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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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Did you think Urban Dictionary  was something new?Like most kids, I amused myself in my youth by looking up certain words as soon as I encountered a new dictionary. Kid Me derived great enjoyment from finding Forbidden Words in school library dictionaries. A “dictionary of the vulgar tongue” may sound like some kind of prank gift, something you pick up as a means of upping the ante on your name-calling or adding some spice to your conversations for all occasions. But you won’t find this dictionary at Spencer’s Gifts. It’s tucked away at the British Library in London, shelved and looking prim and proper in its original 1785 binding. How much better, then, to find the 18th century proto-Urban Dictionary in such a staid institution as the British Library? It's like finding fart jokes at the Library of Congress. [The dictionary] looks a lot like another noted 18th-century dictionary—Samuel Johnson’s Dictionary of the English Language. The only thing differentiating these two is their focus: the English language versus the “vulgar tongue.” As the article points out, "vulgar" meant a different thing back then. Basically it was peasant-speak. Today, “it’s one of the more important slang books ever published,” says lexicographer Jesse Sheidlower, an adjunct assistant professor at Columbia University. “Johnson made a specific effort to keep out this kind of language.” It is not possible for me to think of Samuel Johnson's dictionary without recalling one of the funniest comedy shows of all time, of which the following is but a fragment: Anyway... The entries in Grose’s dictionary run the gamut from words and phrases common to laborers, military personnel, and bar frequenters to cant—the jargony language of criminals. Among the pages are such listings such as “cheeser,” another word for a fart; an “Admiral of the narrow seas,” someone who drunkenly vomits into the lap of the person sitting opposite him; and “to dance upon nothing,” meaning “to be hanged.” One wonders how many words the dictionary contained for private parts. I once participated in an impromptu roundtable discussion where we listed every synonym for "penis" we could come up with, and while I don't remember the exact final tallywhacker, it was well into the hundreds. But this isn’t just a collection of fun phraseology, explains Sheidlower. It’s a window into a crossroads of language at the heart of 18th-century Britain. Terms used in various underground criminal enterprises—like “bean feakers,” or bill counterfeiters—intermingle with simple words used among commonfolk like “lobkin,” which is just another word for a house or home. (Some of the words and phrases included live on into the modern vernacular with their centuries-old meaning, such as “to screw” and “to kick the bucket.”) Whereas I'm willing to bet the vast majority of the words and phrases have been lost from common speech, having lost their relevance, or replaced by more modern equivalents. And yet, a quick glance at the contents shows that others have, indeed, persisted; some have even entered formal language. I will point out, for example, that one of the definitions of "punk" therein is "a little whore." I will also note that, since it still amuses me to do so, I looked up some of the naughtier words and was delighted to find that some of them were included—albeit with apparent self-censorship. Grose and his dictionary gave the world a peek inside various groups in danger of having their cultures steamrolled and made the language of commoners as worthy of study as that of aristocrats. And the article ends with a link to the digitized version of the dictionary. If you're too lazy to go to the article to find it, here it is. .Incidentally, there's a word in there: Frenchified. (I found it when I was looking for other words starting with F.) It means "Infected with the venereal disease." I can only assume that there exists, or at least existed, a French version of the dictionary, in which the word is "Anglified." |
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