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Complex Numbers
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.
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Whilst out and about today, I happened to get hungry when I was near a sandwich shop I hadn't visited before, so I went in to check it out.
It's about 3 pm, so the place was, to quote Leonard Cohen, dead as Heaven on a Saturday night.
Took me a while to figure out what I wanted, but the tiny, cute, young woman behind the counter didn't seem to mind. It wasn't like there were customers behind me. Or anywhere in the deli, for that matter. I should have taken this as a sign, but I just figured it's mid-afternoon when normal people have already eaten lunch and aren't yet ready for dinner. (Me? I was ordering breakfast.)
So I settle on a roast beef croissant sammich, Doritos and a soda. Or "pop" if you're from the North or "Coke" if you're from the South. Anyway, she puts in my order and says, "Can I get your phone number?"
I blink.
"No," was my automatic response.
She laughs. I got the idea a lot of people refuse. I mean, it's a fucking sandwich shop. What are they going to do, call you and tell you if they discover botulism or salmonella? Hey, guess what, by the time you call me, I'll know.
The sammich, by the way, was soggy; the croissant was rubbery like it'd been microwaved; the Doritos were stale; and the drink was watered-down.
But of course, after I placed my order, I thought of several better things I should have said to the "Can I get your phone number" question:
1. "You're too young for me."
2. "You're too old for me."
3. "Can I get yours?"
4. "Can I get your clothes off?"
That's the advantage of writing, you know. You can take your time to come up with a sufficiently witty, snarky and/or inappropriate response to idiotic questions. In person, what do I do? Freeze up and say, "No."
Anyway, feel free to comment and tell me what I should have said. |
March 20, 2012 at 11:14pm March 20, 2012 at 11:14pm
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It seems that tomorrow, March 21, is an important anniversary: the Diamond Jubilee of Rock 'n' Roll.
In 1952, the US was still recovering from WWII - it could be argued that we still are; it was arguably the last war we were in that made sense. Across the pond. Queen Elizabeth II began her reign in that year, the Today Show premiered on NBC (and also continues to this day), and the US ratified a peace treaty with Japan, who would morph like a mutated sea monster from one of our worst enemies to one of our closest allies and trading partners.
And on March 21, 1952, the first rock concert stormed Cleveland, Ohio.
Now, those who know Cleveland might be surprised to know that it gave birth to anything besides misery and suffering, but I hear baseball started there, too. Or does that reinforce the misery and suffering point?
Anyway, rock 'n' roll changed the world.
It doesn't get a lot of love, these days. Like all art forms, it's changed, metamorphosed, spun off numerous sub-genres, and is now unfortunately associated with aging boomers cranking up "classic rock" stations in their BMWs. It's hard to imagine that music as revolutionary, but at one time, it was, in the truest sense of the word.
Here, read this article:
http://www.bbc.co.uk/news/magazine-17440514
Sixty years ago, what music historians regard as the world's first rock concert was staged in Cleveland by two men whose passion for music bridged the racial divide in a segregated US.
Whites and blacks... in the same room? Getting along (mostly)? Horrors! Granted this was Cleveland, the North, not the more segregated South, but that just meant that racism in the North was less institutionalized, not that it didn't exist. While the US has a long ways to go with regard to race relations, we've also come a long way since 1952, and I think that rock 'n' roll played no small part in that.
Music - good music - changes things. That's why it's banned so often; that's why parents can never understand their offsprings' taste in tunes, or vice versa. The Establishment was afraid of rock 'n' roll - and the fear was justified.
"Turns out the place was sold out and they had closed the doors on them. And these people had tickets and were not happy.
"The doors had a glass centre panel and they ended up breaking them so they could get into the building."
Unfortunately, few revolutions are without riots. But as they say, you can't make an omelet without breaking some eggs.
Were the people there aware that they were revolting? I mean, in the sense of change, not like their unwashed successors 15-20 years later at the height of the hippie movement. I doubt it. They just heard music they liked and wanted to have a good time.
