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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June 21, 2022 at 12:03am

#1034052

We're Doomed.

In another case of random number generator coincidence, this Summer Solstice article is about climate change.

Yeah, I'm going there.

Why is climate 'doomism' going viral – and who's fighting it?

1) Because we're doomed.

2) Not me. I'm done.

Naturally, I'll be expanding on these points herein.

Climate "doomers" believe the world has already lost the battle against global warming. That's wrong - and while that view is spreading online, there are others who are fighting the viral tide.

Count me among the former number. The time to do something about it was 40 years ago, kind of like if you're going to deflect an asteroid that's heading for Earth, you gotta catch it early on because it then takes less energy to alter its orbit to miss.

As for the fighters, good luck. Truly. I wish you the best.

Charles is 27 and lives in California. His quirky TikTok videos about news, history, and politics have earned him more than 150,000 followers.

You know what's almost as bad as climate change? DikDok. Neither shows any sign of going away anytime soon, however.

In the video in question, recorded in October 2021, he decided it was time for a confession.

"I am a climate doomer," he said. "Since about 2019, I have believed that there's little to nothing that we can do to actually reverse climate change on a global scale."

Well, at least someone on DikDok has some sense. Or "had," given the way the linked article ends.

Climate doomism is the idea that we are past the point of being able to do anything at all about global warming - and that mankind is highly likely to become extinct.

Oh, we should be so lucky as to become extinct. No, that's not going to happen. What's going to happen is that War, Pestilence, Famine, Death, and Inconvenience (the fifth horseman that the others don't talk about) will reduce the human population of earth drastically.

And then maybe the Earth will begin to recover.

The survivors won't have it easy, either. It's pretty easy to glibly say "back to the Stone Age," but the Stone Age was dependent upon readily available resources such as flint, which is no longer readily available because we used all the easy-to-find stuff. Sure, there will be remnants of metals and whatnot from our lost civilization, but how are you going to use them with pre-Stone Age technology?

That's wrong, scientists say, but the argument is picking up steam online.

It's one thing to say "scientists say." Perhaps they're even right. I'm inclined to believe they're right if there's anything approaching a consensus on the subject. But I take this to mean that there are things we can do to stop and maybe even reverse climate change. Sure. We could.

We won't.

Because it's not a science issue. If it were a science issue, shit would have been done 40 years ago, like I said. No, it's a political issue, and that's not in science's wheelhouse.

Alaina makes a habit of challenging climate doomism - a mission she has embraced with a sense of urgency.

"People are giving up on activism because they're like, 'I can't handle it any more... This is too much...' and 'If it really is too late, why am I even trying?'" she says. "Doomism ultimately leads to climate inaction, which is the opposite of what we want."

Okay, let me make an analogy here: You're looking for a job. You want a job. You need a job. You have to get a job or you're out on the street. So you go to interview after interview, and never hear back from any of them.

There is absolutely no guarantee that someone will hire you. That's the opposite of what you want, but it's reality. So what this woman is proposing is unwarranted optimism: If you keep trying, you might eventually find a job. Or you might die starving on the street. If you give up, you'll die starving on the street. People have been trained to be cluelessly optimistic, and I'll admit that sometimes it even works out. But it's not realistic.

Climate scientist Dr Friederike Otto, who has been working with the UN's Intergovernmental Panel on Climate Change, says: "I don't think it's helpful to pretend that climate change will lead to humanity's extinction."

Again, I don't think it'll lead to humanity's extinction. There's an awful lot of us, all over the globe, and some of us are quite clever and good at surviving (not me, though -- civilization collapses and I'm dead within a week).

In its most recent report, the IPCC laid out a detailed plan that it believes could help the world avoid the worst impacts of rising temperatures.

It involves "rapid, deep and immediate" cuts in emissions of greenhouse gases - which trap the sun's heat and make the planet hotter.

And that's why it ain't gonna happen. If the last two and a half years of global pandemic didn't teach you that, no matter what, some people will never do the right thing, then nothing will. Here's the deal:

Country A proposes "'rapid, deep and immediate' cuts in emissions of greenhouse gases." Somehow, against all odds, they manage to push it through. Perhaps it's an enlightened dictatorship; I don't know, whatever. Country B, on the other hand, keeps going the way they've been. As a slowdown in production reduces Country A's GDP, Country B gains the upper hand and, eventually, invades Country A and starts doing things their way, the financially efficient way, the old way.

After watching what's been happening since late February, don't tell me that's not going to happen.

But even that's not realistic, because here in reality, Country A won't do squattly-dick. Oh, maybe they'll ban plastic straws or promote direct solar power (all of our power right now, except maybe nuclear, is solar power, directly or indirectly, and I'd argue that even nuclear is a kind of solar power because fissionable elements can only be formed in stars -- but I digress).

None of that will make a dent.

"There is no denying that there are large changes across the globe, and that some of them are irreversible," says Dr Otto, a senior lecturer in climate science at the Grantham Institute for Climate Change and the Environment.

"It doesn't mean the world is going to end - but we have to adapt, and we have to stop emitting."

The world will go on. Minus several species.

Last year, the Pew Research Center in the US ran a poll covering 17 countries, focusing on attitudes towards climate change.

An overwhelming majority of the respondents said they were willing to change the way they lived to tackle the problem.

Which, again, won't do squat, and will pay dividends to anyone unwilling to change the way they live. Because that country scenario I mentioned above? It scales down to the individual level. If I'm living like a hippie, I'll be overrun by mobs of gas-guzzling tank drivers.

"The most apocalyptic language that I would find was actually coming from former climate scientists," Charles says.

Just guessing here, but I'd say they know what they're talking about, but no longer have a vested interest in seeing any proposed solutions come to fruition. You spend your life chasing a rainbow, and instead of a pot of gold you get a bucket of coal. Which you can't even use because it'll release more carbon into the atmosphere. That's gotta wear a person down.

TikTok's rules forbid misinformation that causes harm. We sent the company some videos that Alaina has debunked in the past. None was found to have violated the rules.

TikTok says it works with accredited fact-checkers to "limit the spread of false or misleading climate information".

As defined by the CCP, and we all know that "misinformation" to them is "something other than the official Party line."

Although it can take many forms (and is thus difficult to accurately measure), Alaina says doomism is particularly popular among young people.

Good to know I'm young at heart.

Now, don't get me wrong -- as with the job hunt analogy above, the only way to have any chance of winning is to keep trying. One day, maybe, low probability but maybe, Sisyphus will be able to roll that boulder all the way up the hill. That, I think, is why people push the "yes, there is something we can do" line. And I'm not disputing that there's something we can do.

Just that there's anything meaningful that we will do. Not when there's still a significant number of people who aren't willing to make any sort of sacrifice for the common good. Don't believe me? Look around.

Also -- and this is the important point -- it's not on us. It's on large corporations who are the ones spewing out the greenhouse gases. The same corporations who have been publicly denying climate change for over 40 years. I've said this before, I know, and now I'm saying it again. Even if you do something on an individual level -- and I'm not saying that you shouldn't -- it's taking a cup of water out of the ocean while other people are standing around pissing into the same ocean. Sure, it makes a difference. Marginally. But not enough of us can be arsed to do it, and the pissers outnumber the rest of us.

Fortunately, there is one thing that's almost guaranteed to happen, and that will certainly drop global temperatures to something approaching pre-industrial levels: large-scale war leading to nuclear winter.

Sleep tight.

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