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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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January 23, 2019 at 12:02am
January 23, 2019 at 12:02am
#950256
How different was your life one year ago? How different do you imagine your life will be one year from today?

As I noted in a previous entry, my life doesn't change much, and that's how I like it.

I was starting to train for Nerd Camp a year ago, which involved trying to increase my aerobic fitness in preparation for my trip in June. Which I managed to do, but it still wasn't enough to prepare me for a week at 10,000 feet. Now, I'm just walking a mile and a half every day, more for general exercise than for any specific goal.

And I hope nothing changes over the course of the next year. Well, I should put that differently. Of course something will change; that's a basic bug in the software of life. Just - nothing major, such as health or finances. Hopefully I'll be a little bit better at writing, a little bit more knowledgeable, and, if I'm really lucky, a little bit wiser.

But I doubt it. If there's one constant in my recent life, it's been an utter inability to improve in any meaningful way, so I've just gotten better at making peace with that.

Drinking helps. One thing I can be sure of: I will have had more beer pass through me at this time next year.


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