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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December 29, 2022 at 12:03am

#1042315

Consumer

Today in You're Doing It Wrong...

The Shopping Cure

Quick disclaimer: I use a script blocker. I have no idea if the above link will work for you or not.

When I was at my most burnt out pre-pandemic, traveling constantly for reporting, working all the time, the muscle under my eye twitching almost constantly, still without the language to describe what I was doing to myself, the one thing that would temporarily calm me down was buying shit.

So... it worked.

There’s a similar dynamic at play in the desire to go to Target and drop $82 on things that weren’t on your list, in part because you didn’t have a list, because you just wanted to go to Target and encounter solutions for problems you didn’t know you had.

I've noticed that I approach buying shit differently from other people. Other people seem to go shopping and thereby find something that they think will be useful in some way. I do the opposite: decide what I want or need, and, if it exists, buy it.

For me, the most cogent illustration of this phenomenon is halitosis, a fake medical word devised by Listerine to market its antiseptic liquid, previously used to treat bacterial infections, as an everyday necessity.

That's a pretty basic marketing trick: find or invent other uses for your product. Church & Dwight did this very effectively with their Arm & Hammer baking soda, marketed as a fridge deodorizer (one that probably doesn't do dick).

Same for Lux Soap, only with body odor — these ads are everywhere in 1920s and ‘30s fan magazines, just straight up targeting women with desirability anxiety.

As you can tell by the current nonexistence of Lux Soap, this trick doesn't always hold out for the long term. To be fair, that brand does exist in other countries, and the company producing it (Unilever) sells other soaps in the US. Admittedly, one of them is my preferred brand. Shut up; I use soap at least once a year, and I'm entirely too lazy to make my own.

These are textbook examples, the sort so transparent you think how were these people so naive, a company told them they had a problem and they just believed them. But consider Big Pharma, and Big Skincare, and Big Design & Renovation, and Big Tech, and Big Home Remodel, Big Fitness & Wellness, and Big Fashion. None of these industries actually solve the problems they present as pressing, although they certainly purport to. Their products will, however, get you just close enough to catharsis (of completion, of solving your problem, of “fixing” whatever you discovered was broken) that you build faith in a brand as solution — convinced that if you just get the next version, research a bit more, actually take the Wirecutter rec, at least one hole in the leaky bucket of your life will be plugged.

My dentist's office has one of those home improvement channels on permanently in all of his exam rooms. Those shows enrage me beyond comprehension, and I finally figured out why: they're all ads, and I despise ads. It's even worse when they show an actual ad. I can only assume he's getting kickbacks from Big Home Remodel.

I keep hoping that, one day, people will wise up and decide they don't really need to "tear out that kitchen wall and open this space up," but my inner cynic (who makes up 95% of me) knows that's not going to happen. Worse, the shows give people neurosis if their house isn't pristine, new, uncluttered, and museum-worthy. Which it never is.

Going to the dentist is stressful enough without that bullshit. "So find a new dentist." Yeah, right; this was the only one in town that accepted new patients, probably because everyone else got fed up with what passed for entertainment in there and found a new dentist.

But then the summer came, and that friction began to disappear. I funneled my enduring pandemic anxiety into leveling up my lawn dad status — and as any lawn dad will tell you, any level of lawn-dadding requires items.

Same thing with lawns. Worse, even, because if your house is a mess you can simply have no one come over. But your yard is right there by the street, with all passing eyes on it. Some neighborhoods even mandate certain standards. It's a massive drain on both individual finances and the environment in general, but gotta have that status symbol to keep your sacred property values up.

And before you say that many of these activities — including home maintenance — can, indeed, be performed at little to no expense: of course they can. But that’s not the way most of us been trained to approach leisure, lifestyle, ownership or even our own bodies. Nothing is just fine as it is. Everything demands maintenance and, preferably, amelioration — and then more maintenance in its ameliorated form.

I kinda figured that out years ago. True, I had my deck replaced last year, but the old one was seriously about to collapse. It's not like I neglect necessary maintenance, but I got out of the vicious consumerist cycle long ago. Sure, I still buy shit, but that's because I'm lazy, not because I want to work harder.

The envelopment and distraction inherent to these projects — and their normalization through reality TV and fix-it media — makes it all the more impossible to even imagine a different way of organizing one’s life. “Freedom” and “choice” present themselves as the “freedom” to choose between various products; those choices then fill the void where personality or community might have been.

And that's where you lose me.

As far as I can tell, most peoples' home "improvement" projects are the result of too much community. That is, you do all that nonsense to meet peoples' perceived expectations. If you're a hermit, there's no need for all that crap.

The author goes on to contrast this with the SF utopia of Star Trek, which I gotta admit endears her to me despite some of the over-the-top language in the article.

But Star Trek was intrinsically designed to depict a post-capitalist, post-scarcity society, one which, moreover, was only able to be built on the ashes of vast world upheavals. I like the show, as you know, in all its incarnations, but I know it's fiction. We're heading into the upheavals, and won't be able to break out of them so easily.

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