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.
After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.
The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.
Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.
That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.
A reminder I could say to myself before I’m tempted to respond to anger with anger, to fear with fear, to negativity with negativity is...
"It just doesn't matter."
I need to make that into a motivational poster. I wonder what the picture would be? A mushroom cloud? Nah, too violent. Maybe that iconic image of the black hole that astronomers managed to obtain, to remind me of the ultimate fate of everything. No, everything is probably not going to get sucked into some black hole or other, but there's no image I can think of to represent the eventual and inevitable heat death of the universe. Hell, over a long enough time scale, even black holes dissipate.
But I'm not usually tempted to respond in such ways. I've developed coping mechanisms over time. Mostly these coping mechanisms consist of avoidance. It works for me.
Someone gets angry, I leave. Someone gets fearful, I leave. And when someone gets negative... well, okay, you got me there; I'm already a black hole of negativity. ("Are you positive?" "No.")
But on the rare occasion when I can't leave, I remember that soon enough, one or the other of us will be dead, and what little time we have left isn't worth spending on anger and fear. That's why negativity is such a wonderful thing: it makes me realize that nothing matters unless I want it to.
Of course, I dislike it in other people, but hey, who doesn't have internal contradictions?
One-Sentence Movie Review: Eternals
Eternals distinguishes itself well from other comics-derived team movies; it's gorgeous with plentiful effects, solid camera work, and decent acting, with each character well-defined, and it earns its extended runtime (cue "eternal" jokes) by giving us time to get to know each player in the large cast, but somehow it manages to fail to live up to its hype — though that's probably more a fault of the hype than of the film itself.
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