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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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| I'm usually a law-abiding citizen. Or, well, I try to be; sometimes it seems laws are designed so that if They want to get you for something, They can find a reason. But some laws are fundamentally unjust, and need to be broken. Cracked provides some examples in: 6 Loopholes People Used to Break the Law and Get Drunk  Technically, if youâre on a train, everything is legal 6. Pay to See the Blind Pig During Prohibition, a bar could not legally operate and sell alcohol. No one could legally sell alcohol (without receiving special exemptions, such as for medicinal use), or manufacture alcohol, or transport alcohol. The law didnât ban drinking alcohol, however, or handing the stuff to someone else without charging them any money. It could, of course, be argued that it's hard to drink alcohol if one is prohibited from buying, making, or moving it. But, at least here in the US, lawyers thrive on technicalities. But suppose an establishment were to hand out a drink for free and charge customers for something else? Say, they charge a customer for some entertainment â for instance, the chance to look at a marvelous animal. As for the drink the barman serves the customer, well, no oneâs purchasing that. Not mentioned: how the pig got blind. Look, I'm all for eating the tasty critters, but mutilating them doesn't fly. This was nearly a hundred years ago, though, and people didn't generally think that way. This idea is why one alternate name for a speakeasy is a âblind pig.â And if youâre wondering why the police would ever be fooled by this, know that plenty of police didnât really care about Prohibition laws and were possibly drinking right along with everyone else. Which may explain why some cops love do do drug busts: it provides them with free product. 5. Instructions on How to Absolutely Not Make Wine They had this sort of thing for beer, too. Individual families were still allowed to make a limited amount of wine, but if you were to sell people the raw materials for making wine, along with instructions, you might find yourself in trouble. This would be like selling fertilizer with instructions on how to ensure it never becomes a bomb. Except there's good reason to keep people from making bombs. âAfter dissolving the brick in a gallon of water, do not place the liquid in a jug away in the cupboard for twenty days, because then it would turn to wine.â These days, of course, the surest way to get a certain group of people to do something is to tell them not to do it. 4. Stick Everyone on a Train Even when alcohol is legal in the country, you need a license to sell it. One British gin maker, Tapling & Meegan Distilling, dutifully applied for this license, but it was taking too long to get approved. So they did the only reasonable thing and turned to steampunk. Now, there's a story idea. Within all the countryâs many alcohol regulations is a line of law saying the usual license requirements do not apply to trains in motion. The downside of this is obvious: motion sickness exacerbated by drunkenness. 3. Letâs Call Beer Something Else Complex regulations define exactly what beverages are, which is why you generally cannot put lemonade in a bottle and sell it as tomato juice. In Texas, they had a rule about beer: It could not contain more than 4 percent alcohol by volume. Ah, yes, the old "name a thing something else to get around regulations" trick. No wonder fermented beverage categories can be misleading. A lager that appears to be beer by most conventional definitions would be labeled, in fine print, âIn Texas, malt liquor.â I'm pretty sure some states still have ABV maximums for beer. As the article notes, Texas isn't one of them. But it's not a good look for a state that prides itself on limiting government interference in peoples' lives. Which, incidentally, they clearly don't do. 2. Turning Nightclubs into Pop-up Restaurants This next law lasted from 1935 to 2000, in Ireland, a place not entirely unfamiliar with alcohol. Now that's a cheap shot. Pun intended. Establishments were not allowed to serve alcohol at night unless they also served a meal. This sort of thing has been the law here in the US, off and on, depending on where you are. Hell, even my state has a version of the rule, which is why you'll technically never find a bar in Virginia; only restaurants that happen to serve booze. The dish of choice at these clubs? Curry. Yeah, that couldn't have ended well. 1. The Inedible Sandwich That Irish policy hearkens to an older and famous law from New York. Way back in 1896, the same time that they made the controversial decision to raise the drinking age from 16 to 18, the state passed a law saying bars couldnât serve alcohol on Sundays. Like I said. Bars, which served no actual food, qualified for the exemption by offering a sandwich. Not sandwiches, but a singular sandwich that a bar would pass from customer to customer without anyone eating it. This was named the âRaines sandwich,â after John Raines, the senator who wrote the law. I'd heard about this loophole before, of course. It still amuses me. The takeaway here is that, if you're clever, you can find a way around unjust laws without flagrantly breaking them. And I approve. |
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