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Saturday, Dec. 21, 2024

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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:

tj-Merry Mischief Maker

about 17 hours 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

about 22 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 22 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
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

a day ago
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

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

July 21, 2024 at 8:39am

#1074214

Revisited: "Smiley"

My weekly trip into the archives only took me back two years, this time, to July of 2022, almost to the day. It's a fairly long set of musings on a fairly long article from aeon: "Smiley"

And it is, as one might guess, all about smiles.

Now, it's only been two years, as compared to the many years of history discussed by the article. One of the reasons I do these things is to see how things have changed, and, well, not much has changed in two years. There's some discussion of face masks, which were more prevalent in public in 2022, but that's about it.

I will, therefore, just point out a couple of things I either missed or left out in a failed attempt at brevity back then.

First, as academics are wont to do, the article includes a foray into Latin:

Ancient Romans showed another variant. If we take their vocabulary at face value, they did not distinguish between a smile and a laugh, contenting themselves with a single Latin verb – ridere – for both. Only towards the end of the Roman Empire did a diminutive – subridere – enter the language. This came with the derived noun sub-risus (later, surrisus) a ‘sub-laugh’– a little or low laugh – associated with mockery. It retained this lesser status and this diminutive form, distinguishing it from the laugh as it entered the Romance languages in the High Middle Ages. Around 1300, for example, French contained words for laughing (rire) and laughter (le rire or le ris) and smile (sourire, from sous-rire).

I'll point out now that the Latin ridere is the known origin of our words "ridicule" and "ridiculous," which today don't conjure up much in terms of smiley laughter, but rather lip-raising scorn, such as I occasionally heap upon stupid articles in here. Not the one under discussion today, but others.

Second, it's been bandied about that forcing a smile also forces the underlying emotions of happiness, contentment, or relaxation, and supposedly makes one appear more friendly and approachable.

Neither of these things is always good, in my opinion. Sometimes it's best to work with the emotions you're actually feeling (or so I've heard, at least for actual humans). And one does not always want to look friendly and approachable, because someone might approach you and try to get friendly.

It could even be a symptom of the foul practice of toxic positivity.

And to me, forcing a smile is the exact opposite of relaxation. I'm not suggesting frowning as an alternative, but just... letting it be. Unless you're in the kind of situation where people shouldn't know what your actual emotions are, lest you get intrusive questions like "Why the long face?" or "Okay, what are you grinning about?" Or if, you know, you're at a poker table.

I still pity the retail workers who have to go all day with a fake smile plastered upon their face. Even worse are the ones who are genuinely happy to have to present their customer-service face to the world. I mean... why? Smiley faces are for people who aren't paying attention.

So anyway, the original entry and article are there at the link, and I still think the article's interesting. But I don't think I smiled even once.

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