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# Complex Numbers

Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
 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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 Uncomfortably Numb Well, I had some dental work done yesterday. This resulted in far more pain than I'd expected (I mean, sure, I expected some; it's a dental procedure). OTC pain relievers do nothing. So I have, basically, two options: 1) Be in pain, leaving me unable to sleep or concentrate; or 2) Take the good drugs the dentist prescribed, leaving me unable to sleep or concentrate (but at least not in pain), and running the risk of addiction. Yeah, that's right: opioids keep me from getting decent sleep. That alone is probably enough to keep me from developing a habit; I'd rather sleep. Point is, I won't be doing my usual blogging today, or, really, much of anything except staring at streaming video. Hell, I won't even be able to drink (adverse drug interactions). Of course, this will pass, and it's really not a big deal. Perhaps I'll feel better tomorrow.
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 Extinct Nothing is forever. 11 Extinct Foods From History   I didn't fact-check these, so beware. If true, there are some on this list I'd never heard of. As per normal, I'm not copying all of them here. 1. Ansault pear Unlike other items on this list, the Ansault pear appeared relatively recently. First cultivated in Angers, France, in 1863, the fruit was prized for its delectable flesh. Angers, France? That's not Nice. Irregular trees and the rise of commercial farming contributed to the fruit's demise. Seems to me that, if we really wanted to, we could recreate this one. Fruit varieties are generally made by some sort of cloning or hybridization. 3. Auroch You may have heard aurochs mentioned in Game of Thrones, but this creature doesn’t belong in the same category as dragons. The real cattle species was domesticated 10,000 years ago in the early days of agriculture. They were big (“little below the elephant in size,” according to Julius Casear) and leaner than modern cows. Apparently these lasted longer than I thought, all the way to the 17th century. Here, the article leaves out an interesting bit about the aurochs: it was so important, so integral to developing civilizations, that the pictogram for it became a letter. Phoenicians called it aleph. The Hebrew script still does. In Greek, alpha. We know it as the letter A. 5. Dodo Dutch sailors first visited the island chain of Mauritius in 1598, and less than two centuries later the archipelago's native dodo went extinct. Sailors relied on the birds as sustenance during long voyages at sea, but that isn't the primary reason they died out; habitat and the introduction of invasive species like rats and pigs ultimately wiped out the animal. Pretty sure they mean "habitat loss," not "habitat." It's my understanding that it was fairly common, at the time, for people of the European variety to believe that God put all the other animals (and plants, etc.) on Earth for our benefit, and would never allow one to become extinct. That turns out not to be the case. 6. Steller’s sea cow German naturalist Georg Wilhelm Steller identified the Steller's sea cow around the Commander Islands in the Bering Sea in 1741. Growing up to 30 feet long, it was significantly larger than the sea cows alive today. Cue Hindenburg disaster narrator: "Oh, the huge manatee!" 7. Mammoth Wooly mammoth meat was an important component of the diets of our earliest human ancestors. We ate so much of them that hunting may have contributed to their extinction around 2000 BCE (though climate change was likely a bigger factor). So, apparently, there were mammoths wandering around at the same time as there were pyramids in Egypt. Not in the same place, though. 8. Taliaferro apple Thomas Jefferson cultivated Taliaferro apples at Monticello. In an 1814 letter to his granddaughter, Jefferson said the small fruit produced "unquestionably the finest cyder we have ever known, and more like wine than any liquor I have ever tasted which was not wine." Including this one in my commentary for literal local flavor. But also because many people might not be aware that the Virginia pronunciation of Taliaferro is, inexplicably, Tolliver. 9. Great auk Modern humans primarily killed great auks for their down, leading to the species’s extinction in the mid-19th century, but prior to that they were hunted for dinner. I knew about this one because I had an English teacher in high school who loved to point out awkward sentences in his students' compositions by writing a big red AWK and circling the offending phrase. He called it the "Great Awk." It should surprise no one that I had a truly stupendous Great Awk collection. Anyway, there's obviously more at the link, and they're all interesting, even if, as is the case with the passenger pigeon entry, some of them are already well known.
May 14, 2023 at 9:27am
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