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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Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

March 30, 2021 at 12:01am

#1007295

Lawn Order

I've been waiting for a very, very long time to have an appropriate use for this entry's title.

The American Obsession with Lawns
Lawns are the most grown crop in the U.S.—and they're not one that anyone can eat; their primary purpose is to make us look and feel good about ourselves

Yes, the article is nearly four years old. Still relevant.

It’s the time of year when the buzz of landscaping equipment begins to fill the air, and people begin to scrutinize their curb appeal.

Not this people. I have no intention of selling my house or moving, so I couldn't care less what other people think. Well, except for the minimum standards required by local ordinance. Fortunately (and not by accident), I don't live in a place with a Homeowners' Association.

The goal—as confirmed by the efforts of Abraham Levitt in his sweeping exercise in conformity (although it had been established well before that)—is to attain a patch of green grass of a singular type with no weeds that is attached to your home.

Mine currently has dandelions. They add color and nonconformity. When they seed, I'm sure my downwind neighbors curse my name and my ancestors.

Why do Americans place so much importance on lawn maintenance?

I've been asking myself that for a very long time. It's always struck me as horribly inefficient and useless.

The state of a homeowner’s lawn is important in relation to their status within the community and to the status of the community at large.

Oh, right. Status. Status is always inefficient; that's the whole point.

To have a well maintained lawn is a sign to others that you have the time and/or the money to support this attraction.

I have the time. I have the money. What I don't have is the ability to be arsed.

It signifies that you care about belonging and want others to see that you are like them.

Look, by not having the Perfect Lawn, I am actually doing my neighbors a service. Everyone wants to emulate the best lawn in the neighborhood (well, everyone but me), but they'll settle for not having the worst. By having the worst lawn, I'm lowering the bar so my neighbors don't have to work so hard.

You're welcome.

Many homeowner associations have regulations to the effect of how often a lawn must be maintained.

Hence why I don't live in an HOA neighborhood. Sure, the city has standards; the grass can't be more than 12" tall. That's way more lenient than any HOA standards.

But lawns are a recent development in the human history of altering our environment.

And that's the other thing: caring about the environment is incompatible with caring about your lawn. Mowing uses gasoline, albeit a small amount. Fertlizer gets into waterways and contributes to algae blooms and nutrification (which despite its name is actually a Bad Thing). And a perfectly manicured lawn isn't exactly what you'd call conducive to habitat diversity. Probably worst of all, though, is the utter waste of water used in sprinklers.

Lately there have been efforts to mitigate all of these things, but they could be eliminated almost entirely if we collectively decided "fuck this lawn shit."

The article goes into the history of lawns in the US, and it's enlightening to read, if peppered with editing problems.

The rise in economic opportunities meant that homeowners who were inclined to pursue a green carpet of grass could hire someone to attend to its needs—another indicator of success.

Guilty. I pay a service $50 a month to keep the lawn somewhat trimmed.

My home, for example, sits between two extremes: on one side, we have neighbors who meticulously care for their lawn—they have a sprinkler system and regularly scheduled lawn maintenance—and on the other, we have neighbors who let their lawn run wild and will mow once or twice a season—their lawn is riddled with dandelions and other weeds. The homeowner in the former instance stopped by to tell us that she was seeing signs of crabgrass on her lawn. She scrutinized our patch of greenery as well as the other neighbors’ before going home. While this overall dynamic is common throughout our neighborhood—there is a mix of maintenance—she was specifically concerned on how this would impact and reflect on her.

The neighbor on one side of me used to have the perfectly maintained lawn (she died a few years ago and it's declined a bit); I'd see a Chemlawn van out there every month or so, which sucked because I'm downhill from that house and that shit seeped over the property line. The neighbors on the other side seem to have the same attitude to lawn care that I do. Neither of them ever said word one to me about the lawn, though I suspect the snooty one once called the city on me one time when the grass was 12.1" tall. Nor have I heard anything from the other homeowners in the neighborhood. With one exception (and you know the type), we tend to all mind our own business.

We are at a moment when the American Dream, inasmuch as it still exists, is changing. The idea of homeownership is untenable or undesirable for many. While green spaces are important, a large area of green grass seems to be a lower priority for many. With a growing movement that embraces a more natural lifestyle, there is a trend toward the return of naturalized lawns that welcome flowering weeds, and subsequently support a more diverse entomological ecosystem.

Translation: bugs are good now.

Lawns are American. But they're also an anomaly. And they may no longer fit the realities of the world we live in.

Sounds familiar.

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