Complex Numbers (Book)

Blog Calendar

◄ January ► 2021
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

January 29, 2021 at 12:10am

#1003143

Funny

PROMPT January 29th

Write about something funny! Share a joke, recount a humorous story, or tell your readers about a funny experience you had.

Oh man... I don't know if I can do this.

The funny thing about being funny is it's really, really hard to be funny on demand.

Like, I could be telling jokes for hours, and then someone will turn to me and go, "Hey Waltz, say something funny." And the best I can come up with is to say, "Something funny." And that's if I think of it. It's like every cell in my brain runs off to the "I really like beer" cortex and settles down for a cold one.

What's worse is I'm scheduled to do next week's Comedy newsletter, and I haven't thought of a single thing to say. My first Comedy newsletter was 14 years ago this month, though I didn't become a regular editor of it until two months later, in March 2007. Since that fateful March, I've managed to do an editorial every four weeks (give or take, what with scheduling changes along the way), usually finding something to say at the very last minute.

This is why I procrastinate: It works.

Not that they were all great, mind you. Some of them were crappier than a porta-potty at a laxative festival.

In the ancient times B.I. (Before Internet), I had a memory for jokes. Someone would tell me a joke once, and I'd remember it and be able to deliver it at any point thereafter, usually with a few riffs. But at least I rarely fucked up the punch line. Now, though? No point remembering things if I can just look them up on the internet.

Twenty years or so ago, someone scientifically determined the World's Funniest Joke.

It's at the link, but I'll reproduce it here for those of you who don't want to open a link:

Two hunters are out in the woods when one of them collapses. He doesn't seem to be breathing and his eyes are glazed. The other guy whips out his phone and calls the emergency services. He gasps, "My friend is dead! What can I do?" The operator says, "Calm down. I can help. First, let's make sure he's dead." There is a silence; then a gun shot is heard. Back on the phone, the guy says, "OK, now what?"

Now, this joke certainly has aspects that make it funny. The important part is the difference between what is meant by "First, let's make sure he's dead" and what the hunter understands. Misunderstanding is an important part of comedy. From there, you have to set it up so the person doing the calling is expected to have a gun; hence "hunters." It wouldn't work with just "two guys are taking a walk in the woods."

One version of this joke that I saw specifies, for some reason, that the hunters are from New Jersey, which makes me believe that the joke was originally a New York thing. I'd tell it about West Virginians, myself.

The second important part of the joke is that someone dies. Yes, this is part of comedy. Most jokes require someone to be hurt. As Mel Brooks once pointed out when asked the difference between comedy and tragedy, “Tragedy is when I cut my finger. Comedy is when you fall into an open sewer and die.” Jokes help us come to terms with our own mortality and frailty.

I could do without the passive voice, though. "...a gun shot is heard." I imagine that if one were telling this joke the old-fashioned way, in person, one would go "There's a silence, then BANG."

Now, for a while there, this particular "funniest joke" contest was looking like it was going to have a different winner. Here's that one:

Sherlock Holmes and Dr Watson are going camping. They pitch their tent under the stars and go to sleep. In the middle of the night Holmes wakes Watson up: "Watson, look up at the stars, and tell me what you deduce."

Watson: "I see millions of stars and even if a few of those have planets, it's quite likely there are some planets like Earth, and if there are a few planets like Earth out there, there might also be life."

Holmes: "Watson, you idiot, somebody's stolen our tent!"

You'll note that no one dies in this one. But the joke hinges on a different kind of misfortune. The other comedic element is Watson waxing philosophical when he should have been more practical, a reminder to all of us that sometimes we need to focus on what's around us instead of having our heads in the clouds all the time. That combined with the absurdity of someone being able to steal the tent in the first place makes this, objectively, quite humorous.

Nevertheless, I didn't laugh at either of these jokes. Why? Well, partly because you can't build something up by saying, "Okay, I'm about to tell you the funniest joke ever." This sets expectations way too high, and whoever you're telling it to is primed to think of reasons why it's not, after all, the funniest joke ever. Probably if someone just told me one of those jokes at a party (remember parties?) without the buildup, and if I'd never heard / read them, I might have chuckled (genuinely, not just out of politeness).

I'll leave you with one more joke. I don't know if it was ever in the running for this scientific study of comedy, but I've known it for quite a long time, since about ten years B.I. As with many jokes, I don't know the origin of it, and I'm not going to look it up but tell it from memory:

A scientist was developing a serum to vastly extend the lifespan of marine mammals. The primary ingredient in the formula was extract of mynah bird, which was a bit hard to come by, and one day, in the middle of testing this on his pet dolphin, he ran out of extract. So he went to the pet store to pick up a fresh batch of birds.

While he was gone, though, there was a problem at the local zoo, and some of the big cats escaped and started roaming the city. One of them curled up on this scientist's front doorstep and went to sleep.

So here comes our scientist back from the store with a bag full of mynah birds, when he notices the King of the Beasts blocking his door. "Oh, no," he thinks, "What am I going to do? I have to get inside; I'm at a critical stage in my experiments. There's no other way into the house. How am I going to get past this guy without waking him up and likely getting eaten?" He thinks about it for a few minutes and decides on a stealth approach. So he tiptoes up to the house, real quiet-like, and edges his way toward the front door.

He's managed to put one foot over the animal when a dozen cops come out of nowhere, point their guns at him, and go:

"Freeze, mister! You're under arrest...

...for transporting mynahs across sedate lions for immortal porpoises!"

I'll be here all week.

5 Like • Comment • View 10 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.