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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 can only think of one subject more contentious than politics or religion. And this is it. https://www.nylon.com/life/how-much-should-i-tip How To Tip For Americans, this whole thing can be a minefield. For people from other countries, it's bizarre and more than a little irritating. The worst person in New York City is a 29-year-old woman, ostensibly named Sam. No. No, it is not. How do I know to single out Sam, alone amidst a population of eight million people, many of them not so great themselves? Simple. It's because Sam is someone who tips "around $5, whether the bill is $50 or $100." Oh, someone who tips $5 is worse than those Sunday brunch holy assholes who leave religious tracts that look like $20 bills? No. While writer Monica Burton concedes that many people who don't tip just might not know what's appropriate to do, and cites Michael Lynn, "a tipping expert at Cornell University’s School of Hotel Administration," who explains that "40 percent of people aren’t aware that they should be tipping between 15 and 20 percent," I think that's far too generous of a concession to make. The fact that there is someone who calls himself a "tipping expert" makes me irrationally angry. And don't they know that a lot of Americans are innumerate, and a lot more are numerophobes? Throwing around percentages like that will just make their brains snap shut like my last date's legs. I also think that if people don't know to tip properly, then they probably shouldn't be eating out at all. Which of course would be SO wonderful for wage slaves in the service industry, if fewer people went out to eat. As we've seen over the past 6 months. Beyond that, as is clear from reading the article, lots of people who don't tip are fully aware of how much to tip, they just don't want to do it. Total sociopath "James" says: "I will add a few dollars and round it to an even number, say a $36.87 meal being tipped $3.13 to make $40.00... This isn’t because I want to tip, it just gives me a little mental math game and I like even numbers." $40.00 says "James" refuses to wear a mask during a pandemic too. Also, that's not "a little mental math game" unless you're a complete and utter imbecile. A better one would be to shift the decimal point one digit to the left, double the result, and leave that much. No, it's not harder; it's actually easier and then you're tipping 20 goddamn percent. But what's fair? It's pretty simple. There is, of course, the 20 percent rule of thumb, and that's not a bad one to live by. Always leave at least this much at a restaurant. Oh, if only it were that easy. So you go into your favorite brewpub. While eating, you notice that they have six-packs of a favorite beer in the cooler. You want to take some home with you. So you have the waiter add them to the bill. Say the bill is $20 without the six-packs, and you get $60 worth of canned delicious beer. $4 is what you'd normally tip for the meal. But the check reads $80 because of the sixes, so by this you're supposed to leave $16. While that's nice and all, that's a goddamned 80% tip on the part of the check that the waiter actually worked on. At absolute worst, the waiter brought the sixes over to you and punched the total into the order screen thing. Is that worth the price of another six-pack? I have the same problem with ordering wine at a fancy restaurant. You get a $40 meal and a $60 bottle of wine. Okay, I can see tipping $20 at a fancy restaurant, but is opening a goddamned bottle of wine worth the same as bringing you menus, putting up with your inane, arbitrary and bullshit dietary requirements, communicating same to kitchen, bringing you food, keeping your water filled, asking you what you'd like for dessert, bringing you said dessert, and then cleaning up your mess afterward? I say no. No, it's not. But dammit if I don't tip 20% anyway, because social pressure requires that I do so. How about at a bar? One dollar per drink, right? Wrong. One dollar is fine on a $5 beer. Anything other than that deserves at least $2. The 20 percent rule applies at bars, too. I always give bartenders more than 20%. They're bartenders, my equivalent of a priest or psychologist. It's cheaper than tithing or paying for therapy. And finally: Tip the people making your coffee. If you can afford to buy a $6 latte, you can afford to put a dollar or two in the tip jar. No. Under no circumstances. This is where I draw the fucking line. I have no issues with tipping for table service or if I'm sitting at a bar, but if I have to stand in line, order from a cashier, pick up my tea (I don't drink coffee), carry it back to my table, and then bus my own table? That's no different from going to McDonald's, and you don't tip at McDonald's, do you? Or do you? I haven't been in one for a while; for all I know, they've played into that bullshit. There are other times when the 20% rule goes right out the window. The last time I took a cab in Vegas, for instance. Okay, so picture this: the airport is approximately three blocks from the Luxor. I mean, it's right there. So one time, instead of renting a car, I hired a cab to take me on this really remarkably short trip (I know because I've driven it). This cabbie must have thought I was a wide-eyed newbie who couldn't read a map, so he ended up giving me the tour of North Vegas, the Strip, and Nellis Air Force Base before turning around and taking me back to the Luxor. Okay, I'm exaggerating, but only a little bit. Point is, a $20 trip ended up costing closer to $40. Not that $20 is fair, but it's cheaper than renting a car and the distance is just a little too far to walk in 110 degree heat, no sidewalks, while shlepping luggage. Anyway. When I went to swipe my card, they had certain tip amounts preset: 25%, 40%, 50%. Hell to the power of no squared. I declined to tip by card, instead digging into my Emergency Stripper Fund (a wad of $1 bills) and handed the driver five of them. More than 20% of what the trip should have cost, less than 15% of what that con artist ended up charging me. And then he had the audacity to call me a cheapskate for that. Like I said, that was the last time I took a taxi in Vegas. Now, if I fly in, I use Uber. The only difficulty there is that, while the taxi stand is clearly and plainly marked at the baggage claim, and is located right outside its doors, the signage for Uber was about a 6"x8" placard with "rideshare" and an arrow on it. I followed these placards up an escalator, out into the oppressive heat, across an overpass to a parking garage, through the parking garage, down a flight of stairs (no escalator), across to another parking garage, through a door with a smudged sign reading "Beware the leopard," up an elevator, across a tightrope strung over a shark tank, through a bunch of dark, twisty passages, all alike (being careful not to be eaten by a grue), finally leading to an ill-lit and badly organized rideshare pickup area. The Uber driver drove me straight to the Luxor, though, and got a nice tip. What I'm saying is, 20% doesn't always work. I don't mind tipping, especially for superior service. What I mind is living in a society that requires people to tip. If restaurant tips, for example, were done away with entirely, with wait staff paid a decent wage, the cost of dining out wouldn't change much if at all - it would simply be all up front instead of hidden on the back end, and requiring people who failed high school algebra because it was "too hard" to do math. I mean, sure, I'd like to see more math literacy and less fear about it, but we're not accomplishing that by requiring tips -- especially because more and more places have started explaining exactly how much 15%, 18%, 20%, and maybe even 25% of your bill comes to, or just providing buttons on a screen that do the same thing. That's like saying spell checkers have made people better spellers. I understand that, in France, no tipping is expected, though people often do it if they think the server went above and beyond. And I've heard that in Japan, tipping is an insult. I don't know; I haven't been to France since I was a kid, and never to Japan, and I get the impression I'd have even worse culture shock from other things. Oh, and that article? It never does fulfill the promise in the headline: "How to Tip." Oh, sure, it says "20%," but as I've indicated, that's bullshit outside of restaurants. What do you give the concierge who called you a cab? The bellhop at a fancy hotel? What do you slip to the person who did your laundry? Why do you tip your massage therapist and not your head therapist? Should you really give the McDonald's cashier a couple of bills? How often do you tuck a $1 bill into a strippers' g-string? And shouldn't inflation have upped that to $2 bills by now? Make it all go away, and while you're at it, include tax in the advertised price. No, I'm not advocating for paying less for services; I'm saying it shouldn't require an advanced degree in Gratuity Studies to figure all of this out. |
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