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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May 9, 2024 at 10:00am

#1070769

Super Stew?

I've done entries about categorization problems before. Is it a sea or a lake? A dwarf planet or a planet? A hill or a mountain? Is a hot dog a sandwich or a taco, or is it just a hot dog? Well, here's one that I've wondered about for a long time, yanked from the website at Country Living.

Stew vs. Soup: Everything You Need to Know
They're both served in a pot—so what's the story?

Served in a pot? Maybe in your country. In my country, they're cooked in a pot and served in bowls.

The article is from January of 2020, but surely nothing's changed since then.

When it's cold outside or you're not feeling well—no matter the time of year—there's nothing more comforting than a hearty soup recipe or a slow cooker stew recipe.

Sure there is: the actual soup or stew, preferably made by someone else because it's cold outside and I'm not feeling well.

On that we can agree—but when you break it down, do you really know the difference between stew and soup?

No, but I guess you're about to tell me. Incidentally, I don't really care; I only care that it tastes good.

The main difference is the amount of liquid that's used for each. In a soup, the ingredients will generally be completely submerged in liquid, while in stews, they're just barely covered.

Okay, but what about when you have ingredients that float? Carrots, e.g., or pasta. You look at it, it's only partly submerged. Like the iceberg, not like the Titanic.

The main component of a soup is the liquid. Soups can be brothy (think: a timeless chicken noodle soup), puréed (classic tomato purée soup), or creamy (potato cheddar soup, anyone?).

I'm not reproducing the links here, but I'm starting to think this "article" is just meant to promote their recipes.

Oh, and to further complicate matters, there are other names for soups. Bisque, a subcategory of creamy soup. Chowder, same. Pho, which I maintain stretches the definition of soup, because it cannot be eaten with a spoon alone unless you have superpowers.

Soups are generally easy and fast to make—some can be made in as little as 20 minutes!

20 minutes? To source all the ingredients, prep them, fumble around with cookware, etc.? Hell, if your batch of soup is voluminous enough, it'll take 20 minutes just to bring it to a boil before you turn it down to a simmer.

On the other hand, I've made soup in 3 minutes: 1) Open a can of Campbell's 2) Mix it with a can full of water 3) Nuke for 2 minutes.

The general rule is that no ingredient should be larger than a soup spoon.

See, that's a tough rule for pedants like me. First, define "soup spoon." After that, consider ramen. Each ramen noodle is, well, a noodle. Even if it were possible to fish out the noodles one by one, bits of them would hang over the sides of the spoon, making it larger than a soup spoon. Sure, if you got it all coiled up, an individual noodle could maybe fit in one spoon, but who does that?

Also see: French onion soup.

Stew tends to be more complex and takes longer to cook than soup.

Betting we could find counterexamples if we tried.

Unlike soups, which rely mostly on water or stock as the main liquid, stews can contain beer, cider, or wine for additional flavor.

I put brandy in my French onion soup.

But. The end of the article addresses a long-standing question, one of great import and whose definitive answer could change the world.

Is chili considered a soup or a stew?

Still, I don't care; I consider it delicious.

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