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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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April 27, 2022 at 12:02am
April 27, 2022 at 12:02am
#1031448
Got a taste for some history?



One of the funniest things I ever saw on the road was a sign for Donner Camp Picnic Ground  Open in new Window., an actual place near Truckee, in what became known as Donner Pass and now is basically just I-80.

Someone in charge knew exactly what they were doing, so it's even funnier than if it were a naive reference.

If, somehow, you've never heard of the travelers we're talking about here, the first part of the article above helpfully explains the background.

I also don't really have much to add to the article. I just often wondered whether what they had to do was eventually worth it, and now, after reading this, at least I know more about the rest of the story, after the sordid bits.

Their names still grace streets, schools and even a town, and the villain of the expedition was the first man to introduce lager to California.

So the answer, in that case, was yes, absolutely it was worth it. Whoever later introduced IPAs to California, though, should get a one-way trip to the Donner Picnic Ground.

However, Keseberg’s legacy as a brewer endures. In 1853, he founded Sacramento’s Phoenix Brewery, the first to introduce lagers to the region. The Sacramento Bee referred to him as “the first brewer in Sacramento.”

Villain? Hero? Why not both?

Anyway, okay, the other stories are probably just as interesting, but I was naturally drawn to the beer one. Like I said, not much to add, but at least there was beer.


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