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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.
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I have a system (not a perfect one) in place to avoid duplicating links here. I also try not to repeat entry titles, but with 2300 entries, I know I've got some duplicates and maybe even triplicates.
What's worse, though, is when I thought I did an entry about something and now I can't find it. Such is the case with famed proto-astronomer Tycho Brahe. I mentioned him briefly in an entry a while back in response to someone's comment, but that seems to be the extent of things.
Until now.
Unlike most Cracked articles, this one's not a numbered list.
To non-astronomers, there aren’t a huge amount of A-list astronomers. Most people could probably name Copernicus, Galileo and Hubble, but realistically, they learned those names from the dog in 1955 in Back to the Future, the lyrics to Bohemian Rhapsody and a big-ass telescope that occasionally features in “yo mamma’s so fat…” jokes.
Hubble's successor, the JWST, is not named after an astronomer but an administrator. Which I think is a step down, and that's not even getting into the controversy around Webb's policies.
Amazing telescope, though.
One guy whose name might ring only a faint bell is Tycho Brahe, a 16th-century Danish astronomer who made some remarkable innovations that helped to bring about the Scientific Revolution.
Speaking of telescopes, he did all his work without one because they hadn't been invented yet.
For exactly how influential this guy was, there's the article, and of course also the Wiki page  about him (which may or may not be less error-prone). I'm skipping it because the clickbait headline is about his personal life (and death), which was almost as interesting. I will note, however, that his contributions were significant enough for later astronomers (ones with telescopes) to name one of the largest and most recognizable lunar craters after him.
Speaking of cutting edges, Brahe had his nose sliced off at the age of 20. He got in a duel with his third cousin, who accidentally sliced a big chunk of his honker off...
And this is what he's probably most well-known for. No, I have no idea how he smelled.
The big-brained, metal-nosed polymath undone by humble urine.
No, he didn't discover Uranus. That would have to wait for telescopes.
The story goes that Brahe was at a banquet and needed a pee, but etiquette forbade him from leaving, so he held it in. Unfortunately, when he got home and could safely drain the lizard, nothing was forthcoming.
Sounds to me like he wasn't done in by piss, but by stringently following etiquette. The cautionary tale here is: fuck etiquette.
And then, in the words of Victor Thoren and John Christianson’s 1990 book The Lord of Uraniborg: A Biography of Tycho Brahe, “through five days and nights of sleepless agony, he pondered the agony of paying so great a price for, as he thought, having committed such a trivial offense.”
Uraniborg is unrelated to urine. It was, if you read the text I'm leaving out here, one of his pre-telescope observatories. Nor is it related to Uranus (other than maybe etymologically), or the Borg ("Borg," by my understanding, is or was a Danish word for "castle.")
He had several more days of pain, fever and delirium before dying. He was 54, and had spent 38 years documenting the stars.
Which is approximately 39 years longer than I can ever concentrate on one subject.
Just in case readers might be worried that this could happen to them, the article reassures us:
“The good news is that, while uncomfortable, occasionally holding back a pee shouldn’t harm us,” explains Ajay Deshpande, senior clinical lead at London Medical Laboratory.
Also, medical science has advanced somewhat in more than half a millennium. Hell, they can even reconstruct noses now. To your specifications. Which makes a plastic surgeon's office the only place where it's socially acceptable to pick your nose.
In other words, it isn’t out of the question that the father of astronomy sat on his keys, filled up with pee and died. All that time looking up, not enough looking down.
Perhaps this inspired Oscar Wilde's famous quotation: "We are all in the gutter, but some of us are looking at the stars." |
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