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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March 8, 2022 at 12:01am

#1028548

Real Men Don't Worry About What a Real Man Is

A Cracked link today, talking about men, which is odd because its readership demographic is 12-year-old kids... at heart, at least.

5 Ways America's 'Masculinity Industry' Eats Men's Brains

"What brains?" women who think they're funny are thinking right now.

It feels like journalists and YouTubers are legally obligated to talk about how masculinity is in crisis.

Funny, this is the first I've heard of the subject in a while.

Traditional manhood is supposedly going the way of the dodo, and yet at the same time there’s a huge industry offering me everything from jewelry to body washes that will keep my manliness intact amid my gender’s death throes.

Pro tip: jewelry and body washes are incompatible with "traditional manhood."

Unless you count my body wash, which is also a shampoo, conditioner, salad dressing, cake icing, and engine lube.

5. The Manliness Industry Has Become Stupidly Huge

Cue "stupidly huge" jokes here.

Products have targeted men for as long as advertising’s existed. In the '20s, deodorant ads told women it was a necessity but only informed men it was an option, because not smelling like a flop house could be seen as “feminine” and “sissified.” Making yogurt and grooming products look manly was important in getting men to buy them at all. Somewhere in ancient Ur, a market stall owner probably told some gangly dork that he’d look tougher with a leather bracelet.

Honestly, I never thought much about it. I always figured that the "for men" products were labeled as such due to different biology, not sociological principles.

Which means I've probably been suckered in.

4. That Industry Promotes A Very Specific Worldview

The good people at Active Doodie say you need one of their diaper bags because holding a normal one will be even more humiliating than holding your wife’s purse.

Huh, and here I thought "real men" made the wimminfolk do all the diaper changing and stuff. Oh, and can we find the person responsible for naming that company and remove him (it was almost certainly a "him") from society?

America has a proud tradition of reducing politics to asinine vagaries crammed onto t-shirts, but these companies are all pitching a very specific and isolating vision of masculinity. Nine Line decries that “patriotism and national pride is disappearing daily” and say they want to reverse that trend, but half their product descriptions are about how the “woke” are turning America into an irredeemable hellhole.

I know who's turning America into an irredeemable hellhole, and it's not the "woke." It's the people peddling this toxic masculinity bullshit. And people who shoot video in vertical format.

Not coincidentally, there’s a whole media ecosystem warning that modern manhood is vanishing. PragerU warns that men aren’t allowed to be masculine anymore, and thus no longer “defend, protect, or provide.”

Right, because that's all men are good for. That and getting things down from the top shelf. Which I guess is part of "provide."

3. The Modern View Of Masculinity Is An Aberration

I was hoping they'd acknowledge this.

Hey, maybe all those videos have a point. Look how this typical soy boy talks to his “male” friend, writing girly crap like “You know my desire to befriend you is everlasting” and “I do not feel my own sorrows much more keenly than I do yours” before signing off “Yours forever.” Why not just have a couple of appletinis and cry about your menstrual cycles?

Those are excerpts from letters by noted wimp Abraham Lincoln to his good friend Joshua Speed. And I mean good friend; they shared their deepest anxieties with each other, while also sharing a bed for four years.

But no, nowadays any expression of platonic affection between males is smirkingly called a "bromance." I hate that word and want it to die.

Flowery language, inspired by the heroic bromances of classical literature, was common.

Goddammit, Cracked.

But dudes who invoke Sparta’s cool quotes about not having their weapons taken away probably aren’t planning to reclaim their habitual pederasty, lengthy stretches of communal living, total subservience to the state, long braided hair, progressive (for the time) attitude towards women, or the time they surrendered and whined about the enemy’s use of arrows.

The more I hear about the past, the more I'm glad I live in the present. But we can still learn from it.

Masculinity isn’t a series of boxes to check that were handed down by nature. It’s always varied by time and place, and you can only “reclaim” it in the same sense that you can reclaim bell bottoms.

Now, those were the true aberrations.

2. Our Narrow, Modern View Of Manliness Is Taking Us To Strange Places

As the pro-gun diaper bags implied, Americans are increasingly told that being a good man means believing that a significant number of other men are waiting for their chance to murder you.

Oh, be fair. Lots of women want to murder you, too.

But … why? A majority of Americans have, for decades, believed that crime rates are rising. And, for decades, they’ve been wrong. Media and politicians mislead us about how dangerous America is, petty crimes like vandalism lead to the mistaken assumption that serious crimes are also rampant, a high-profile crime across the country can convince us that we’re next, and all while the actual statistics keep improving. America’s no paradise, but it’s safer than it’s ever been and we act like we’re about to erupt into Civil War 2: This Time We’re Angry About Pronouns.

To be fair again, a civil war is definitely imminent. The signs are all there (mostly they look like confederate flags because we learn nothing).

1. And So Men Are Now Lonely, Isolated, And Scared

But they can't admit that, because that would be unmanly.

Between 2019 and 2021 the U.S. Concealed Carry Association, which teaches self-defense and trauma care, saw its membership jump from 300,000 to 600,000. Their success came from their focus on family protection. The USCCA is far less combative than the NRA, and they emphasize that part of being safe is avoiding fighting.

You know, I think I've managed to avoid talking about guns in here for all this time, though I don't remember for sure. What I have mentioned is that I spent my childhood on a farm. A gun, out in the country, is a tool, like an axe or a tractor, that provides some sort of benefit while also being dangerous. So I'm not anti-gun, but I don't worship them either.

So America is more armed than ever, yet it’s supposedly suffering a manliness nadir. Ironically, the 1950s that are idealized as a peak in American manhood thought they were suffering from a testosterone crisis, because soldiers came home and had to learn how to move on and become family men. Now family men supposedly need to become lone warriors in case radicals seize the local Steak 'n Shake. Again, we’ve been reframing and arguing about manhood forever.

I think one of the biggest issues is conflating "gender" with "how you have to act." There was a book out, I think back in the 80s, called "Real Men Don't Eat Quiche." I never read it. Perhaps it was satire; I don't know. But real men -- real people -- do whatever the hell they want so long as it doesn't infringe on others' rights.

So if we’re going to cherry pick from yesteryear’s men, hell, let’s pick the part where men went out and tried to make the world a better place.

Meh. There are people out there. Shudder. I'd rather sit at home and try to make the world a better place.

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