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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July 4, 2022 at 12:01am

#1034670

The Fourth Is Strong In This One

Today's is a lengthy article, and though it was chosen randomly from my rather long list, it's appropriate for today because it's all about the US -- though there are probably things that residents of other countries can learn from it.

The escalating costs of being single in America
Why is life in this country so hostile to single people?

Yeah, I know, it's even more hostile to other demographics, but that's addressed in the article. Kind of.

Think about your household’s monthly expenses. There are the big-ticket items — your rent or mortgage, your health care, maybe a student loan. Then there’s the smaller stuff: the utility bills; the internet and phone bills; Netflix, Hulu, and all your other streaming subscriptions.

I just want to say how unutterably thrilled I am that the author didn't include cable TV on the list (yes, for some it's bundled with internet; still, excluding it is a Very Good Sign and Pleasing In My Sight).

If you drive a car, there’s gas and insurance. If you take the subway, there’s a public transit pass. You pay for food, and household items like toilet paper and garbage bags and lightbulbs. You buy furniture and sheets and dishes.

Now imagine paying for all those things completely on your own.

Um... I don't have to imagine? Of course, I suspect I'm a bit older than the target audience of the article -- the mortgage is paid off; I never had a student loan; I don't have a car or a commute (though I still intend to buy a car -- it's been one year as of tomorrow since mine got ungulated). I haven't bought lightbulbs since a few years ago when I blew a lot of money to convert every bulb in the house to LED (no regrets there). Still, the point remains: though I have a housemate, when it comes to consumer stuff, it's just me paying for shit.

For the more than 40 million people who live in this kind of single-income household, it’s also become increasingly untenable.

This is where I note that the article is from December, before inflation started really getting out of hand.

Overall, 31 percent of US adults identify today as single, defined as not married, living with a partner, or in a committed relationship.

Honestly, that's quite a bit more than I expected.

The article dives deeper into the demographic breakdown of singlehood; I won't repeat it here, but it's worth glancing at.

To be clear, these numbers aren’t increasing because society has shifted to accommodate the single or solo-living. Quite the contrary; they are increasing even though the United States is still organized, in pretty much every way, to accommodate and facilitate the lives of partnered and cohabitating people, particularly married people.

I notice this especially at the grocery store (or, rather, their website; I've been getting groceries delivered for a long time now). Sure, some things are sold in single-portion packages, but most things are cheaper in bulk -- though it can be a false economy for a single person, because unless it's something like a pack of cookies, which can disappear in an hour, shit goes off on me long before I can finish a "family pack."

Single people should, in theory, be the purest embodiment of American values of self-sufficiency and individualism. That they’re not speaks to the fact that we don’t venerate the individual — we venerate the individual family.

And that, I've always thought, desperately needs to change.

The family fosters the conditions for the individual’s success: The spouse helps create the conditions that make success possible; children (at least theoretically) keep the individual grounded, focused, and humble.

Huh. It looks like the article misspelled "grouchy, frazzled, and exhausted."

We don’t call single or unmarried people spinsters, deviants, or social problems anymore, at least not explicitly. But that underlying hostility to single and solo-living people? It’s everywhere.

There are few checks on the behavior of a solo. We tend to forge our own path. People distrust that, because some of the most famous solos include such luminaries as Ted Kaczynski and Ed Gein. Me? I mostly just take advantage of being single to be able to put up exactly what art I want on the walls, not make the bed every damn day, and not hear crap about my vices.

Anyway, the next bits of the article goes into anecdotes about individuals' (all women) struggles with being solo. As writing, this is a good thing because it puts a face (metaphorically) on the statistics. As science, it's garbage.

I'm also not going to rehash the specific examples of (mostly) big-ticket items that are optimized for the married. The article's there if you want to read it.

It seems clear, if we want to actually support “liberty” or lift people out of poverty, or even make it easier for people to have traditional (or nontraditional!) families, then we need to reconsider the way we organize tax policy and public benefits.

It seems clear that we don't want to 'actually support "liberty" or lift people out of poverty.' No, the people in charge seem to want to make things better for corporations -- ostensibly so they'll keep people hired; how's that working out?

Here's the big bucks quote, though (in my view)...

Some people crave something more than what marriage can provide. They wonder: What would it look like to create small systems of care for one another that go beyond one other individual? What if we could figure out how to acknowledge that the most important person in our lives isn’t always someone bound to us by family or sexual relationship? How can we think about housing, health care, caregiving, and work in ways that actually acknowledge and actively include single and solo-living people — not as afterthoughts but as the third, if not more, of the population that they are?

Well, we can start by actually catering to individuals rather than "families."

There’s also a lot to learn from other countries where single populations thrive. Denmark, for example, has offered three cycles of IVF to residents up to the age of 40 since 2007, leading to a sharp increase in “solomor” or elective single mothers.

*record scratch* and that's where they lose me. Granted my perspective is way different as a dude, but why should we encourage breeding at all, let alone IVF treatments, in a world that could absolutely use fewer people (through attrition, not by deliberate death, so stop encouraging me to commit suicide).

Giving single people access to parenthood — and, just as importantly, the assurance of support once it happens, for whatever reason — could dramatically change the experience of single parenting.

But, okay, I know -- without understanding why -- that some people just want to become parents.

People will continue to bemoan the erosion of the traditional family and the decline in the birthrate, because that is what people do when they feel the world is changing and they, personally, are not — maybe out of fear, but maybe, too, out of lack of imagination.

Again: an increase in population is ultimately unsustainable. Oh, sure, we're not there yet (probably), but do we really want to wait until the situation becomes completely untenable, when the water runs out in certain areas, or the food? Or can we change attitudes now? Ever-increasing population is necessary for our current economic conditions, sure, but as it's unsustainable, perhaps we can start to think about retooling the way things work to accommodate a decrease in population.

Because if we don't, it'll happen outside our control. But if you want to know a group that's even more distrusted than the solos, just look at the childfree.

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