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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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Earlier this month, in "Too Little, Too Late"  , I noted how I was Done With Caring About Climate Change. We had a high here of over 70F on Christmas Day (great weather for walking to the movie theater), and all I could think about was how nice it was to be warm (average high for late December around here is low-40s).Anyway, here's another article that tries to sugarcoat our impending doom. I'm posting this because it's another angle on the topic. The rare spots of good news on climate change It looks increasingly clear that we'll at least sidestep the worst-case scenarios. You know, one of the most frustrating things about being right and actually doing something about it is that nothing happens, so people think the original prognostication is overblown. For example, back in 1999, a lot of people were concerned about a "Y2K problem" that, as I recall, had some people screaming doom and gloom over its potential impact on computer systems everywhere and what happens to them when their odometers turn over. A bunch of people took this seriously, tackled the problem, and solved it before the end of that year. Then, as the clock ticked midnight, nothing that was predicted came to pass -- because people had done something about it. As another example, suppose some terrorists have a plan to, I dunno, blow up the Washington Monument. Their plan comes to the attention of the NSA or whatever, and they stop it from happening. And all the general public knows is that the National Phallic Symbol is still standing; they're blissfully unaware that we were about to lose our permanent erection. Or the people who warned that COVID could kill millions by the end of 2020 if nothing was done. Then, the end of 2020 came along, and it "only" killed half a million (or whatever the hell the actual numbers were; it makes no difference to the point I'm making). So you get people who scoff at the original prognostications, forgetting the qualifier of "if we do nothing" and the fact that we actually did something. No one notices when nothing happens. And that leads to thinking that nothing would have happened, when the fact is that it absolutely would have happened had we not staged an intervention. So if, as I maintain, we'd done something about climate change when it was still possible to avoid extreme outcomes, then the extreme outcomes wouldn't have happened, opening the door for idiots to go, "See? We did all this shit and nothing happened." Yes, idiots; that's because we did all the shit. Or would have. All of this is to comment on the subhead above: "we'll at least sidestep the worst-case scenarios." Yes, that's because while we haven't done anywhere close to enough, we've at least done something, and the worst-case scenarios were based on us doing nothing. To be sure, the limited progress isn’t nearly enough. We’ve taken far too long to begin making real changes. World events and politics could still slow or reverse the trends. "Could?" Probably it'll make things worse. So what are the signs of progress amid the climate gloom? Well, we're still brewing beer. Today, if you layer in all the climate policies already in place around the world, we’re now on track for 2.7 °C of warming this century as a middle estimate, according to Climate Action Tracker. Look. You don't get to be relieved at 2.7°C just because someone warned that it could have been twice that. That amount of temperature increase is Bad. It would be like warning that Grandma might have liver cancer and bladder cancer, and then saying, "Well, turns out she doesn't have bladder cancer after all, so what a relief, right?" If you assume that nations will meet their emissions pledges under the Paris agreement... HA! Given the increasingly strict climate policies and the plummeting costs of solar and wind, we’re about to witness an absolute boom in renewables development. And just to be clear, if this is true, it's undeniably a good thing -- with or without climate change. Meanwhile, there are plenty of signs of technological progress. Researchers and companies are figuring out ways to produce carbon-free steel and cement. Plant-based meat alternatives are getting tastier and more popular faster than anyone expected. This has nothing to do with climate change, but I finally got to try a Beyond Burger at the drafthouse. I ordered one because I was curious about it. It was pretty good. It tasted almost entirely like meat doesn't, so I don't know where people get off thinking it's anything close to tasting like dead cow -- but it was good in its own right. The kicker, though, was that the menu included calorie counts, and the calorie load of the fauxburger was about 10% higher than that of the actual beef burger. So if you're eating it to save the planet? Fine. If you're eating it to be healthier? Jury's out. But like I said, at least it tasted good; most vegan food tastes like penance. And here’s an important and counterintuitive finding: While dangerous, extreme weather events are becoming increasingly common or severe, the world seems to be getting a lot better at keeping people safer from them. The average number of deaths from natural disasters has generally dropped sharply in recent decades. Gee, that's nice, but what about property damage and the resulting costs to individuals and insurance companies who then pass the costs on to individuals? Peoples' loss of houses and businesses, like we just saw with the tornado in the Midwest? Displacement? Poverty? Death isn't the worst possible outcome here. Progressive US politicians now casually repeat the claim that climate change is an “existential threat,” suggesting it will wipe out all of humanity. That's probably hyperbole, but consider all the scaremongering articles about lower birth rates and you'll understand that you don't have to wipe out all of humanity for society to collapse; just decimate it. (I use that word with its proper definition of "remove 1/10th of.") While I'm admittedly a fan of the idea of reducing the population, I'd rather it be by reducing the birth rate gradually and sustainably, not losing a big chunk of living, breathing people to floods, famines, or fires. But insisting that the world is at the edge of collapse, when it’s not, is a terrible message for young people and carries some real risks as well. It clearly undermines credibility. It could lead some people to simply lose hope. We should be losing hope. I know mine's completely gone. Anyway, the article makes good points and ones that are maybe not so good, but there's a lot more to it than I quoted, and it's worth a look. |
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Talk about retaining water... 
