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Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
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.




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March 2, 2022 at 12:04am
March 2, 2022 at 12:04am
#1027749
As I've noted before, I have the utterly unattainable goal of visiting every brewery in the US (and a few elsewhere for good measure).

It's unattainable because those things open and shut down on a weekly basis. By the time you've hit a hundred on your list, some of the ones on the list will have gone out of business, and more will open up behind you. But that doesn't stop me from trying; everyone needs a hobby.

Some breweries are easier to get to than others. There was, for example, one on a military base in New York; I haven't checked to see if it's still there, but it's not always easy for civilians to get access to those bases.

And there's one on Catalina, that island you see on the map just off the coast of L.A. As far as I can tell, there are only three ways to get there:

1) Helicopter;
2) Boat;
3) Swim 35 miles.

(3) is right out, and (1) is probably expensive. (2) takes an inordinate amount of time, but doesn't cost a couple of limbs. By "time," I mean that from where I am it takes 1/2 - 1 hour (L.A. traffic, you know) to get to the dock, which you're supposed to get to an hour early, and then the crossing time is a bit over an hour also. So that's potentially somewhat more than three hours there and the same going back.

Just for one brewery that only has two of its own beers.

But hey, at least I can cross that one off my list. If another opens up on the island, though, I'll utter a few choice words.

(Yes, the title of this entry is an intentional pun.)


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