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 2 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 4 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.

January 26, 2023 at 12:02am

#1043676

Monopoly

By now, the true origins of Monopoly (the game) have been circulated pretty widely, so, like me, you probably already know that the official origin story is a bunch of horse hockey. But it's true that the classic game's spaces were lifted from Atlantic City.

How Atlantic City inspired the Monopoly board
The popular game has a backstory rife with segregation, inequality, intellectual theft, and outlandish political theories.

Which made it all the more amusing when, on a trip to an Atlantic City casino, I ended up playing a Monopoly-themed slot machine.

More on that later.

There have been several attempts to turn Monopoly the game into a Hollywood movie, one with Ridley Scott directing, another starring Kevin Hart.

I'm not aware of a single instance of a movie adaptation of a game being anything better than "meh." "But The Witcher." Well, The Witcher started out as a book and the game was an adaptation of that. Besides, that's not a movie but a series. A very good series, in case you haven't seen it. No, you don't need to have read the book or played the games.

Point being, even though he directed the greatest movie of all time, even Ridley Scott wouldn't be able to save a movie adaptation of a board game. No one would.

Dig deep, and you’ll find racial segregation, economic inequality, intellectual property theft, and outlandish political theories.

Dig deep into anything American and you'll find all those things.

But let’s start with the board—a map of sorts and a story in itself.

This is where you'd have to go to the linked article, as embedding pictures here is a pain in the ass. The map there shows exactly which Monopoly properties come from which streets.

To aficionados of the game, however, the names of the streets on the “classic” board have that special quality of authenticity, from lowly Baltic Avenue to fancy Park Place. Those places sound familiar not just if you like Monopoly, but also if you drive around Atlantic City, New Jersey’s slightly run-down seaside casino town.

And you will want to drive around if you're there. I tried walking there, for about a mile, in broad daylight, on a weekday, along Pacific Avenue, and got two offers of sex, three offers of drugs (there was a bit of overlap there), and the opportunity to witness a violent confrontation between two locals.

On the plus side, I didn't get mugged, so there's that.

Atlantic City was never not "slightly run-down." It's only worse now, as the surrounding states have introduced casinos and other gambling venues.

The bulk of the article describes the mapping of Monopoly properties to AC streets, and I'm skipping most of that, except:

Light purple
Three streets branching off Pacific Avenue: Virginia Avenue, a long street towards the northwest; and St. Charles Place and States Avenue, two short spurs towards the southeast. St. Charles Place is no more; it made way for a hotel-casino called the Showboat Atlantic City.

It was the Showboat where I played the Monopoly slots. Slot machines suck, but I couldn't resist playing a Monopoly one in Atlantic City. Last I heard, the hotel took out the gambling section, opting instead to concentrate on resort and convention functions.

I haven't seen that particular machine anywhere else in AC. They used to have a few in the casinos I visited in Vegas, but those are gone, too. The slots, I mean; not the casinos.

The article then delves into more of the history, with all the racial segregation and other fun stuff mentioned above. However, unlike Atlantic City itself, it's not all bad:

Belying both the binary prejudices of the time and the sliding price scale of the Monopoly board, Atlantic City back then was in fact a place of opportunity where a diverse range of communities flourished. Black businesses thrived on Kentucky Avenue. Count Basie played the Paradise Club on Illinois Avenue. There was a Black beach at the end of Indiana Avenue. For Chinese restaurants and Jewish delis, people headed to Oriental Avenue. New York Avenue had some of the first gay bars in the U.S.

An Atlantic City-based board was sold to Parker Brothers by Charles Darrow, who claimed to have invented the game in his basement. Parker Brothers marketed the game as Monopoly from 1935. The rights to the game transferred to Hasbro when it acquired Parker Brothers in 1991.

Hasbro also publishes D&D, and they're in the process of destroying that property, too.

But the original Monopoly was, as this article notes, the actual antithesis of what Monopoly is. For the full effect, again, check the article, which also includes a graphic featuring an early board, as designed by the credited inventor, whose name was Lizzie Magie.

She created two sets of rules: an anti-monopolist one, called Prosperity, in which all were rewarded for any wealth created; and a monopolist one, called Monopoly, in which the aim was to crush one’s opponents by creating monopolies. In the latter version, when a player owns all the streets of one color, they can charge double rent and erect houses and hotels on the properties.

Taken together, these two versions were meant to illustrate the evil of monopolies and the benefit of a more cooperative approach to wealth creation. It’s very telling of human nature that it’s the opponent-crushing version that came out the winner.

It's more telling of corporate nature, as it was a corporation that published the game. Why would they undermine their own philosophy?

And I don't know... maybe if the collectivist version had won out, the divorce rate wouldn't be so high. Never play Monopoly with family, unless you don't want a family anymore.

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