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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.




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October 3, 2021 at 12:03am
October 3, 2021 at 12:03am
#1018576
Usually, people cling to the first thing they hear about a subject, ignoring or dismissing any further evidence. This is called the Irrational Primacy Effect, and it's a form of confirmation bias.



It's worst, I think, when the first thing you hear already speaks to your inherent biases (and we all have them). Then, when you get evidence to the contrary, your first reaction is often, "bullshit."

I'm not going to go through this item-by-item, but it's a Cracked link, so at least there's some humor sprinkled in, which (for me anyway) helps to soften the blow of being told what I thought I knew is wrong.

History is so complicated that it’s arguably a minor miracle the average person knows as much as they do. Sometimes dumbing down complex events is enough to help us get the point of how it’s shaped the modern world; you don’t need a PhD to understand that the Nazi were bad. But sometimes simplifying accidentally leaves everyone with the completely wrong impression...

All of the things at the above link are subject to misreporting and simplification, and I think it's important to get a fuller picture, including facts learned later on in the process. Science and knowledge are supposed to correct as well as refine old ways of looking at things, as the section about Galileo hints at.

And we see it all the time, even now. Perhaps the worst example, both in terms of outright falsehood and deleterious effect on society, is the reported link between childhood vaccines and autism. Leaving aside for the moment that believing this is basically saying, "I'd rather have a dead child than an autistic one," which is a big slap on the face to anyone on the spectrum, the entire report was completely fabricated in order to sell a book. Not only is there absolutely no link between vaccination and autism, but the person who perpetrated the hoax in the first place ended up losing his license. I won't name him, because I don't like giving oxygen to frauds, but you probably know who I'm talking about.

And yet, you still have people clinging to that complete falsehood. They might say, "why take chances?" Well, because the alternative is sick or dead kids, and more epidemics. They might say, "But my kid was fine until he got vaccinated, and then he became autistic." If true, that's coincidence, not causation.

There are, of course, likewise falsehoods being spread about other, more recently developed vaccinations. This is not a matter of people having different opinions; it's about some people simply clinging to the wrong set of facts.

None of us should feel bad if we fall victim to the irrational primacy effect, though; it can -- and does -- happen to everyone. But once you know about it, you have a mental check on it. Not that every bit of contradictory information suddenly changes the truth, so a healthy skepticism is still required.

So yeah, if you want humor, read the link. I'm entirely too frustrated with willfully ignorant idiots to even make jokes right now.

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Thanks for all the ideas for replacing the utterly despicable "revenge bedtime procrastination" label. Honestly, I thought all of them were better than the original. I'm going to award the one by Writer_Mike for its appropriate acronym: TIMES UP. (See yesterday's entry's comments for what that is, and for the other good ideas.)

I'll do this again soon, so there will be more chances at a Merit Badge!


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