I've been studying and practicing guitar lately, and my quest for music inevitably led me to Pete Seeger. I'd heard of Pete before, of course, and the music that he wrote and/or popularized, but hadn't really delved into his life. Seeger predates rock 'n' roll - he's still alive and kicking, though. While his style is considered "folk," his music contributed to all the revolutions of the latter half of the 20th century. From his Wikipedia page:
As a song writer, he is best known as the author or co-author of "Where Have All the Flowers Gone?", "If I Had a Hammer (The Hammer Song)", (composed with Lee Hays of The Weavers), and "Turn, Turn, Turn!", which have been recorded by many artists both in and outside the folk revival movement and are still sung throughout the world. "Flowers" was a hit recording for The Kingston Trio (1962), Marlene Dietrich, who recorded it in English, German and French (1962), and Johnny Rivers (1965). "If I Had a Hammer" was a hit for Peter, Paul & Mary (1962) and Trini Lopez (1963), while The Byrds popularized "Turn, Turn, Turn!" in the mid-1960s, as did Judy Collins in 1964 and The Seekers. Seeger was one of the folksingers most responsible for popularizing the spiritual "We Shall Overcome" (also recorded by Joan Baez and many other singer-activists) that became the acknowledged anthem of the 1960s American Civil Rights Movement, soon after folk singer and activist Guy Carawan introduced it at the founding meeting of the Student Nonviolent Coordinating Committee (SNCC) in 1960. In the PBS "American Masters" episode Pete Seeger: The Power of Song, Seeger states it was he who changed the lyric from the traditional "We will overcome" to the more inspirational "We shall overcome".
And in the 1950s, Seeger was hauled before the American Inquisition (the McCarthy hearings) and summarily blacklisted because of his pollitical leanings.
"Un-American Activities?" I'll tell you what's un-American. It's un-American to use the power of the government to limit peoples' freedom to sing, and to listen to, whatever they want. Or read, or write, and so forth.
Getting back to rock 'n' roll, though:
Less well known is the reason why the Moondog Coronation Ball ended in disaster: a minor printing error.
The mistake was caused by someone forgetting to add the date to tickets issued for a follow-up ball, which Mintz had set about organising immediately after the initial one sold out.
As a result, an estimated 20,000 people showed up on the same night for the first concert - at a venue which could hold half that number.
I think as we look back on history, the effect of accident can't be dismissed. How would things have been different if not for one little typo? Who can say, really? Without the notoriety of one night's near-riot, would rock 'n' roll have developed the counterculture reputation it sported? Could it have been a mere aberration, a blip, like 70s glam-pop or Elton John's Crocodile Rock?
It's possible. Music has power, yes, but writers take note: so do typos. |
March 13, 2012 at 10:08pm March 13, 2012 at 10:08pm
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I came to a sudden realization of Ultimate Truth the other day.
Here's the background: I heard that Guinness World Records was going to vastly reduce the scope of its print edition, relying more on its online edition. While I can't find any confirmation of that, it doesn't really matter for the purposes of my point here. (Encyclopaedia Britannica, by the way, is totally doing that - eliminating its tree-murdering edition entirely so it can focus on its website and on fending off the attacks of its main competitor, Wikipedia).
I vaguely remembered being presented with a copy of what was then known as the Guinness Book of World Records as a kid, so I went on Wikipedia to get some background on the famous reference book (Britannica is a paysite, you see).
There, I discovered that (according to Wikipedia, anyway), GBWR, now known simply as Guinness World Records, got its start in the 1950s when some dude from the Guinness brewery in Ireland needed to settle a drunken pub argument about which bird was faster. No, it wasn't about African vs. European swallows. Realizing that people needed something to settle drunken bar arguments, he conceived of a book that would list superlatives in hundreds of categories: tallest, heaviest, shortest, fastest, most, whatever.
I guess if you couldn't find the answer to your drunken pub argument in GBWR, you could always hit your opponent over the head with a copy, thus settling the argument once and for all. This option is not available with the online edition, unless you want to pay $400 for a new iPad.
Anyway, over the years, it became disassociated from the actual Guinness brewery, though it retained the name. And while early versions had categories like "most beer consumed in an hour," such categories were expurgated from later versions, because the publisher might get sued when someone died of alcohol poisoning while trying to break that record.
So, to sum up, a book that had its origins in a drunken pub argument (including someone who worked at a brewery) can, for legal reasons, no longer contain a "drinking" category.
Resulting epiphany: Life is cocked-up on a very fundamental level. |
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I'm more than happy with Carrion Luggage, however.
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