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 |    Not for the faint of art. |
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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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| This one, from Big Think, is one of those articles that expresses what I've been thinking about for a long time, but haven't found the words for. How glorifying ignorance leads to science illiteracy  If we wish to tackle the very real problems society faces, we require expert-level knowledge. Valuing it starts earlier than we realize. I know something like this has been said before, but if you want someone to fly the airplane that you're in, you find a trained, licensed pilot, not someone who's read a book on birds and thus thinks they know all about flight. All across the country, you can see how the seeds of it develop from a very young age. When children raise their hands in class because they know the answer, their classmates hurl the familiar insults of “nerd,” “geek,” “dork,” or “know-it-all” at them. And yet, people who know things like who lost the AFC championship in the 1989 American football season are valued. Everyone's a nerd about something. It’s a version of the social effect known as tall poppy syndrome: where if someone dares to stand out, intellectually in this case, the response of the masses is to attempt to cut them down. Human life, especially kid life, can be viewed as a tension between wanting to fit in and wanting to stand out. Someone who knows more, is more successful, or who seems to be smarter than you is often seen as a threat, and so in order to prevent them from standing out too much (or surpassing too many others), we glorify ignorance as the de facto normal position. I've said this before, too, but the truth is, ignorance is the default position. We all start out ignorant, and there's so much knowledge out there that we can't help but remain ignorant of all but a few things for our entire lives. But, in my view, what we should be glorifying is not the default position, but the desire to get just a little less ignorant. And I should make this clear: ignorance isn't the same thing as willful ignorance. Choosing to remain ignorant harms your development as a child, but leads to science illiteracy, which harms the entire world. For instance, my limited knowledge of English tells me that there should have been a "not only" in that sentence. That, or change the conjunction from "but" to "and." I get it. I make editing mistakes, too. I find them in previous blog entries, from time to time. There's probably some in here I didn't catch. But I always strive to do better. There are so many remarkable things that we — as a species — have figured out about existence. I cannot argue with this, but there's much left to learn. We know what life is: how to identify it, how it evolves, what the mechanisms and molecules are that underpin it, and how it came to survive and flourish here on Earth. I could get picky about that assertion, and it's a prime example of what I just said. For example, while we have some really good hypotheses about how life started, we haven't quite figured that out to a high degree of certainty. We know what reality is made of on a fundamental level, from the smallest subatomic particles to the nature of space and time that encompasses the entire Universe. I'm not sure this is entirely correct. But, again, we know more now than we did even 100 years ago. Our most valuable explorations of the world and Universe around us have been scientific ones: where we learn about reality by asking it the right questions about itself, and by listening to the answers that are revealed to us through experiment, observation, and careful measurement. And, yes, sometimes it turns out the previous answers were wrong or incomplete, and get replaced by new answers. This is still a better system than the old one, which declared that something was so and brooked no argument or counterexamples. Those, it turns out, are almost always wrong. It’s impossible, in this day and age, for any single individual or entity to be an expert in all possible things. I would go so far as to say that this has always been impossible, but now, we have a better understanding of just how impossible it is. Even as a child, you know when the adults are lying to you, to themselves, and to everyone else in the room. As Mike Brock just wrote recently, it’s the “capacity to think clearly about reality itself” that must be our most unbreakable trait as individuals, particularly when there’s pressure — peer pressure, social pressure, political pressure, etc. — to surrender that capacity over to whatever some arbitrary authority figure says. But here's at least part of the problem, as I see it: Since I don't know everything, cannot know everything, I have to rely on experts and authorities in whatever subject. If I'm going to court, that would be an attorney. If I'm curious about the function of interatomic bonds in a solid, it would be a physicist. If I want to know who lost the AFC championship in the 1989 American football season, that would be a sports nerd. If I want the plane to fly, it would be a pilot. So, some amount of trust is necessary. One way to know who to trust is by credentials, for which one also must trust the credentialing authority (if the pilot, for example, got their license from Bubba's Lurn 2 Flie in rural Nevada, no thanks, I'll walk). Despite whatever your initial intuition might have been about an issue, you must always — every time you acquire new, valid information — re-evaluate your expectations in light of the new evidence. This is only a possibility if you can admit, to yourself, “I may have been wrong, and learning this new information is essential in getting it right in the end.” The willfully ignorant don't take this approach. They're Right, always, and to admit that they weren't would mean others might think they're weak or wishy-washy. You see this all the time. I bet you can come up with at least one example right off the top of your head. (No, I don't mean me, though I do need to fight against this tendency like most people.) Changing one's mind in the face of new evidence is true strength. Changing one's mind without substantial new evidence, now, I can see how that could be perceived as being flighty. There’s a reason why admitting, “I was wrong” is so difficult for so many of us, and why it is rarely an innate talent for humans to have, rather than a skill we must acquire. All of the solutions that require learning, incorporating new information, changing our minds, or re-evaluating our prior positions in the face of new evidence have something in common: they take effort. Yes, well, at least it's not physical effort, so I can do these things and still admit I'm lazy. Glorified underachieving, proclaiming falsehoods as truths, and the derision of actual knowledge are banes on our society. The world is made objectively worse by every anti-science element present within it. This may seem like an assertion without evidence, hanging there in quote form as it is, but I think reading the actual article provides the logical framework to back it up. Or, you know. I could be wrong. The Doctor: Ignorance is… um, what’s the opposite of bliss? Clara: Carlisle? The Doctor: Yes! Yes, ignorance is Carlisle. (If you don't know why that's funny, you can look it up. Then it won't be funny anymore, but at least you'll know a bit more.) |
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