Not for the faint of art.
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.
Time for some physics!
How Black Holes Nearly Ruined Time
Quantum mechanics rescued our understanding of past and future from the black hole.
Is there anything a black hole cannot ruin?
As exotic structures of spacetime, black holes continue to fascinate astronomers, physicists, mathematicians, philosophers, and the general public, following on a century of research into their mysterious nature.
And don't forget nearly a century of science fiction authors getting the science wrong and thus contributing to the general public's misunderstanding of black holes.
The most striking feature of a black hole is its event horizon—a boundary from within which nothing can escape.
No, the most striking feature of a black hole is the singularity at its heart, a place where relativity breaks down and strange physics takes over. Without the singularity, there's no event horizon - and the event horizon isn't anything physical; it's a mathematical boundary, albeit an important one.
But, okay, I'll grant that the opinion of an actual physicist is probably more relevant than my own.
Entropy and the Arrow of Time
The article goes into some depth about how the second law of thermodynamics defines the arrow of time. I've been reading up on this sort of thing recently, and I have to say, the explanation leaves me unsatisfied. This is not to say that I think it's wrong - again, this was proposed by people way more knowledgeable and intelligent than I am - just that it's either a) a failure on my part to understand or b) a failure on their part to explain it well.
Basically, to me it sounds like a circular argument: Entropy can never decrease over time; therefore, time is the direction of non-negative entropy.
But, to be fair, I've never heard a better definition of time. After all, it may be something we can measure, but it's not exactly something we can touch, like a rock or a tree. So maybe there are just things we still don't understand. That's cool.
So, after that (necessary) detour into entropy, the article comes back around to black holes.
The resolution to this problem is to add quantum physics into the mix.
You know, back when the British were doing their colonial empire building thing in India, they had a problem with malaria. It turned out that an effective treatment, if not cure, for malaria was quinine, which is found in tonic water. The difficulty is that quinine tastes a lot like ass, so they added gin to it to make it more palatable - and threw in a lime for scurvy while they were at it. Thus was born one of the greatest inventions of history, the gin and tonic. The point here is that it's rare that you find phrases like "the resolution is to add gin" or "the resolution is to add quantum physics."
Anyway, I thought the essay explained things well and is largely accessible, so if you ever wanted to know shit about black holes, time, and entropy, well, it's a good introduction.
Might help to have a gin and tonic first.