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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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| https://aeon.co/ideas/monopoly-was-invented-to-demonstrate-the-evils-of-capitali... Monopoly was invented to demonstrate the evils of capitalism When I was young (quand j'étais jeune - yep, still learning French), I learned the "official" version of the invention of Monopoly. It's a carefully constructed capitalist story about a dude from Atlantic City who, during the Great Depression (an oxymoron if there ever was one), invented a board game populated by the streets and businesses he knew, and later sold the rights to Parker Brothers - as noted in the above linked article. Like most of the myths of our civilization (and by myths I mean "stories we tell ourselves" and not the more recent "falsehoods"), it doesn't tell the whole story and embellishes the parts it does get right. I got really good at Monopoly, learning the best strategies for acquiring choice blocks of real estate and optimizing my returns on them. The orange properties represent the best return on investment, by the way; people go to "Jail" remarkably often, and there's a really good chance of rolling a 6 or an 8 upon release (especially since, if you roll double 3s or double 4s, you get out of Jail), plopping you squarely onto my hotel-festooned lots and enhancing my personal coffers at your expense. Yes, Boardwalk charges the most rent, but you don't land there very often on your own, and there's only one card sending you there; plus, buying it and building on it is expensive. I can't say that Monopoly is what made me decent at personal finance, but it didn't hurt. Only thing it hurt was a few friendships. Okay, all the friendships. Point is, almost everything you thought you knew about Monopoly is wrong. The game’s little-known inventor, Elizabeth Magie... Actually invented by a chick. Born in 1866, Magie was an outspoken rebel against the norms and politics of her times. She was unmarried into her 40s, independent and proud of it, and made her point with a publicity stunt. Taking out a newspaper advertisement, she offered herself as a ‘young woman American slave’ for sale to the highest bidder. Her aim, she told shocked readers, was to highlight the subordinate position of women in society. ‘We are not machines,’ she said. ‘Girls have minds, desires, hopes and ambition.’ This year marks the 100th anniversary of the ratification of the 19th Amendment (August 18, 1920, according to the Googs), which was a much better idea than the accursed 18th. So, as of this writing, women have had the vote for less than a century. Let that sink in. (The article doesn't specify when Magie pulled her stunt, but likely it was before 1920. Of course, voting is an important civil right, but to put it in context, it was only last month that the final state needed for ratification of the Equal Rights Amendment passed the thing. I'd be proud to say that it was my state, except that I'd be even prouder if it'd been the first. It's been an uphill battle, and it's still ongoing. ...Magie invented and in 1904 patented what she called the Landlord’s Game. Laid out on the board as a circuit (which was a novelty at the time), it was populated with streets and landmarks for sale. The key innovation of her game, however, lay in the two sets of rules that she wrote for playing it. No, they're not talking about the common house rule to stick taxes under Free Parking, to be picked up by anyone fortunate enough to land there. Another misconception about Monopoly: that's never been in the official rules. It can be game-breaking. Under the ‘Prosperity’ set of rules, every player gained each time someone acquired a new property... and the game was won (by all!) when the player who had started out with the least money had doubled it. Under the ‘Monopolist’ set of rules, in contrast, players got ahead by acquiring properties and collecting rent from all those who were unfortunate enough to land there – and whoever managed to bankrupt the rest emerged as the sole winner (sound a little familiar?). You know what else sounds familiar? This presages the modern tug-of-war between "capitalism" and "socialism," as if those two concepts were pure and not on a continuum. The game was soon a hit among Left-wing intellectuals, on college campuses including the Wharton School, Harvard and Columbia, and also among Quaker communities, some of which modified the rules and redrew the board with street names from Atlantic City. I have many questions, chief of which is: What's the connection between the Quakers and Atlantic City? And before you say anything, yes, I know that gambling there is a relatively modern addition. One time, I was in Atlantic City and they had Monopoly-themed slot machines at the casino. I laughed. I'm not here to start a debate between capitalists and socialists. I just find the whole history of Monopoly fascinating - both its reality and the mythology around it. Still not playing it anymore. |
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