Complex Numbers (Book)

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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/

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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 4 hours ago
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

about 6 hours ago
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

Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

November 14, 2024 at 11:16am

#1079935

Global Domination

Back in the early days of this blog, I had a running joke about ragging on Hello Kitty. Very recently, I found this article from Fast Company:

Hello Kitty turns 50: Here’s how she became a global moneymaker
As Hello Kitty’s commercial success expanded beyond Asia, so did her personal profile.

At least, I thought of it as a running joke. Looking back, it might have seemed like a serious hate-on. Either way, though, the whole reason for the gag was the Nefarious Neko's worldwide appeal, how the character seemed to be everywhere, on all things, in all contexts.

This, of course, is successful marketing. As I've said before, I sometimes put marketing articles in here because many people have things they want to promote, like, maybe, their books. And also, the psychology of it can be interesting.

Hello Kitty turns 50 on Friday.

For context, if you don't want to click on the link, "Friday" was November 1 of this year.

As a tabula rasa open to interpretation, the non-threatening creation was the perfect vehicle for making money, she said.

This strikes me as opposite to most marketing advice, which is to know your audience and pander to it. In the past, I'd have taken issue with the "non-threatening" description, but again, I think those jokes fell flat.

There have been anniversary editions of merchandise ranging from pet collars, cosmetics and McDonald’s Happy Meals to Crocs and a Baccarat crystal figurine.

On the other hand, I'd have had a field day with Hello Kitty Crocs. Hell, I might still be able to work up a rant about that particular combination.

By the late 1970s, Sanrio revealed the character’s name as Kitty White, her height as five apples tall and her birthplace as suburban London, where the company said she lived with her parents and twin sister Mimmy.

That much, I knew. ("Know your enemy," I might have said in the past.)

Her TV appearances required co-stars, including a pet cat named Charmmy Kitty that made its debut 20 years ago.

This was also always suspect to me. A cat owning a cat? Isn't that, like, slavery?

But Hello Kitty’s 40th birthday brought an update that astonished fans. Sanrio clarified to a Los Angeles museum curator that Kitty, despite her feline features, was a little girl.

Thus sidestepping the "slavery" issue and pushing the conversation back to animal rights. Just kidding; I doubt anyone else thought deeply about the ethics involved.

“She is supposed to be Kitty White and English. But this is part of the enigma: Who is Hello Kitty? We can’t figure it out. We don’t even know if she is a cat,” art historian Joyce S. Cheng, a University of Oregon associate professor, said. “There is an unresolved indeterminacy about her that is so amazing.”

Like if she were in a box with a radioactive atom. Schrõdinger's Hello Kitty.

Part of the confusion stems from a misunderstanding of “kawaii,” which is Japanese for “cute” but also connotes a lovable or adorable essence.

It may be cliché, but some things really do get lost in translation.

During a presentation earlier this year in Seoul, Hello Kitty designer Yamaguchi said one of her unfulfilled goals was finding a way “to develop a Hello Kitty for men to fall in love with as well.” But she’s still working on it.

I have some ideas, but I try to keep this blog 18+.

Even if I'd been serious about my ragging on Hello Kitty, that came to an end some years ago, when I read an article (which I can't find now) featuring some village in Northern Siberia, considered the most remote human settlement in the world (pretty sure they didn't include Antarctic research bases, just places where humans naturally settled). Of course, the village isn't entirely unreachable, or they wouldn't have done an article on it, but apparently, it's only accessible by some rickety train line in the week when there's summer there.

The article included pictures, and in one of them, a little girl in this remote village unconnected to the world at large was wearing a Hello Kitty shirt. That is when I knew that her dominance was complete, and no amount of rage, joking or otherwise, would end her hegemony.

Honestly, these days, I think we could do a lot worse.

5 Like • Comment • View 2 comments

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