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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. ![Merit Badge in Quill Award
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Yay, here we go again. I've talked about this sort of thing before, specifically in "How Low Can You Go?"  from December, but this is a different article.Technically, more than three ways, but I'll get to that. First I want to address the actual headline: "Why U.S. Population Growth is Collapsing." First of all, it's US-centric, which, okay, fine, that's your audience. But then it gets all misleading. I'm not sure I can explain this very well without graphics, but I'm going to try. You have population, which is a fixed number at any given moment. As an analogy, imagine driving your car on the road. At some given moment, this corresponds to your position. Call it x, because mathemagicians love x. You also have an instantaneous velocity. You can call that v. Or you can call it x' (x-prime) because it's the first derivative of position. I'll call it x' for reasons. That velocity could be constant, or you could be braking or stomping on the go stompy thing, causing acceleration (deceleration is negative acceleration). Call that x'' (x-prime-prime). That's the analogy. What it's an analogy to, of course, is the population of a geographic area, in this case the US. That's x. The population is still increasing; that's x'. The headline makes it sound like population is, or is at least in danger of, decreasing (negative x'). But that's not what it's actually saying. It's saying that x'', the rate of change of population increase, is not itself increasing as fast as it used to. And the cherry on top of that parfait of clickbait is the use of the word "collapsing," which makes it sound like it's a fucking catastrophe. But it's not. Population is still growing. Population growth is still increasing. It's just not increasing as fast. Makes sense? Maybe? I don't know; ask someone else who understands derivatives of mathematical functions. U.S. growth didn’t slowly fade away: It slipped, and slipped, and then fell off a cliff. The 2010s were already demographically stagnant; every year from 2011 to 2017, the U.S. grew by only 2 million people. In 2020, the U.S. grew by just 1.1 million. Last year, we added only 393,000 people. See? Still adding people. A country grows or shrinks in three ways: immigration, deaths, and births. Four: Taking over another country and adding its population to its own. I'm looking at you, big country in Eurasia. America’s declining fertility rate often gets the headline treatment. Journalists are obsessed with the question of why Americans aren’t having more babies. And "fertility rate" makes it sound like it's a medical problem. While it's certainly such for some people, I mean, look around. Kids are a drain on financial resources, and a lot of people just aren't making enough money to buy a house big enough to shove kids into, let alone the cost of the brats themselves. Add to that the knowledge that the next generation will almost certainly have it worse than we do, as regards the economy and climate change catastrophes, and I can understand choosing not to have kids. Because those are some of the reasons I didn't. First, we have to talk about COVID. Sigh. I suppose. The pandemic has killed nearly 1 million Americans in the past two years, according to the CDC. Those are official numbers. The actual number, going by deaths in excess of average, is higher. This is important because more people than usual have died over the last two years, and it matters when you're talking about a decrease in rate of growth of population. Excess deaths accounted for 50 percent of the difference in population growth from 2019 to 2021. That’s a clear sign of the devastating effect of the pandemic. But this statistic also tells us that even if we could have brought excess COVID deaths down to zero, U.S. population growth would still have crashed to something near an all-time low. Yeah, I'm not sure about that. At least some of that excess was people not seeking out medical treatment for other issues because hospitals were full or they didn't want the 'rona on top of cancer or heart disease or whatever. As recently as 2016, net immigration to the United States exceeded 1 million people. But immigration has since collapsed by about 75 percent, falling below 250,000 last year. And this is a sore point for a lot of people, but I'll say it again: An adult immigrant is more useful to the US economy than a child. America’s bias against immigration is self-defeating in almost every dimension. “Immigration is a geopolitical cheat code for the U.S.,” says Caleb Watney, a co-founder of the Institute for Progress, a new think tank in Washington, D.C. “Want to supercharge science? Immigrants bring breakthroughs, patents, and Nobel Prizes in droves. Want to stay ahead of China? Immigrants drive progress in semiconductors, AI, and quantum computing. Want to make America more dynamic? Immigrants launch nearly 50 percent of U.S. billion-dollar start-ups. The rest of the world is begging international talent to come to their shores while we are slamming the door in their face.” All of this, of course, doesn't take into account the loss to whatever country they're coming from. But again, the article is US-centric. Declining births get a lot of media coverage, with mandatory references to Children of Men, followed by mandatory references to Matrix-style birthing pods, followed by inevitable fights over whether it’s creepy for dudes like me to talk academically about raising a nation’s collective fertility. My personal opinion is that wanting and having children is a personal matter for families, even as the spillover effects of declining fertility make it a very public issue for the overall economy. And here we get to the brunt of the issue: our economy absolutely depends on population growth. Scare articles like this one always concentrate on just how absolutely catastrophic it would be were the population to decline. And yet, as I've said before, a declining population -- not just a decrease in population growth, but negative population growth -- would begin to solve a lot of other issues, mostly environmental. The implications of permanently slumped population growth are wide-ranging. Shrinking populations produce stagnant economies. Stagnant economies create wonky cultural knock-on effects, like a zero-sum mentality that ironically makes it harder to pursue pro-growth policies. (For example, people in slow-growth regions might be fearful of immigrants because they seem to represent a threat to scarce business opportunities, even though immigration represents these places’ best chance to grow their population and economy.) The sector-by-sector implications of declining population would also get very wonky very fast. Higher education is already fighting for its life in the age of remote school and rising tuition costs. Imagine what happens if, following the historically large Millennial cohort, every subsequent U.S. generation gets smaller and smaller until the end of time, slowly starving many colleges of the revenue they’ve come to expect. As scary as it may be to contemplate a negative-growth population from an economic perspective, I need to point out that the opposite is, in the long run, even scarier: how sustainable do you really think it is to demand exponential population growth... indefinitely? Keep that up, and you're looking at Malthusian collapse, and it won't be a nice steady decrease in population, but a sudden, drastic, massive die-off of humans. That's a Thanos snap. I don't want that. Only psychos want that. Even if you’re of the dubious opinion that the U.S. would be better off with a smaller population, American demographic policy is bad for Americans who are alive right now. Dubious, my ass. Look at the price of housing and how it's increased recently. This is, at least in part, due to econ 101: supply and demand. Demand goes up, price goes up. Supply goes down, price goes up. Add people without adding housing? Price goes up. Fewer people competing for the same number of homes almost has to drive the price of housing down. Obviously there are other factors involved and it's never that simple, but you're going to have to do better than "bad for Americans who are alive right now." So that's my rant. I hope it made some kind of sense, even if you disagree with it. |
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