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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.
October 20, 2024 at 9:02am October 20, 2024 at 9:02am
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Going back over 5 years, today's peek into the past takes us to an entry from July of 2019: "Unlucky"
I've written about luck several times in here, but this entry isn't directly about that; it's a play on the word "potluck." The entry is a response to a prompt, most likely from 30DBC: "What is your go-to dish to bring to a potluck? Does your family have any traditional recipes? (In Hawaii, these appetizers are called 'pupus'"
What I apparently didn't catch at the time was the reference to appetizers; in mainland North America, a potluck is when you bring a dish of any sort to a communal gathering. The dish could be an appetizer, but it could also be a main course (my entry goes on about casseroles for a good bit) or a dessert.
Casseroles, however, mystify me. I'm not sure why. They can't be that hard to do, or millions of Southern Baptists wouldn't do them, in all their various incarnations. You'd think that would teach them something about variety and the wonders of diversity, but... no. They just plop down their armies of Corningware, oblivious to the obvious metaphor.
Since then, I've tried my hand at various casseroles, with a good bit of success. They're less work than other dishes, but still harder than, say, popping a frozen thing into a microwave.
But what stumps me is that I don't know what the essential thing is that makes a casserole a casserole and not something else. Baking? You also bake lasagna; is that a casserole? Meat? Nonsense; there are plenty of vegetarian casseroles.
I've also had several entries about classification problems, like my perennial assertion that a hot dog is not a sandwich, but a taco.
So, yeah, no traditional family recipes here. Just stuff I've picked up along the road.
As I noted in that entry, if there were traditional recipes in my family, they'd be borderline inedible, and I'd have no problem letting them fade away.
Fortunately, one of the comments helped me to clarify the "what exactly makes a casserole a casserole" conundrum. I occasionally get comments here that thank me for helping the commenter learn something new, but I assure you, that works both ways.
Just lucky, I guess. |
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