Today on the internet I saw the calculation for i^i, where i is the square root of -1. It can be solved pretty easily using Euler’s formula, where any number z in the complex plane can be expressed as
is the absolute value of the number,
is the base of the natural logarithm,
is of course
is the angle in radians of the number measured counterclockwise from the positive real axis, essentially giving the complex number in polar coordinates. So for example
, etc. We know that
is going to be some
number in the complex plane, so we can express that number as
is itself a complex number.
Over at Cracked they have an article called The 10 Best Sci-Fi Films Never Made. It’s a good read for anyone that enjoys sci-fi and has been regularly disappointed over the last decade or so as the likes of George Lucas and [shudder] Uwe Boll have taken the beloved worlds of our youth and imagination and have summarily killed them, dumped them in an unmarked grave, and then desecrated said unmarked grave.
About a quarter of the way through the story though, I realized I had read this story before! I quick search for text from the story ( -cracked ) and google gave me the original link over at pointlesswasteoftime, an older humor site on that’s been around for a while (I think it predates the first internet bubble) but never had a lot of traffic. The author of this article and editor for pointlesswasteoftime is a guy named David Wong, who has become an assistant editor for Cracked and has such merged his site with Cracked. On the main page for pointlesswasteoftime he explains he edited and updated the original story and re-posted it on Cracked. Either way it’s a good read. Wong has a humorous writing style that I really like. On Neal Stephenson’s Snow Crash he says the following:
The hero is an expert swordsman, in an America that has dissolved into hundreds of independent states so that a stroll down the street takes you through a half dozen different legal systems. The finale takes place aboard a gigantic floating complex where a million refugees have strapped makeshift boats to an abandoned aircraft carrier.
It’s so cinematic that I didn’t just desperately want a movie to be made from it, I was always shocked they didn’t make one.
So what happened? There are two eras for the Hacker Movie genre. Pre-Matrix, hacker movies were always horrible and always box office poison (see Hackers and Johnny Mnemonic) that only appealed to a tiny segment of geeks. After The Matrix in 1999, every hacker movie was unfairly compared to The Matrix (including that film’s own sequels, but we’ll get to that in a moment).
I have to concur on the awesomeness that is Snow Crash. It’s full of great characters (Raven, Uncle Enzo, Mr. Ng, just to name a few), great action sequences (The initial pizza delivery, Y.T.’s escape from the Feds, Hiro’s first encounter with Raven, and many more), and great quotable lines (The one quoted in Wong’s article is great, as it the classic “I just hope they can listen to reason” ). Snow Crash is one of my all-time favorite novels, I highly recommend it to anyone who doesn’t hate sci-fi and hasn’t read it.
Here is Wong on why all movies based off of video games have completely sucked:
So what happened?
The Chicago Cubs, that’s what. The Cubs haven’t won a World Series since 1908. Why? Because Cub fans sell out Wrigley Field every game, regardless of how bad the team is. Management makes money regardless of whether or not the team is winning, so why bother?
Likewise, studios think video game fans will pile into the theater on opening weekend regardless of whether or not any effort was put into the film. Will that change? Come ask me after I’ve seen the Peter Jackson-produced Halo, should they ever decide to actually make it.
I’ve actually heard of this in other situations where performance is abysmal because there’s no motivation to do better, referred to as ‘The Chicago Cubs Effect’.
Finally, on The Star Wars prequels:
Everyone remembers the exact moment when they realized their Phantom Menace sandwich was filled with s***. For me, it was the scene on Tatooine where Qui-Gon was talking and Jar Jar was snatching fruit from the bowl with his tongue, eating like an insect. Annoyed, Qui-Gon reached out and snatched Jar Jar’s tongue out of the air, then held it in his fist while he talked. That was when I realized I was watching a cartoon.
Worse, it was a cartoon I already knew the ending to.
For me, that moment that I realized the prequels were crap is easily summed up in one word: midichlorians.
Anyway, you should read the rest of the article (old or new, there isn’t much of a difference) if you haven’t already.
David Wong also has another great article I really enjoy called The Ultimate War Simulation: A little bit of Starcraft, a little bit of Iraq.