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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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Perhaps appropriately, our final venture into the shadows of the past involves examples of beautiful retribution: "In Spite Of"  The linked article, from Mental Floss, is still available, which is good because that means I get to highlight some of the examples I didn't last time.But first, some commentary on the original post. Me: Few things in life feel better than nuclear revenge. One of those few things that does is the schadenfreude I feel when someone who deserved it suffers misfortune, and I didn't have to be its vehicle. While I believe in disproportionate retribution, setting it up takes a lot of work, and not getting caught while still having them know it was you takes more. Me: I mean, sure, it's nice to be able to forgive sometimes, too. I realize this contradicts what I said above. Whether I forgive or retaliate, and the degree to which I do either, depends on the deed as well as the other party's motivations (to the extent that they make them clear) and level of remorse. Since it's so situation-dependent, the best advice is: don't piss me off. Honestly, though, it's most likely that I just avoid the offending person entirely. Anyway, here are a few of the items that I now feel are also worthy of quotation: 2. The Tyler Spite House In 1814, as soon as ophthalmologist Dr. John Tyler discovered that the city officials of Frederick, Maryland, planned to build a road on an empty plot of his land, he started searching for a way to stop them. What he found was a law that prohibited road construction if a building was in the way. I have many questions here, not least of which is: what exactly did an ophthalmologist do in 1814 (apart from building a spite house)? Anesthesia hadn't been invented yet, nor had sanitary practices in medicine. This was the era when barbers doubled as surgeons simply because they had steady hands and sharp blades. It wasn't exactly the Dark Ages, but it's also around the same time as when the cutting edge (pun absolutely intended) of dentistry was wooden teeth, and leeches had a far more active role in patient care. But, since one of my few actual phobias involves eye stuff, I'm not going to look this up. Tyler hired a builder to break ground immediately, and city workers were forced to abandon their assignment when they arrived the next day (apparently, Tyler was there when they arrived, seeming very pleased with his endeavor). My other question involves the application of eminent domain, which I guess wasn't as developed (pun also intended) then as it is now. 6. Adidas and Puma Brothers Adolf and Rudolf Dassler had a hit on their hands in 1936 when athletes won seven gold medals at the Berlin Olympics while wearing the sneakers the duo had created. But by 1948, a feud between the two led to a split in their shoe business: Rudolf launched Puma (after a brief flirtation with the name Ruda), while Adolf formed Adidas (a portmanteau of his first and last name). There is, and I don't mean this as a slight because it's part of my ancestry too so please don't retaliate against me if you're German, no revenge like German revenge. Based on the link to their names at the source link, they were from a small town called Herzogenaurach, the pronunciation of which probably contributed to the feud. If you worked for Adidas, you wouldn’t be caught dead in a bar favored by Puma employees, and if your Adidas-employed family loved a bakery on the Puma side of town, you’d have to get your streuselkuchen elsewhere. When I was a kid, we convinced each other that Adidas was an acronym for All Day I Dream About Sex, and Puma was Pee Under My Ass. I was a Reebok kid, anyway. 8. The Alameda Spite House One legend holds that a previous landowner retaliated against the city of Alameda, California—and an unsympathetic neighbor—after his property was seized under eminent domain; he built the tiny house on what land he had left. I'm just including this one now because it also might have been related to eminent domain, though in a state on the other coast. But as the article notes, we don't know that for sure. 13. The Hess Spite Triangle I'm going to go out on a limb here and suggest that maybe this was due to German ancestry, as well. It all started in 1913, when the city began seizing properties and razing buildings in the area to make room for an extension of Seventh Avenue. At least this time, it was individual vs. government, which is almost always more satisfying than interpersonal feuds. Incidentally, if you're not American, or even if you are, you may not understand how eminent domain works here today. A government entity can, indeed, take an individual's land at will, but, supposedly, only for public projects, and they have to pay "fair market value." In reality, lawyers almost always get involved in arguments over what that value actually is, and I imagine they eat up more of the payment than they advocate for. Also in reality, the line between public projects and private ones can be blurred, thanks to things like zoning laws and pro-business decisions by a former Supreme Court. But don't take my word for it. I'm not a lawyer, as is evidenced by my lack of a vacation house, spite or otherwise. 14. Brückenmännchen Brückenmännchen translates to “little bridge man,” and this sculpture—of a man bent over, butt out—was added to the old Rhine river bridge connecting Bonn and Beuel in Germany in the late 19th century after the two villages argued over the construction project. Like I said: Germans. When the old bridge was destroyed in the Second World War, the Brückenmännchen was recovered and attached to a new bridge. It was eventually destroyed by vandals in 1960, and today a replica is displayed on Germany's Kennedy Bridge. I have many questions. 31. Redneck Stonehenge The point had been made. “Don’t mess with a redneck who has a backhoe,” he said. Truer words were never spoken. 38. Striped House It’s no secret that stripes tend to clash with whatever’s around them. Such was the case in London, where a property developer named Zipporah Lisle-Mainwaring decided to paint her townhouse with vivid red and white stripes in 2015. This sort of thing is why so many subdivisions in the US are ruled by the iron fist of a Homeowners' Association, or HOA. I tried to explain HOAs to someone in Belgium, and the best I could come up with was "You know all the stuff you hear about individual freedom and property rights in the US? Well, HOAs throw all that in the crapper, and Americans join them on purpose." Lisle-Mainwaring had originally intended to demolish the space and transform it into a luxury home; when those plans were denied, people speculated she gave the building its garish makeover out of spite. (She, however, said that she painted the building to “add to the gaiety of the nation.”) Nah, if she wanted to do that, it should have been a rainbow theme. And that's it, then: an appropriate enough final Revisited for this blog. I just hope no one retaliates. |
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