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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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| Well, might as well dive right in on this one. Massive rant ahead. If you're not in the mood, skip to the bottom for a one-sentence movie review. Ten ways to confront the climate crisis without losing hope  It’s easy to despair at the climate crisis, or to decide it’s already too late – but it’s not. Here’s how to keep the fight alive Oh, it's already too late, and has been for some time. But I'm not despairing; oh, no. I'm going to enjoy every bit of our skid to the edge as best I can. It’s the end of the age of fossil fuel, but if the fossil-fuel corporations have their way the ending will be delayed as long as possible, with as much carbon burned as possible. If the rest of us prevail, we will radically reduce our use of those fuels by 2030, and almost entirely by 2050. We will meet climate change with real change, and defeat the fossil-fuel industry in the next nine years. Hahahaha. Oh, wait, you're serious. HAHAHAHAHA We must remake the world, and we can remake it better. The Covid-19 pandemic is proof that if we take a crisis seriously, we can change how we live, almost overnight, dramatically, globally, digging up great piles of money from nowhere, like the $3tn the US initially threw at the pandemic. The pandemic that's still going strong? The one that continues to muck up travel, gatherings, businesses, and politics? The one that is still tearing apart families and threatens to start a civil war? The one that would have been over by now if more people took it seriously? That pandemic? No. If the covfefe pandemic is proof of anything, it is that if there is a crisis, half of the US (and roughly the same fraction in other countries) will not only not take it seriously, but many of them will actively work to undo what the rest of us are trying to do to fix it. The only way to deal with climate change is for all of us to rally together, and if the last two years have shown us anything, it's that this will never, ever happen. I know all the reports like to say "It's bad, but there's still hope," but I think they're only doing that to keep us from panicking in the streets and rising tides. I'm under no such restriction. In summary, we are doomed. The emotional toll of the climate crisis has become an urgent crisis of its own. It’s best met, I believe, by both being well grounded in the facts, and working towards achieving a decent future – and by acknowledging there are grounds for fear, anxiety and depression in both the looming possibilities and in institutional inaction. And that's the other thing, and I can't emphasize this enough: Stop putting the onus on us. (Sorry, I couldn't resist that bit of linguistic whimsy even when prophesying doom.) Anything you do will no more stop the inevitable than pulling a bucketful of salt water out of the ocean will keep the tide from rising. It's utterly insignificant. Oh, sure, if everyone pitched in, maybe there would be a noticeable change, but, again: that will never happen, and any attempt to make it happen through laws or mandates will be met with the same sort of mulish arrogant ignorance as the measures we're taking against covfefe. For every bucket we pull out, they will pour two back in, and piss in the ocean after them for good measure. What's left if it's not up to us as individuals? Making companies do the work. Do you think that will happen? No. We'll end up with the same sort of shit that we've seen before: there's a lot of talk, a lot of bluster, a lot of we-need-to-do-something, and then they proudly announce something like they did when they announced that all toilets must be low-flow. So they eagerly roll out the new porcelain thrones, and what happens? Exactly diddly and squat, because while a flush uses half the water as before, you have to flush two or three times so your shit isn't floating around in the bowl. Net gain: something between jack shit and negative numbers. All of this will happen again. So there's the actual Top Ten List, which, because this is The Guardian and not Cracked, is in ascending order. 1. Feed your feelings on facts Oh yeah, that's going to happen. One of the curious things about the climate crisis is that the uninformed are often more grim and fatalistic than the experts in the field – the scientists, organisers and policymakers who are deep in the data and the politics. Too many people like to spread their despair, saying: “It’s too late” and “There’s nothing we can do”. It's too late and there's nothing meaningful we can do. 2. Pay attention to what’s already happening Oh, I am. One of the victories of climate activism – and consequences of dire climate events – is that a lot more people are concerned about climate than they were even a few years years ago, from ordinary citizens to powerful politicians. Oh, they're concerned. How nice. Local measures can seem insignificant, but often they scale up. For example, a few years ago the Californian city of Berkeley decided to ban the installation of gas appliances in new buildings. And this is a perfect example of doing jack diddly squat. Drive through Oklahoma or North Dakota at night. Or if you can't bring yourself to do that (I wouldn't blame you), I don't know, find pictures or something. They're fracking for fossil fuels there. At night, you can see fires all over the fields. What are these fires? They're flaring off natural gas, a byproduct of petroleum extraction, because they can't sell it fast enough. It's being wasted at the source. They can burn it there, or they can pump it to my house and I'll use it to keep myself warm and cook my dinner. Also, you can pry my gas stove from my warm, dead hands. Also also, what's the fracking point of banning gas, only to force the use of centralized power plants that run on who knows what? Maybe green, maybe not. Probably not. (Oh, sure, solar panels, if you happen to live in a place that sees enough of the accursed daystar and can put in a battery bank to run at night.) And then, especially in places like California and Texas, the power goes out at the most inopportune times, usually when you have the most need for electrcity. One of the reasons I have gas appliances is so I can use them in a power outage. And then I installed a generator to get me through such times. It runs on, guess what, natural gas. If we stopped using petroleum right now, natural gas would still be there. When we've sucked the last drop of crude from the lower crust, natural gas will still be there. No, it's not sustainable in the long term, but it's better than many alternatives until we invent, I don't know, the Mr. Fusion or something. Yes, it produces carbon dioxide when burned. There are far worse sources for that to deal with. Banning gas is even less useful than mandating low-flow toilets. It makes it look like you're doing something, but given the voluminous waste burned off at the source, it's actually making things worse. Pant. Pant. Pant. Okay, look. I'm not going to copy the rest of their points. Read them for yourself. Draw your own conclusions. They might be different from mine; I don't know. And that's fine. But I have, indeed, given up. I can do that. Not that I'm going to go be deliberately wasteful or anything, but I will be damned if I inconvenience myself for an impossible cause. Hell, one of the reasons I never wanted kids is because I saw this writing on the wall thirty years ago, which is when we should have started doing something, but didn't. And I didn't want to bring someone else into a decaying world. My carbon footprint ends with me, and it won't be long now. But I am done. Unless we all work together, ain't nothing gonna happen, and the last two years have made it abundantly clear that we will never be able to work together. This is still the best damn slide into oblivion of any culture ever, and I'm just going to ride this sucker down with a grin on my face, a beer in my fist, and the hot wind in my hair.   One-Sentence Movie Review: House of Gucci Even the brilliant performances of Adam Driver (who miraculously manages to keep his shirt on the entire movie), Lady Gaga (who doesn't), Al Pacino, Jeremy Irons, Jared Leto, Salma Hayek, and Lady Gaga's breasts were not enough to keep the plot from being choppy or the story from being way longer than it needed to be; still, it's worth seeing for those performances, excellent camera work, and a soundtrack that features, among other things, an Italian cover of a Monkees song. Rating: 4/5 |
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