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 19, 2022 at 12:01am

#1041916

Soup Chef

From the "whatever happened to" department...

Soup for You: Seinfeld’s Infamous Soup Nazi Serves Up A Big Bowl of His Favorite Fall Soups

Right about the time the "Soup Nazi" episode came out (it was one of the few I actually watched at the time), we had a pizza chef here in town that reminded everyone of that fictional soup-slinger. He was never rude, really, but his pizza was so good that he was always busy, and he had to keep the line going. He did so by conducting the line and his employees in a very loud and boisterous, but serious manner. Guy was obviously from Brooklyn and of Italian extraction, so most everyone was cool with it even though that's not how we do things around here.

But I don't think he much liked being labeled the "Pizza Nazi." Can't say I blame him. It would be many years before we had problems with actual Nazis in Charlottesville, but associating his no-nonsense behavior with actual racist, genocidal fascists was probably a step too far. He ended up selling that restaurant, which immediately went from "excellent" to "meh." Then he opened another one. Then he sold that one, too. It's still around, even opened up a second location quite close to my house.

This is, of course, extremely dangerous for me. And not because it's run by Nazis (as far as I know, it isn't), but because their pizza is almost as good as when he was running the place.

Anyway, according to Cracked here, the actor who played the Soup Nazi is still around, too... and actually cooks soup.

But despite the fact that he’s been mock-denying people a bowl of soup for more than 25 years, Thomas himself is actually a pretty generous guy — especially when it comes to the subject of soup. To prove it, he was more than happy to provide us with his favorite fall soups.

Yeah, yeah, I know, we're basically in full-on winter now, meteorologically if not astronomically (the solstice is Wednesday). That's how long this link has been hanging around in my queue.

He even went a step further and shared a few recipes from his memoir/cookbook, Confessions of a Soup Nazi: An Adventure in Acting and Cooking.

Might as well lean into the role, right? I've heard of method acting, but it's not like he's going to play the Soup Nazi again.

The rest of the article is in interview format, a refreshing change from the usual Cracked countdown.

First thing first: Do you know how to make your own soup?

Oh yeah. I grew up cooking. My dad was a cook. He took off when I was a little kid, but he inspired me to be a good cook. My mom had to be a single working businesswoman and never really learned to cook; so I just grew up cooking and had a knack for it. And since I’d played the Soup Nazi, I had friends telling me I should write a cookbook.

I think there are two primary ways to get a cookbook published: 1) be famous 2) have good recipes. Failing those things, sometimes you can get away with it if you have a hook. Like, I have copies of cookbooks that replicate recipes featured in video games.

The problem, for me at least, is that it's damn near impossible to find a recipe these days that doesn't start with a Ph.D. dissertation on the food's background, the cook's life story, and something about their dog. The advantage of cookbooks is that it's easier to ignore these things if you're so inclined, and get straight to the recipe.

What’s your favorite kind of soup?

I’d say white clam chowder. From the time I was a kid growing up on the East Coast, it was always my favorite soup. When I was a teenager, I was washing dishes at a place here in Los Angeles called The Chili Place, and all the guy made was chili and clam chowder.

Coincidentally, those are some of my favorites as well. However, we get into a classification problem here: while clam chowder might be soup, chili technically is a stew.

Now, you might ask, what's the difference between soup and stew? Well, that's the classification problem. There's probably some overlap. It's a bit like the question, "Is a hot dog a sandwich?" (It's not; it's a taco.)

The reason it doesn't matter is that regardless of what pigeonhole you stuff it in, the important thing is if it's good. So don't stuff it into a pigeonhole; stuff it into your piehole and find out.

Yes, the article provides the actual clam chowder recipe, and I gotta admit, it looks pretty good.

Did you have a favorite soup that your mom or grandmother or someone in your family made?

My favorite family soup growing up was the chicken noodle soup my grandmother used to make around Jewish holidays. She made her own kreplach.

I want to emphasize here that I picked this article at random, as usual, and it's complete coincidence that I'm writing this on the first night of Hanukkah.

What about French onion?

I like French onion! That’s a great soup. I don’t have a recipe myself, but whenever I see it on a menu, I get it.

Ha! I have something the actual Soup Nazi doesn't: a recipe for delicious French onion soup. No, I'm not posting it.

Then they post the recipe for Mulligatawny soup. Unlike the other one, this doesn't appeal to me. (Pun intended, because it involves an apple, and an apple has appeal. ...I'll be here all week.) But someone else might like it.

The article ends with another classification problem:

Lastly, please settle this online debate: Is cereal soup?

Is cereal soup? I’ve never heard that before. I guess, in a way, it is — it’s like cold milk soup. I’ll say “yes” cereal is soup.

That's a stretch. But next time you hear someone talk about eating cereal, please, by all means, go "You know that's soup, right?"

I've skipped some things, but the link's there for you. Unlike my recipe for French onion soup. Okay, okay, I have mentioned it in here before: "Souperman"

. I still didn't provide the recipe there, but there are a few hints at least. So unless you can find one online...

...no soup for you!

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