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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 6 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 8 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.

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.

July 29, 2022 at 12:19am

#1035823

Mommy

Okay, look. I drank yesterday. Quite a bit. Then I passed out. Then I woke up, hung over and still drunk. But here I am, posting (nearly) at my usual time. Screw you, everyone who said I was irresponsible and can't keep a schedule or commitments.

However, when I selected the article at random from my queue, I couldn't for the life of me remember why I saved it there to begin with. Or reading it in the first place. So... whee! Let's figure this out together.

Epiphany in the Baby-Food Aisle On a trip to the grocery store one day, I had a realization about me, my son, and the meaning of life.

Why would I decide that, one day, I would like to blog about this? It is, by the way, clearly marked as a book excerpt, so again, we have someone trying to sell their book. As I've noted repeatedly in here, this is a writing site, so I'm okay with that.

I’m driving the three-minute scoot to the supermarket to pick up a few boxes of very safe, instantly dissolving toddler cookies called something like Nom-Noms, which is really what all cookies should be called (and, while we’re at it, all food).

The only thing I hate worse than self-absorbed blather is self-absorbed blather from mommies. So I should have given this article a complete miss. But I have to admit it: this first sentence reeled me in. Take note.

While in the car, I’m listening to the writer Elizabeth Gilbert on Oprah’s Super Soul podcast.

And then you lost me again. It's a three-minute drive, but you need to distract yourself with a podcast? (Full disclosure: I have never, not once in my life, listened to a "podcast.") Also, Oprah? Now I know that, despite your remarkable opening line, we are complete opposites and have absolutely nothing in common.

And finally? If it only takes three minutes to drive somewhere, why not walk?

Gilbert is the author of Eat, Pray, Love, the 2006 best seller about her soul-awakening travels to India, Italy, and Bali; it’s a book I love and have read an embarrassing number of times.

Now I'm starting to have a vague recollection of why I saved this article lo these many weeks ago: I hate nearly every single thing about it.

Well, good. That suits my mood right now. Damn, I type loud.

Nom-Noms are these magical little biscuits that are probably about 99 percent air. The rest is a mysterious blend of, I think, sweet-potato juice and Styrofoam.

My mother wouldn't have indulged me like that. Spoiled brat kid.

Every cookie is reliably about five inches long and shaped like a mini-surfboard with very minor irregularities around the edge. (I’m sure they could be baked to be perfectly smooth, but I think they’re going for some kind of wabi-sabi “hand-hewn” aesthetic, which I appreciate in theory, but it also feels like an unnecessary effort given the audience?)

You... you don't understand marketing, do you? The audience isn't your crotchfruit. The audience is you, and it's working exactly as planned.

The day stretching out before me as I drove the three minutes from my house to the supermarket was itself a bit like a Nom-Nom; it would be the same as all the other days I’ve been living since my son was born, since we moved to Los Angeles, and since I’ve been working part time.

Ah. Got it. L.A. That's why she can't walk. There's probably a parking lotfreeway involved, which makes me doubt the "three minutes" thing.

As I finally threw the Nom-Noms into my shopping cart, Gilbert was talking about the archetypal “hero’s journey” and how throughout the history of literature, the hero’s journey has been represented as, specifically, a man’s journey to a faraway place.

Hey folks, it's sexism time!

I hadn’t heard of the book Gilbert referenced at length, Joseph Campbell’s The Hero With a Thousand Faces, in which he distills the 17 universally traversed steps of this tale as it’s been told forever by cultures around the world. I realize as a writer I probably should have read (or at least known about?) Campbell’s book, but there are so many episodes of The Bachelor to watch that I’m not sure where I would have ever found the time.

Yes. yes, you should have. Shallow excuses won't cut it.

Even after I loaded my recyclable bags (good person) into the back of my car and began the drive home, that concept and those words, “hero’s journey,” kept echoing inside me.

Hey, "good person." Do a little research and you'll find out that those "recyclable bags" are worse for the environment than plastic bags (though they don't generally introduce quite as many microplastics, which is a separate issue). I know you live in California and plastic bags are no longer an option there, but you're actually best off with the old-fashioned brown paper bags. Environmentally-speaking.

Gods, I hate virtue signaling, even when it's self-aware.

Campbell’s conception of the journey begins with a potential hero who is just going about his life as normal — you know, texting and taking antidepressants or whatever.

And it's this sort of thing that, despite my polar opposition to everything that this woman stands for, I kept reading for. I mean, not only is she talking about one of the greatest archetypes in storytelling (albeit from a newbie perspective), but it's this sort of turn of phrase that makes me appreciate the writing.

In this moment of silent anticipation, for the first time since my son was born — having spent each day since feeling invisible to the mainstream world, over the hill, like a Swiffer on legs, wiping his nose with my hand and not having sex and generally functioning as a kind of automated milk-and-comfort-dispensing machine — I began to entertain a thought …

You know, it's your choice to pop out a sprog. You probably spend a lot of time justifying your decision to do so: "Oh, it's SO worth it!" But these little complaints are far more revealing than all the "parenthood is wonderful" anecdotes in the world.

Is it possible I’ve been on a hero’s journey this whole time? Is it possible I am on one right now?

No.

The only qualification for shitting out a sextrophy is the proper biology.

What shook me about Campbell’s words is how perfectly they describe motherhood.

That's a stretch.

Pun intended.

And of course, these are the exact same moments in which there is no more “superhuman deed” than steadfastly caring for and feeding your child and not giving in to the temptation to flee the entire situation.

Mantra: I chose this life. I chose this life. I chose this life.

And you cry because this is why you chose his name: Asher, Hebrew for “happy,” the emotion you’ve struggled so hard to feel your whole life.

The meaning is closer to "blessed." I'll give this author the benefit of the doubt; based on her last name, she very well might be Jewish and gets to give her brat an unvarnished Hebrew name without being a cultural appropriator. Also, I'm pretty sure the vast majority of names common in English are Hebrew in origin, or at least Aramaic. But the implication here is that happiness depends on reproducing, which, while admittedly a very Jewish idea, just doesn't track today.

So I have been thinking and thinking about this. Is it really possible that my trip to buy Nom-Noms is part of a meaningful narrative, a hero’s journey?

No, you self-important idiot. It's a goddamned trip to the nethers-licking grocery store. I'd bet you could order a case of those nasty things and have them delivered right to your door. Even in a backwoods hellhole like Los Angeles.

To illustrate, I invite you to investigate your gut reaction to the term “mommy blog.”

Hurk.

I guarantee you if Ernest Hemingway were alive and writing an online column about his experience of being a father, no one would call it a “daddy blog.” We’d call it For Whom the Bell Fucking Tolls.

I guarantee you Ernest Hemingway wouldn't make the main focus of his blog his experience of being a father.

The truth is that motherhood is a hero’s journey.

And yet, every other species on Earth does it without turning it into an epic saga.

Every mother you know is in this fight with herself. The sword that hangs over her is a sword of exhaustion, of frustration, of patience run dry, a sword of indignation at how little she feels like a human when she so often has to look and behave like an animal. Mostly, it is the sword of rage: the rage and shock of how completely she must annihilate herself to keep her child alive.

Ah. There it is. The confession that made me hit "save" on this article.

Okay, look, like I said, I'm writing this with a pounding headache, so I'm probably just a bit less chill than I usually am. And I'm not trying to deny how important motherhood is. Hell, my mom did all that without even the dubious benefit of having popped me out herself. I genuinely like this lady's writing, regardless of its content. So here I am, sharing it.

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