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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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| It may seem unbelievable today, what with the push toward so-called "natural" foods and supplements, but there was a time when technology was all the rage in popular culinary culture. This article is from December of 2019, so the writer was contractually obligated to mention the "holiday season." I'll just conveniently ignore that some Americans never used lard for religious reasons and take the history at face value. But for all Crisco’s popularity, what exactly is that thick, white substance in the can? If you’re not sure, you’re not alone. I can't remember the last time I saw Crisco. I'm vaguely aware that it's still around, but it's just not part of my worldview. Neither is lard. Oh, I long ago got over my upbringing with its aversion to all things swine; I simply detest animal fats. I won't even cook my eggs in bacon grease. Nor will I accept bacon with too much fat on it. But okay, that's me, and I know I'm an outlier. For decades, Crisco had only one ingredient, cottonseed oil. But most consumers never knew that. That ignorance was no accident. Lesson learned: keep the populace ignorant and you can sell them anything. A century ago, Crisco’s marketers pioneered revolutionary advertising techniques that encouraged consumers not to worry about ingredients and instead to put their trust in reliable brands. Think that would work today? No? Have you seen the supplement industry? "Made from all-natural ingredients" can mean anything from diddly to squat. For most of the 19th century, cotton seeds were a nuisance. I suspect that for at least one demographic, for most of the 19th century, anything related to cotton was a nuisance. When cotton gins combed the South’s ballooning cotton harvests to produce clean fiber, they left mountains of seeds behind. Early attempts to mill those seeds resulted in oil that was unappealingly dark and smelly. Many farmers just let their piles of cottonseed rot. Admittedly, I don't know a lot about the life cycle of the cotton plant. I could learn, of course, but I don't care enough right now. But before hybridization and complete corporate control over seed stock, couldn't they have, you know, replanted the seeds? I guess not. I'll delve into that when I have more time and energy. It was only after a chemist named David Wesson pioneered industrial bleaching and deodorizing techniques in the late 19th century that cottonseed oil became clear, tasteless and neutral-smelling enough to appeal to consumers. Yes, this is the third blog entry in a week focusing on technological innovations of the late 19th century. I assure you this is a randomly-generated coincidence. Oh, and you've probably heard the name Wesson before. I don't know if it's still around, but when I was a kid, his name was on cooking oil bottles. The key word in the quoted bit there, though, is "industrial." While lard prices stayed relatively high through the early 20th century, cottonseed oil was abundant and cheap. Americans, at the time, overwhelmingly associated cotton with dresses, shirts and napkins, not food. Which is understandable, but, for example, trees are associated with food, lumber, and firewood, not limited to one use. Things can have more than one association. Hemp, e.g., or barley, which is versatile enough to make beer or whiskey. Nonetheless, early cottonseed oil and shortening companies went out of their way to highlight their connection to cotton. I'd think that by that point, cotton could have acquired a bad reputation since it was just as associated with slavery as with clothing. But then I stop and think some more, and realize... nah, few would have cared. When Crisco launched in 1911, it did things differently. Meaning, as the article points out, it didn't mention cotton at all. But it was also a new kind of fat – the world’s first solid shortening made entirely from a once-liquid plant oil. Instead of solidifying cottonseed oil by mixing it with animal fat like the other brands, Crisco used a brand-new process called hydrogenation, which Procter & Gamble, the creator of Crisco, had perfected after years of research and development. It would take nearly 100 years for it to be properly demonized as a trans fat (which can unfortunately be confused with a fat trans, so please don't make that joke because it's rude). Again, though, at the time, it was innovative. Instead of dwelling on its problematic sole ingredient, then, Crisco’s marketers kept consumer focus trained on brand reliability and the purity of modern factory food processing. Sounds a bit discordant to modern ears, doesn't it? Back then, though, it worked. Today, Crisco has replaced cottonseed oil with palm, soy and canola oils. Canola oil is another product of marketing. Based on my limited understanding, it was developed in Canada (hence the "can" part), with the -ola suffix associated with oils (see also once-popular margarine brand Mazola, contracted from "maize"). But that naming convention conveniently hid the true origins of the oil: a mustard family crop called rape. Some other Anglophone countries are okay with this linguistic coincidence. Not us. Words have power, and nowhere is this more obvious than in marketing. Anyway. I'm pretty sure palm oil is even worse for you than cottonseed oil, notwithstanding their vegetative origins. But I've been informed that they cut out most of the trans fats in their new formulation. Once ingredient labeling was mandated in the U.S. in the late 1960s, the multisyllabic ingredients in many highly processed foods may have mystified consumers. But for the most part, they kept on eating. I've said this before and I'll say it again: to encourage people to "not eat anything you can't pronounce" is to encourage ignorance. Everything you eat is made up of chemicals. Here, take a glance at this paper  which lists several of the compounds present in that Platonic ideal of health foods, an apple. You can't pronounce most of them. Hell, I have trouble with some of them and I have a background in chemistry. Spoiler: most of them are "healthy."That said, I'm pretty sure it was the 1960s that also saw the shift begin away from processed foods and toward so-called "organic" (all food is organic) produce. Was that a backlash to mandatory ingredient labels? Maybe. We're talking about a populace that rejected a 1/3 pound burger because it sounded smaller than a 1/4 pound burger. Anyway, I'm not here to try to tell you what to eat and what not to eat. No one's paying me and I'm not selling anything. I'm only here to make jokes and note things that I find interesting. |
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Damn your pedantic ways. I was hoping to justify a vacation to Venus (which I still argue would be a much better holiday destination than fr-fr-freezing Mars, Elon. Ugh.) Now I guess I'll have to settle for the Cancun plans we already made, since my mass (and waist diameter, and thigh diameter) will be exactly the same regardless. 
