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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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| "Hey, Waltz, you should do another article on something that's positive." Here you go. You should get a charge out of this: Inside the Proton, the ‘Most Complicated Thing You Could Possibly Imagine’  The positively charged particle at the heart of the atom is an object of unspeakable complexity, one that changes its appearance depending on how it is probed. We’ve attempted to connect the proton’s many faces to form the most complete picture yet. I don't know; the most complicated thing I can imagine is a romantic relationship. A proton ain't got nothin' on that. More than a century after Ernest Rutherford discovered the positively charged particle at the heart of every atom, physicists are still struggling to fully understand the proton. Maybe their attitude is too negative? High school physics teachers describe them as featureless balls with one unit each of positive electric charge — the perfect foils for the negatively charged electrons that buzz around them. You know, I kind of understand why the protons in a nucleus, all positively charged, don't fly away from each other: it's because on small scales there's another force stronger than electromagnetism that binds them together. What I never did get is why, since positive and negative charges attract, the electrons stay in a probability cloud around the atomic nuclei instead of just slamming into the protons. It's not really analogous to planets orbiting the sun, though that's the model they teach you in elementary school. The reason is some really damn complicated quantum shit that I don't understand. Apparently it takes a hell of a lot of energy to get them to actually collide (this is alluded to later in the article). Getting back to the subject, though: College students learn that the ball is actually a bundle of three elementary particles called quarks. Which I really don't understand. But it's still fun to say. But decades of research have revealed a deeper truth, one that’s too bizarre to fully capture with words or images. Because of course. As the pursuit continues, the proton’s secrets keep tumbling out. Most recently, a monumental data analysis published in August found that the proton contains traces of particles called charm quarks that are heavier than the proton itself. And that, dear readers, is deeply, deeply weird. I mean, quantum anything is pretty weird, but that goes way beyond weird. There's not even a word for how profoundly, utterly, mind-blowingly strange that really is. Proof that the proton contains multitudes came from the Stanford Linear Accelerator Center (SLAC) in 1967. In earlier experiments, researchers had pelted it with electrons and watched them ricochet off like billiard balls. But SLAC could hurl electrons more forcefully, and researchers saw that they bounced back differently. The electrons were hitting the proton hard enough to shatter it — a process called deep inelastic scattering — and were rebounding from point-like shards of the proton called quarks. “That was the first evidence that quarks actually exist,” said Xiaochao Zheng, a physicist at the University of Virginia. Always nice to hear from my university. (Except of course when they beg me for money.) Incidentally, you might want to go to the link to look at the helpful pictures. But the quark model is an oversimplification that has serious shortcomings. Because of course. The rest of the article describes the experiments and what they're finding, and I certainly think it's fascinating in addition to being really quite incredibly weird. I won't transcribe more, because it's Friday night and I have other things to do. But it's absolutely worth a look, even if you don't fully understand it. I sure as hell didn't. |
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