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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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

March 21, 2023 at 8:53am

#1046787

Faux Past

Nothing particularly deep today, fortunately...

The Fakelore of Food Origins
Where did potato chips come from? How about clams casino? Are the origin stories for these foods true, or do they fall into the category of “fakelore”?

Lots of origin stories are fauxlore. I've covered, in entries here in the past, misconceptions about the origin of our favorite F word, the "rule of thumb" thing, and, my personal hill to die on, the Blue Moon mistake.

But this one's specifically about one of my favorite things: food.

Can anyone own a recipe?

Ask Coca-Cola.

“Throughout history, claims for how new dishes were introduced range from the reasonably plausible to the absolutely impossible. Generally, most new dishes are not invented; they evolve.”

Distinction without a difference. Pizza, for example. The idea of putting stuff on bread dough and baking it couldn't have been too revolutionary. Changing up toppings was just a matter of using whatever was on hand. Adding pepperoni, now: that was the real revolution, the moment actual pizza was invented.

Several foods have fallen victim to fakelore. Take one of our most beloved snacks—the potato chip. As folklorists William S. Fox and Mae G. Banner explain, many believe that the chip originated in Saratoga Springs, New York, in the mid-nineteenth century. After several complaints that his fried potatoes were sliced too thickly, a frustrated cook “sliced the potatoes paper thin, fried them in deep fat, salted them heavily, and served them up.”

Yeah, that one always struck me as suspect.

All food fakelore isn’t as bitter, though. The origin of clams casino, a clam served on the half-shell and stuffed with herbs, aromatics, and bacon, is also one with questionable beginnings. As with the potato chip story, this dish was purported to be invented in 1917 to satisfy a wealthy and demanding customer, this time Mrs. Paran Stevens, the wife of a hotelier. She was described in her New York Times obituary as “never hesitating to give full expression of her opinions about everybody and everything,” so it probably wasn’t a huge shock when she showed up demanding something special.

More like Karen Stevens, am I right?

And here, I feel cheated, because those are the only two examples given. I think we need more, but I've been immersed in a video game, so can't be arsed to do anything else. I know there was some discussion about the origins of hamburgers a while back; I don't remember if I put it in the blog or not.

You know what else we need? Drink origins. As with food, drinks evolve, like how the martini wisely lost most of its original vermouth, and then, unfortunately, started to be made with vodka. Nothing wrong with liking vodka, but that's a vodka martini, as opposed to a martini, which is made with gin. And don't get me started on those sweet "-tini" abominations that were popular in the noughties.

Hm. Someone should research that and write articles or blog entries about the history of drinks. Someone who's not obsessed with a video game.

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