Complex Numbers (Book)

Blog Calendar

◄ October ► 2023
S	M	T	W	T	F	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

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:

Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

October 12, 2023 at 10:31am

#1057227

Weird Barbaric Idiot Geek Dicks

Another scholarly linguistics article today... wait, did I say scholarly? I meant amusing, because it's from Cracked.

5 Infamous Insults That Used to Mean Something Totally Different

When picking a new insult to throw at someone, current comedic convention suggests you string together a series of random incongruous words. You type, “Yeah, like I’m going to take advice from a lopsided milk-stained piss plank.”

This works great when you're typing, because you have time to think and/or randomly choose the next word. Not so easy in person, but for that, there's always "Your mama."

5. A Geek Was a Carnival Worker Who Bit Heads Off Chickens

I'm old enough to, if not remember this definition, at least remember older people remembering this definition.

A geek worked at a carnival, in an act called a geek show. Some carnival performers exhibited impressive talents, and the freaks showed off strange physical features, but here’s what the geeks did: They bit the heads off of life animals.

Another expression that's lost its meaning is "copy editor."

“Geek” started to attain its current meaning in the 1980s.

Wrong. 1970s. A wrestler called Fred Blassie (among other monikers, but that one was actually based on his real name) had used the catchphrase "Pencil-necked geek," and he wrote a song called that in, like, '75. I'm pretty sure he was the main reason the meaning changed.

4. An Idiot Was Anyone But a Politician

I'm pretty sure I've mentioned this sort of thing before.

An idiot was someone with an I.Q. less than 25, while other words described people that fell in other ranges — an imbecile scored between 25 and 50, while a moron managed between 50 and 75.

No matter what words we come up with to describe those of lower than standard intelligence, they will always, always morph into a general insult, requiring us to come up with new connotation-neutral words to describe them, which will inevitably morph into a general insult, ad infinitum.

But this is the interesting part (and it does seem to be at least partially true):

“Idiot” has deeper roots, however. It comes from the Greek idiotes, which described a private person... A private person wasn’t someone with a private personality but the opposite of a public figure. It meant a non-politician.

So, one of those cases where the word came to mean its opposite.

3. Dicks Were Older Than Penises

No real surprise here. Linguistically, anyway.

Naturally, Dick has been a name for many centuries, while “dick” has only meant penis since the 19th century. Less obviously, a dick meant a man since before it meant a penis. In the 16th century, the word just meant “guy,” and you’d call someone an odd dick just as you’d call them an odd fellow.

Really, just about any word can mean penis if you want it to, depending on context. Like geek, for example. "That woman only dates geeks," someone might say, to which a guy might respond, "She can try my geek."

Okay, maybe that doesn't always work.

2. A Barbarian Spoke Gibberish

Today, a barbarian is a specific type of warrior, capable of relentless rage and proficient with medium armor.

Depends on your preferred game system. I think it was D&D version 3.5 where a barbarian could actually add their wisdom modifier to Armor Class, thus negating the need for armor if you happened to have a decent Wis score. This, I think, was meant to explain how famous literary barbarians such as Conan and Red Sonja could wear a loincloth and a chain bikini (respectively) and still be decent in combat.

But yes, in D&D 5 and Pathfinder (a fork of D&D 3), barbarians can rock medium armor, such as hide or chain mail.

Before that, it was a word to levy at any of various peoples to dismiss them as savages. But let’s go even further back, to the Greeks, who originated the term. They used the word to describe anyone who didn’t speak Greek.

Many of the peoples called barbarians by the Greeks and, later, Romans, had a well-developed culture. The Norse, e.g.

The reason they came up with the word barbarian (or the root, barbaroi) was that people speaking anything but Greek sounded to them like they were just saying “ba-ba.” Barbarians were “blah blah” speakers.

And in earlier versions of D&D, they were generally illiterate. Which is also unrepresentative of actual barbarians.

1. ‘Weird’ Meant You Have the Power to Magically Control Fate

Being literate, I knew this. But it's still an interesting case study of how words change in meaning.

Originally, the word said nothing about the wrong kind of nonconformity but instead referred to the magical power to control fate.

The article provides examples.

Wyrd was an old Norse word meaning “fate,” and in its earliest English form, it was associated with the Fates from Greek mythology.

See? Barbarians can and do contribute to culture.

4 Like • Comment • View 2 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.