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 8, 2022 at 12:01am

#1033590

Not So Far Away

In an ongoing effort to understand people who are not me, I took a look at this article that someone sent me.

Disaster news on TV and social media can trigger post-traumatic stress in kids thousands of miles away – here’s why some are more vulnerable

I don't find endless speculation helpful concerning the root causes of, for example, why some people shoot up a school or other place where it's like shooting fish in a barrel. Everyone has their little pet theories: lack of mental health services; the existence of football (okay, that one is mine); video games (oh come on); religion; lack of religion; guns; not enough guns; drugs; not enough drugs... whatever. None of that helps. I want to see solid science, and I haven't seen a whole lot of it. You might think your pet theory is based on "common sense," but you know how much I hate that concept, and besides, it's obviously not working.

But this article got me speculating myself, and since this is my blog, you get to read the speculation. Or you can skip it; to quote the rallying cry of my generation, whatever.

When disasters strike, the flood of images on TV and social media can have a powerful psychological impact on children – whether those children are physically in the line of danger or watching from thousands of miles away.

This is somewhat interesting to me, because when you hear about trauma, it's usually in the context of adult PTSD or, in the case of children, abuse. This is more like second-hand triggering.

Our latest research uses brain scans to show how simply watching news coverage of disasters can raise childen’s anxiety and trigger responses in their brains that put them at risk of post-traumatic stress symptoms. It also explores why some children are more vulnerable to those effects than others.

Now, see, this is science. Though I'd take it all with a huge grain of salt until I knew more about things like sample size, and whether getting poked into a brain scan machine itself causes baseline anxiety to rise for some people.

With climate change, researchers estimate that today’s children will face three times as many climate-related disasters as their grandparents. And the pervasiveness of social media and 24-hour news make exposure to images of disasters more likely.

Which is one reason I never wanted kids; I knew that the world I'd leave them would be worse than the world I lived in.

But while around 10% of people who are directly exposed to traumatic events develop symptoms that are severe enough to meet diagnostic criteria for post-traumatic stress disorder, or PTSD, a majority do not.

I felt like this is important to emphasize. It's never as simple as "if x happens, then y will also happen" with psychology. People react differently. It's good to see a number attached to that, though.

The Adolescent Brain Cognitive Development study followed 11,800 children across the United States over a 10-year period using a variety of brain imaging and mental health assessments.

Well, that answers my question about sample size. Seems large enough. Though the study they quote about long-range second-hand trauma appears to have used a smaller subset of that sample.

We found that greater media exposure was associated with higher reporting of post-trauamtic stress symptoms – and the link was just as strong in San Diego youth as it was in Florida youth.

Well. I guess maybe ignorance is bliss, after all. Or was that not the point?

So what can parents do? For starters, parents can monitor and limit access to some internet content for young viewers.

Gosh. I've never heard that bit of advice before, ever.

I don't want to be all "When I was a kid we didn't have the internet and things were better," but when I was a kid we didn't have the internet and things were better. Honestly, though, I'm not convinced there's a direct causal relationship there. Blaming the internet, which after all has managed to connect people from all over the world and broaden everyone's horizons, is just too simple. As with automobiles that kill 40,000 Americans a year, it's still preferable to not having it -- though it's worth exploring ways to make things safer.

So here's my worthless speculation: what if the recent mass shootings could be traced to people who had experienced such first- or second-hand trauma while they were younger? It tracks. You get someone obsessed with disaster news; it follows, logically, that such a person might be focused on creating his (it's mostly "his") own disaster.

I'm not saying this is right, of course. Just that, as I said, I wanna see the science.

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