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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.
January 4, 2024 at 9:15am January 4, 2024 at 9:15am
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This one's gonna get controversial. Maybe even offensive.
Continuous human population growth is unsustainable. At what point the crisis will occur is debatable, but if the increase in global population doesn't turn into a decrease, or at least a flat line, we'll find out.
And if you go by country, rather than globally, well, now we're getting into xenophobia territory.
If history is any guide, none of this will work: No matter what governments do to convince them to procreate, people around the world are having fewer and fewer kids.
Good.
In the US, the birth rate has been falling since the Great Recession, dropping almost 23 percent between 2007 and 2022.
We have to be very, very careful parsing the math in an article like this. There's the population, then the birth rate, then changes in the birth rate. If more people took calculus, the differences would be easy to explain. Instead, we get "When are we ever going to use this?" Well, now. Now is when we use this. Not necessarily the nitty-gritty math parts, but the knowing whether you're talking about position, velocity, or acceleration.
That said, I didn't spend a lot of time working through the math.
Today, the average American woman has about 1.6 children, down from three in 1950...
Before birth control and while women were still treated as accessories.
...and significantly below the “replacement rate” of 2.1 children needed to sustain a stable population.
The difference could be made up for with immigration from countries not listed, ones with greater-than-replacement-rate. Oh, but, xenophobia. Right.
In Italy, 12 people now die for every seven babies born.
Interesting phrasing. Every other listed country's birth rate is given as a decimal number. This one seems tailor-made for emotional reactions, containing as it does the word "die" right up front.
The drop has frightened lawmakers and commentators alike, with headlines warning of a coming “demographic crisis” or “Great People Shortage” as economies find themselves without enough young workers to fill jobs and pay taxes.
Fewer people means fewer consumers, which in turn means fewer necessary jobs but also lower corporate profits. I don't have a lot of evidence for this, but it's my impression that this is what drives a lot of the low-birth-rate panic: stock prices might fall.
As for taxes, countries somehow find ways to cope.
To stem the tide, the world’s leaders have tried everything from generous social welfare programs to pink-and-blue awareness campaigns to five-figure checks to veiled threats, all to relatively little avail.
It takes way more than five figures (I'm assuming this is being translated to USD) to raise a kid from childhood to college-age, and way more than that if they actually do go to college. This is a false benefit, like when a new car purchase comes with a small rebate instead of, you know, just lowering the price of the car.
I also wonder if there's a difference between "awareness campaigns" and "propaganda," and whether people are "aware" they're the same thing.
In many ways, the falling birth rate is a success story — the result of young people, especially women, having more options and freedoms than ever before.
And, as a result of that, there could be fewer people burdening the environment. If global birth rates were really dropping. Which they are not.
It's kind of like... you're working for a company, mainly doing your job at home. Then, one day, you get notice: "At ZZZ Corp, we care deeply about the environment, so, henceforth, we are no longer providing plastic coffee swizzle sticks or cups in the break room. In other news, all work-from-home is cancelled and now you have to commute in to the office."
Fewer births do have real consequences for how families and societies operate. In 2010, for example, there were more than seven family members available to care for each person over the age of 80; by 2030, there will be only four.
Providing free labor.
An aging society also means fewer workers in key industries and fewer people paying into programs like social security.
The "fewer workers" thing is bogus, because it also means, as noted above, fewer consumers. Also, the more companies have to compete for labor, the better wages are likely to be. That's just the free market at work. We're starting to see some of that already.
As for "programs like social security," here in the US at least, it was set up assuming an ever-growing population. Bullshit assumption. But again, we could be making up the difference via immigration. A kid is a non-contributing person for at least 15 years, probably more (except in some states that have embraced the idea of putting the little bastards to work in the factories). An immigrant, assuming they're an adult, could start contributing right away.
These prospects tend to elicit panic among conservatives, who take a moralistic — and sometimes xenophobic — tone in addressing the issue.
Like I said.
Bonus points to the author for using "elicit" properly, instead of "illicit," which means something else entirely and isn't even the same part of speech.
Sen. J.D. Vance (R-OH) has warned of the dangers of the “childless left” and its “rejection of the American family.”
Look, I'm not calling out the conservatives, here; the article is. But if he's correct, then wouldn't that mean fewer libby-libs and more conservatives? Assuming the kids pick up on their parents' politics, which isn't always the case.
In China, male Community Party officials at a recent meeting on women’s issues bypassed any talk of gender equality and instead urged women to “establish a correct outlook on marriage and love, childbirth, and family.”
Well, look at that. The CCP aligned with US conservatives. Who could have predicted that? Except everybody.
But concerns about birth rates go beyond the rhetoric of right-wing politicians.
Just leaving this here to show that it's not necessarily a left vs. right issue.
So far, most countries have tried either asking people nicely to reproduce or sweetening the deal with money. If that doesn’t work, however, restricting people’s reproductive choices may be on the table, especially in more autocratic regimes.
Already happened in the theoretically-not-autocratic US.
Fears for the future may also play a role in declining birth rates around the world. “Young adults are living in a world which is characterized by many crises,” from war to climate change to the erosion of democratic norms in the US and elsewhere, said Jessica Nisén, a family demographer at the University of Turku in Finland.
In other words, as I've said before, choosing whether or not to have kids can be an ethical decision.
That leaves policymakers with the question of what they can do. For a lot of experts, the answer is nothing. “I’m basically against having birth rates be a policy target,” Cohen said. “Anything you do to influence this is going to have very probable bad side effects, and any benefits you get are likely to be very small and very long term.”
I believe that was meant to be "very short term."
They might also recognize that shrinking family size isn’t necessarily a bad thing. Lower birth rates around the world could lessen environmental degradation, competition for resources, and even global conflict, Wang Feng, a sociology professor at UC Irvine, writes in the New York Times.
I'm going to give the author credit for including this, even though it's way down in the article.
Lawmakers might just have to accept that they can’t control how many children people have.
Which won't happen so long as their corporate overlords are screaming for cheaper labor. |
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