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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Writer_Mike

about 9 hours ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

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QPdoll

a day ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

a day ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:46am
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:16am
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

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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