Complex Numbers (Book)

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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.

http://www.ddewey.net/mandelbrot/

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December 31, 2022 at 12:02am

#1042384

Syne of the Times

Breaking from my usual random post this New Year's Eve. You'll see why.

Do Americans Sing ‘Auld Lang Syne’ Because of a Frat Party?
Or maybe it was the cigars that gave us this New Year’s Eve staple.

Article is from Atlas Obscura, and I haven't bothered to fact-check it. Just thought it was interesting, and timely.

Guy Lombardo wasn’t thinking about tradition as the clock struck midnight in New York on New Year’s Eve 1929. He was probably thinking, as so many people were after the stock market crash that fall, about money.

Even musicians have to eat.

In front of a crowd at the Roosevelt Hotel in Midtown Manhattan, Lombardo raised his violin bow and launched his 10-piece band, the Royal Canadians, into a sweet and soothing rendition of “Auld Lang Syne.”

Speaking of money, that hotel remained in operation until 2020, when... well, you can guess.

The revelers on the sunken dance floor likely did not know the meaning of its Scots-language title. When the song went out over the radio waves in the first minutes of 1930, it was not yet a New Year’s Eve staple throughout the United States—and it may never have become one if not for a promised cigar company sponsorship and a raucous University of Virginia frat party.

That, of course, is why I'm featuring this article today. Though... shame on the author for not researching UVA; we're adamant about calling our campus "the grounds," our founder "Mr. Jefferson," freshmen "first-year students," and fraternities "fraternities."

The song—the modern lyrics of which are most commonly credited to 18th-century Scottish poet Robert Burns—was commonly sung in the old country when friends parted. (The title translates to “Old Long Since,” meaning something like “Since Long Ago.”)

As I understand it, the usual lyrics sung these days are a mix of Scots and English, which I suppose is only appropriate.

So Lombardo reached for the tune just as the band signed off from CBS, where it had been booked until midnight. As the ball dropped in Times Square, the band was actually heard on rival NBC, which picked up the Roosevelt feed.

One thing I know I will never do and have never done: Times Square on New Year's Eve.

And that might have been that—an old Scottish folk song, played by a Canadian band in a New York hotel late one night at the end of a tumultuous year. No one was thinking about the playlist for next New Year’s Eve. Lombardo and his bandmates had other things on their mind, mainly how to make a living as musicians in the first days of the Great Depression.

Bring their trombones down to Wall Street and play the wah-wah sound as stockbrokers' bodies hit the pavement? I'd pay for that.

But things were starting to look up for the band by around Easter 1930. They were playing regularly on the radio, which brought more people into the restaurant and earned the band numerous invitations to perform on college campuses. In April, they traveled to Charlottesville, home of the University of Virginia. “It’s funny how that college date remains in my memory,” Lombardo later wrote. It’s funny, too, how it contributed to an enduring American tradition.

Article doesn't say, but UVA always used to hold a massive party around Easter. Demonstrating that all of their creativity was used up by "grounds" and so forth, the party was called Easters. It became internationally famous, which is much better than the other thing Charlottesville became internationally famous for.

Sadly, they ended Easters in 1982... right after I got accepted into fall semester 1983. Fuck you, Universe.

Point being, this might very well have been an Easters gig.

After the formal dances—alcohol-free occasions—students often invited the men in the band back to fraternity parties. They brought along their instruments and “libations flowed freely,” Lombardo recalled.

Yep. I'm betting Easters.

One night the band decided to end the evening with “Auld Lang Syne,” as they had so often in Ontario. We “were amazed by the reception it got from the students. They demanded one encore after another.” Finally, Lombardo leaned down from the bandstand to ask, “What’s so great about ‘Auld Lang Syne’?”

At this point, I knew the answer to that question. The school song uses the same melody.

For the students, the answer was obvious: Lombardo was leading them in the school’s de facto fight song. “The Good Old Song” had the same tune as the Scottish standard, but instead of “Should auld acquaintance be forgot, and the days of auld lang syne,” the students heard “Let’s all join hands and give a yell for the dear old UVA.”

Fun fact: the song also contains the lyrics "We come from Old Vir-gin-i-a, where all is bright and gay," after which the school homophobes had to yell "NOT GAY." Dicks.

Hopefully. they don't do that anymore. I wouldn't know, because while I can hear a lot of the sportsball games from my deck, I can't make out the singing. Obviously, the lyrics were from an older time before the meaning of the word changed.

“We would always keep ‘Auld Lang Syne’ after that,” Lombardo wrote in his autobiography decades later. “The boys at Virginia had given us a reason to retain it.”

I'll also point out that UVA didn't start admitting chicks until, I don't know, somewhere in the late 60s, if memory serves. Now, of course, it's mostly dames.

By the time 1930 became 1931, the song was the band’s anthem—a joyous callback to those nights at the University of Virginia—and its signature signoff. At midnight, live from the Roosevelt Hotel, Lombardo, as he did most nights, led the Royal Canadians in “Auld Lang Syne.” He did the same for nearly half a century.

And that, folks, is the story of how a fraternity party in my hometown changed the world for the better. Unfortunately, the name of the fraternity in question appears to be lost to history.

“Should he and his Royal Canadians fail to play ‘Auld Lang Syne’ at midnight on New Year’s Eve at the Hotel Roosevelt Grill in New York, a deep uneasiness would run through a large segment of the American populace—a conviction that, despite the evidence on every calendar, the new year had not really arrived,” LIFE magazine wrote in 1965.

But, of course, it arrives whether you like it or not, because time is, as I've banged on about in here before, not an illusion. The convention of celebrating it when we do is arbitrary, but sticky; there's no doubt that the vast majority of folks on the east coast of the US—which includes NYC and UVA, as well as WDC World Headquarters—will recognize the flipping of the digit in just a bit less than 24 hours after I post this.

On that note, it should be self-evident that I will not do my usual midnight posting tomorrow night, for obvious reasons. Likely I'll post something later in the day, during hangover recovery.

Until then, I wish everyone a happy New Year, and may 2023 exceed your expectations.

And there's a hand my trusty friend
And give us a hand o' thine
We'll take a cup of kindness yet
For auld lang syne

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