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Sunday, Nov. 17, 2024

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Complex Numbers

by Robert Waltz

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

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Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Turkey DrumStik

a day ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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

April 14, 2024 at 7:19am

#1068727

Revisited: "Getting the Lead Out"

Today's historical excavation takes us back to 2019, at a time when I was apparently participating in the 30-Day Blogging Challenge... though I neglected to note that in the entry: "Getting the Lead Out"

For context, my current >4 year daily blogging streak wouldn't start for about another month, and, obviously, this was in the Before Time.

The prompt I was writing to started with "What characteristics do you admire in a leader?" and continued to build on that. I'm not sure I really addressed all the nuances of the prompt, but I'm okay with that, especially now that it's >4 years later.

I am a Bad Example. I even printed up "business" cards with my name followed by "Bad Example."

My friend's ex-wife never liked me. She called me his "bad influence." I should have run with that, instead.

But I'm not always. Case in point: it might have been the month after this entry appeared, maybe not, but let me set the scene: California, the home of two of my friends, married to each other, and their kids. Breakfast time. Someone made pancakes. I poured a small amount of syrup onto said pancakes.

The mom, talking to the youngest kid, maybe 12 or so: "See how he doesn't drown the pancakes in syrup?"

The dad, to me: "Bet that's the first time you've been held up as an example of self-restraint."

Everyone involved, especially me, had a good laugh at that one.

Basically, I don't want to be a leader. I don't like it. The benefits don't outweigh the constrictions, for me. I admire those people who can do it...

I worded this poorly, I think. There are lots of people who are "leaders" that don't deserve, or get, my admiration, or even respect. Evangelical TV preachers, for example. Most politicians, from any political party. Certain billionaires. Thing is, those types get all the press. I'd be hard-pressed to cite an example of a leader I actually admire, at least in terms of naming someone well-known. Being well-known probably works against you, there; not one of us is without our follies and drawbacks, and being in the public eye tends to put a magnifying glass on them.

What I should have said was probably that I have some respect for those who can balance things well enough to be both a good leader and, mostly, still be what I'd consider a good person.

But there's one thing I hate more than being a leader, and that's being a follower.

Still true.

Fortunately, life isn't binary, and I choose Option C: going my own way. It's enough to be responsible for my own situation, and I'm not always so good at even that.

Not everyone has that option, I know.

Another thing I'm terrible at is motivating people. I like it when people motivate themselves. Any attempts I make in that direction always seem hollow to me. But I think good leaders find ways to motivate their team, though how they do it might as well be sorcery for all I understand it.

A few weeks after this entry, I did one on Emotional Intelligence, or EQ. I only remember this because I was skimming nearby entries while trying to remember the context of this one. I probably could have related the two concepts at that time, but I didn't. In summary, I question the whole concept of EQ because it seems self-referential: they define EQ as the quality needed to achieve success (based on a narrow definition of success), and to achieve that kind of success, you need a higher EQ.

My point being that I imagine it takes those same qualities to be an effective leader.

Anyway, yeah, this is kind of rambling, but the bottom line is: don't look to me to set examples, unless you enjoy drinking at bars.

Again, this was the Before Time, so the difference now is I'd end that sentence with "home."

1 Like • Comment

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