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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Write_Mikey_Write!

about 9 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 11 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.

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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').

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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.

June 14, 2021 at 12:02am

#1011839

Dunning-Kruger-Rand

Sometimes I need to be reminded that words have power -- for good or ill.

4 Famous People Driven Insane By Ayn Rand

And sometimes it takes a juvenile dick joke website to remind me of that.

(Incidentally, today's title is also related to my name for cryptocurrencies, "Dunning-Krugerrands." Unfortunately, I don't get enough opportunity to use that phrase, because I'm always concerned that people won't get the joke.)

Ayn Rand is unfortunately still popular, because reading good books is hard. She's best known for Atlas Shrugged, a boring lecture on the tenets of objectivism disguised as a boring novel. Objectivism, if you don't want to read the angry 5,000 word comments that spawn whenever Rand is mentioned, boils down to the belief that pure self-interest is the highest ideal humanity can have.

The way I see it, it's in my self-interest to be kind to, respect, and help other people.

We're here today because a bunch of Rand-worshipping bozos fought reality and lost, or at least made asses of themselves. So let's look at some asses.

I'm not really a butt perso- oh. You meant that figuratively.

4. Ayn Rand Inspired The CEO Of Sears (To Ruin Sears)

In academia, Rand's reputation is about level with phrenology's. A Rand biography wrote that critics "dismiss Rand as a shallow thinker appealing only to adolescents" and, perhaps not coincidentally, celebrities are big fans. But a lot of people only cite Rand as an influence because she's trendy, or offers superficial thoughtfulness.

I dunno. Compared to Rand's philosophy, phrenology is settled science.

In 2008, Sears was struggling. But that was okay, because Eddie Lampert -- the "Steve Jobs of the investment world" -- was CEO. His solution: skim Rand CliffsNotes. Lampert split Sears into divisions ordered to selfishly compete for his time and money, because he believed that with only their own self-interest to pursue each division could achieve record profits.

I'm not a philosopher, or a CEO. Yes, I co-ran a business for a while, but it was a small business. That hardly makes me an expert. But even I can see that there's no way this ends well -- even if I didn't already know how it ends.

The story of Sears should be used to warn MBA candidates about what not to do, even before Lampert took over -- you know, the way they show engineering students the video of the Tacoma Narrows Bridge failure.

. That company was on top of the world for a very long time -- not just figuratively, but for a while there they owned and occupied the tallest building on the planet. They got that way by providing mail-order goods to rural locations, through their famous catalog, and stayed that way by providing quality merchandise. Hell, for a while there, they sold freakin' prefab houses by mail-order.

Had they played their cards right, they'd have been on top of the internet, and Amazon would be a second-rate contender. But they ignored this internet thing, even though it aligned with their original mission, because by the time the internet came along, Sears had ceased being a retailer and became a finance company with showrooms. And it all went downhill from there, which is when Lampert got involved and, because he read puerile literature (as opposed to puerile comedy websites), he started that whole "internal competition" thing.

Naturally, he's still worth over a billion dollars and owns a yacht called Fountainhead, because if there's one thing Rand definitely loved it was rewarding the incompetent.

Obviously, the damage Rand has done to society isn't limited to one finance / showroom company, but I see that debacle as a fractal microcosm of the bigger problems.

3. The Co-Creator Of Spider-Man And Dr. Strange Created (Terrible) Objectivist Superheroes

They really didn't have to add "terrible" in parentheses there. It's redundant.

To summarize the first bit here, Ditko was partly responsible for Spider-Man and Dr. Strange, so his creations weren't all terrible. But...

Mr. A tended to murder criminals or, worse, lecture them about the beauty of the free market. The thin plots often grind to a halt for his monologues, because one of the key tenets of objectivism is that morality plays must make Goofus and Gallant look nuanced.

Clearly, he also took writing lessons from the Rand School of Expository Monologue

Ditko also created The Question, who's basically the indie Mr. A toned down for mainstream comics. If these characters sound familiar, that's because Alan Moore's Rorschach was inspired by how much Moore loathed them.

I always thought Moore killing off Rorschach at the end of Watchmen was a kind of revenge fantasy (yeah, I know, spoiler, but if you haven't experienced Watchmen by now it's on you), and this just confirms it.

2. Rand Fandom Made Penn Jillette Act Like An Obnoxious Teenager

Not every Rand fixation has to end in tragedy or disaster; it can merely be embarrassing. And, like many embarrassing things, we begin with magicians.

Yes, I like Penn and Teller. But just as with any human beings, they have flaws. Being an Objectivist is a serious flaw, but they still do good work.

Coincidentally, another flaw with objectivism is its adherents' belief in the unique rationality of their framework. They'll tell you they have the only philosophy unfettered by dogma, and if you disagree then you just have to read their favorite books until you realize they're right.

"Unfettered by dogma" except for the utterances of their Great Goddess Rand, of course.

1. Silicon Valley Loves To Cherry Pick Ayn Rand

In Rand's work, a happy ending is when successful people swat aside whiners to get even more money. Not surprisingly, she's big in Silicon Valley. Travis Kalanick, who invented a taxi company that dodges responsibility for sexual assaults, is a fan. So is Brian Armstrong, who asks Coinbase employees to not be political about the cryptocurrency pyramid scheme that uses more electricity than Ireland. And of course there's Elon Musk, who's hard at work saving humanity with ideas like "What if roads were useless death traps?"

Uber (the company formerly associated with Kalanick) has much bigger ethical issues than dodging responsibility for sexual assaults (which is saying something), and everything about them screams "Randian Dystopia."

Doesn't stop me from using them, because it would be more unethical for me to drive drunk. "But Waltz... couldn't you just... you know... not drink?" "Shut up."

In Rand's defense, the average reading of her is superficial. Her heroes are supermen, but part of that superiority comes from their sense of justice. A Randian hero demands hard work, but also rewards it; ignoring a toxic workplace or firing people because you're grumpy would get you an angry ass-kicking from Mr. A. Whether you want a world where CEOs are the ultimate arbiters of justice is another matter, but Silicon Valley's worship of Rand is like making Captain America your role model because he gets to beat up people.

And to be fair, it's been a while since I had a nice slog through anything that horrid woman wrote, so my memory may be only of the superficial as well. But fortunately, there's Cracked.

Just to be clear, I'm not saying "Ayn Rand's books should be canceled" or any crap like that. But I do suggest reading them with a healthy dose of cynicism. Which is how I read almost everything.

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