I'm entirely too lazy, and what would I do with bird minions, anyway? Get them to attack surveillance drones? No, they might get hurt. Besides, my cats might get jealous.

Obviously, I can't leave this entry without an appropriate video:

If you think you need to go
If you wanted to be free
There's one thing you need to know
And that's that you can't count on me

2 Like • Comment • View 2 comments

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