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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

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:

Kåre Enga in Montana

about 17 hours ago
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

about 22 hours ago
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

a day ago
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

August 11, 2021 at 12:06am

#1015475

Whipshrek

This one's about a movie, but not one I've seen recently. No, earlier this year I was treated to the Guardian's brutal takedown of a 20-year-old movie. And it's just now come up for me to review the review.

Shrek at 20: an unfunny and overrated low for blockbuster animation
The fairytale comedy was a hit with critics and audiences but its toilet humour, glibness and shoddy animation mark it out as a misfire

So... audiences liked it, critics liked it... but some elitist asshole is here to tell us all that we're wrong and we should be ashamed of ourselves by calling it a "misfire."

Hopefully y'all know by now that I like different kinds of movies. Highbrow, lowbrow, unibrow, whatever... I won't be browbeaten into joining the consensus or rebelling against it. And I'm certainly not above laughing at juvenile humor, though I can also appreciate fancy French art flicks.

Hating on Shrek is just plain snobbery.

I'm not saying it's a great movie, mind you. But it certainly doesn't suck.

Shrek has an outhouse with a working toilet.

Oh yeah, let's open up by pointing out the bathroom humor. It's a kids' movie for shit's sake; there's going to be bathroom humor.

Twenty years later, that flushing sound seems to signify the moment when blockbuster animation circled the drain.

Right, because no animated movie has succeeded since then.

Shrek is a terrible movie.

No it's not.

It’s not funny.

Yes it is.

It looks awful.

No it doesn't. Okay, yeah, animation has come a long way in 20 years, along with the computers that generate it, but it's perfectly fine for the time.

And yet Shrek was a sensation with critics and audiences in 2001.

So, this guy is positioning himself as the ultimate arbiter of how good a movie is, and not other critics or, you know, the people who actually pay money to see them. Look, I get it; I have opinions, too, and not all of them align with the consensus. I disliked The Matrix. I liked Cats. I never saw Titanic and don't plan to. Whatever. We all like what we like and hate what we hate. I'm waiting for an objective argument to support the author's hate.

Even the stuffed shirts at the Cannes film festival, who usually separated Hollywood summer fare from its official selections, brought it into the competition slate, where it premiered alongside new work from world masters like David Lynch, Jean-Luc Godard, Hou Hsiao-hsien and Jacques Rivette.

You do not get to look down your nose at a lowbrow children's comedy (that also has adult appeal) and then call the Cannes judges "stuffed shirts." Pot, meet kettle.

Worse yet, it encouraged a destructive, know-it-all attitude toward the classics that made any earnest engagement with them seem like a waste of time. Those once-upon-a-times were now rendered stodgy and lame, literally toilet paper.

Yes. That's how storytelling evolves. Shakespeare was sop for the working classes of London; his works only gathered a patina of respectability with time, and people continue to riff off of the plays. As I noted in an entry a while back, it's likely that the works we know as "fairy tales" changed multiple times, with new audiences and new context, before they were written down in their "final" form. Playing with those ideas, updating them for the times, is what storytellers do.

But the balance in Shrek is off on both ends: there’s an excess of anachronisms and buddy-movie riffs from Myers and Murphy that have little relation to the backdrop and a woe-is-me soppiness to the love story between two lonely, misunderstood freaks. (Nothing screams “unearned gravitas” like slipping in a cover of Leonard Cohen’s Hallelujah.)

YOU SHUT YOUR PUDDINGHOLE RIGHT NOW.

But once Shrek and Donkey cross the kingdom on a quest to bring Fiona to Farquaad, the storybook references are all but abandoned. Even when Robin Hood and his Merry Men appear in the woods, the film blows past that boring old mythos in order to pay homage to The Matrix and Riverdance.

Yes. That's a feature, not a bug.

Last year, the National Film Registry added Shrek to the Library of Congress, which seals its canonization, but it’s remarkable how much of an early aughts relic it’s become, an amber-preserved monument to phenomena (Mike Myers, Smash Mouth, Michael Flatley) that hasn’t stood the test of time.

"Noughties," not "aughts." Come on, even the BBC has adopted my word for that decade. Probably not on purpose, though.

Even the film’s referential style looks resolutely slow and unhip next to the whirring pop Cuisinarts of Lord and Miller productions like The Lego Movie and Spider-Man: Into the Spider-Verse or even IP-heavy Disney fare like Wreck-it Ralph and its sequel.

Yes, because those movies came out later and had the benefit of better technology. This is like comparing the original Godzilla to this year's Godzilla vs. Kong.

Don't get me wrong; I like the Guardian in general (their harsh review of Hudson Yards sticks out in my mind as the greatest piece of architectural criticism in the history of ever, though to be fair, it's an opinion I already shared), but this would be something like the British equivalent of a small-town newspaper from Alabama reviewing Broadway plays. They're entitled to their opinion, but they're not the target audience. And the UK is hardly innocent in producing lowbrow humor. (I should note that for all I know, the reviewer is from the US, but he's still writing for a British journal.)

So, okay, I get it; he didn't like the movie. Fine. A lot of the reasons he hated it are the same reasons I liked it. I hope I never see his opinion of Despicable Me. Or, actually, I hope I do so I can rag on that review, too.

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