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 13 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.

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Adherennium Plotting something

about 15 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.

April 5, 2022 at 12:13am

#1030097

Greenwashing

I'd like to propose an alternative definition today. For "Journalistic Intentions"

[18+]:

Greenwashing

From what I understand, "greenwashing" is intended as a riff on "whitewashing," which, despite its name, is not meant to be about racism, but rather about the covering up of flaws through surface cosmetic measures. Originally it was literal, as you'd whitewash, say, a barn, to make it look better and protect it from the elements (it's a particular cheap type of paint that relies on a chemical reaction to make the surface it's on look bright white). Then they started applying the word to covering up a person's scandals by downplaying their bad acts and making them look like better people. Still later, it did acquire a race connotation, like when people of European descent portray characters of color in plays, TV shows, and movies.

The point being that definitions evolve; someone had to use the term in the new way for the first time, and then it caught on.

So this is me, proposing an alternative definition for greenwashing, not based on whitewashing, but on brainwashing.

First, the accepted definition of the term, in my own words:

Greenwashing is when a company markets itself and/or its products as environmentally friendly, while they're actually polluting like a little bitch. Like claiming to have a "sustainable" food, which, when you dig into it, is actually grown in cleared areas of former rainforest in northern Brazil. Or pretending the clothes you sell are Earth-friendly, while the bleach used on the fabrics kills all the fish in the Congo River.

And now, my proposal:

Greenwashing is the process of attempting to convince the average person that the planet's environmental problems are all our fault, and if we'd just change our habits and attitudes, we could reverse global warming, clean up all the lakes, and de-plasticize the oceans.

It relies on the same neuroticism as any other form of advertising: Something is Wrong in Your Life, and Here's What You Need To Do About It.

Thing is, it's not entirely wrong. Consumer habits certainly contribute to environmental degradation. The problem is that if you leave it up to us to fix it, ain't nothin' gonna happen.

If the pandemic showed us anything, it's that there will always be people who are not on board with the solution to a global crisis. Not only not on board, but also actively working to thwart any efforts at amelioration. For instance, trucks modified to "roll coal" at bicyclists and/or Prius owners.

There's no reaching those people, and it amounts to the equivalent of: for every cup of water we each pull out of the ocean in an attempt to battle sea level rise -- because that's what any one individual's effort can amount to -- you get someone else scoffing at their puny, insignificant effort and, moreover, pissing two cups of urine back into the same ocean.

Attempting to convince us that it's All Our Fault only plays with our little minds, and the result goes nowhere. Not only are we fooled by the original definition of greenwashing, believing every corporate claim about environmental friendliness while said corporation is busy dumping toxic waste into the harbor, but in the bigger picture, putting the onus on us (pun intended, as always) to fix, say, global warming only inconveniences us while other people benefit from their own flagrant flaunting of any attempts to get them to do better.

Take littering, for example. There were campaigns against throwing shit out of your car onto the side of the road. Places introduced substantial disincentives in an effort to stop littering, and they did work, to some extent. And yet... there is still litter. Maybe not as much, but all it takes is one or two plastic coffee cups to disturb the pristine green of the road verge. Some states, like my own, try to further fix the problem by some sort of adopt-a-highway program, where organizations or individuals are tasked with picking up litter from the roadside in exchange for some free publicity.

The obvious problem with that is: there's a certain subset of people who, if they know someone's going to come along and pick up the trash, will be more likely to throw their faux-environmentally-friendly McDonald's bags out the window when they think no one's looking.

In other words, we're being greenwashed into believing that something we, as individuals, do can actually make a difference. And sure, if everyone were on board with it, that might actually be the case. But everyone is not on board with it, there is no practical universe where everyone will be on board with it, and in accordance with Lone Asshole Theory, all it takes is one person to destroy the hard work of thousands.

All of which is not to say that you or I should be the Lone Asshole. But there's no sense in believing that you can actually make a difference.

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