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Complex Numbers
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.
September 29, 2021 at 12:03am September 29, 2021 at 12:03am
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I have to get up at an ungodly cow-milking hour (8) for a routine tooth torture session, so it's just as well that I don't have much commentary on this one.
I saw the original Star Wars in a theater in 1977 (and of course its direct sequels later). When I went to see some other movie in the 90s -- pretty sure it was a science fiction flick, but I can't remember what it was -- they showed the preview of the re-release Episode IV. I remember that the theater was completely packed full of people primed for space movies.
At the end of the trailer, when (spoiler alert) the Death Star blows up, there was a moment of awed silence. Then someone said, "I think I just saw God," and the whole theater erupted in whoops and cheers.
If only we'd known...
Rolling Stone interviewed Lucas later that summer, and he bemoaned how the movie was insufficient and only "about 25%" of what he wanted it to be, adding: "There is nothing that I would like to do more than go back and redo all the special effects." And that was way back in August 1977. So when the film's 20th anniversary rolled around, and Lucas wanted to update the movie, it shouldn't have come as a shock. Lucas convinced Fox to pony up $10 million in what was advertised as a restoration of George Lucas' artistic vision, which had been tragically ruined by 1977's conspicuous lack of desktop computers.
I took a cinema class as a humanities elective in college one semester for the easy A and an excuse to watch movies every Wednesday night. This would have been nearly 10 years after the original Star Wars. I don't remember much about the class, but I do remember the otherwise very stodgy professor proclaiming that there were two movie eras: pre-Star Wars, and post-Star Wars. Whatever you think of the movie itself, the way it changed the way movies were made clearly made an impression on stodgy film class professors.
It's 35 years later now, so maybe there's another era. Post-Matrix, maybe. I don't know; I'm not a professor or a critic; I just like movies (but not The Matrix).
No, Lucas trumpeted that he had "gone back and fixed the trilogy." To him, this was Star Wars, and the public had merely gotten accustomed to his rough drafts along the way. And it's not as though we didn't get a heads up about this; the '95 VHS release advertised that it was everybody's "last chance to own the original Star Wars."
I actually own those. Of course, I can't fucking watch them.
While many of the new effects blew away audiences at the time, other changes immediately rubbed some fans the wrong way. Most notoriously, the awkward shot of Greedo ineptly firing his blaster milliseconds before Han drew fan outrage even before the film hit theaters, thanks to primordial internet communities.
Goddammit, HAN SHOT FIRST. I have spoken.
After all, in hindsight, why would a trilogy that ends with a tribe of woodland teddy bears begin with a dude murdering someone in cold blood?
"In hindsight," I should have taken the Ewoks as a sign that Star Wars had jumped the shark.
The article argues that this is something different than Director's Cuts, which I can kinda see. But I'd counterargue that the idea of re-releasing new versions of old movies owes its proliferation to the success of the Director's Cut of Blade Runner, which was the first movie I was aware of being re-released as something substantially different from its original theatrical form. The DC was, by every measure, a far superior movie, though it was not without its flaws as well, leading to the eventual release of the "Final Cut" (which I don't believe for a second that it actually is).
Since it was so much better, I think audiences were primed to believe that updating would improve the movies.
I insist that it's entirely a coincidence that Harrison Ford was in both films.
Anyway, this was supposed to be short, dammit. I didn't quote much of the article; it's there for you to read if you're interested. |
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