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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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May 23, 2024 at 10:01am
May 23, 2024 at 10:01am
#1071563
Appropriately from Atlas Obscura, the tale of a great world explorer:

    The First Viking Woman to Sail to America Was a Legendary Traveler  
Back when the Icelanders called a part of Canada the “land of grapes.”


Now, it's possible that we shouldn't be using the word "Viking" like that, as I mentioned long ago here: "The Once and Future Viking. But I'm just quoting the article here.

Her full name, in modern Icelandic, is Guðríður víðförla Þorbjarnardóttir—Gudrid the Far-Traveled, daughter of Thorbjorn.

I'll just note here that some of those weird-to-us letters used to be in English, too.

She was born around 985 AD on the Snæfellsnes peninsula in western Iceland and died around 1050 AD at Glaumbær in northern Iceland.

Just looking at that, one might conclude that she didn't travel very far at all.

What little we know of her comes from the Saga of Erik the Red and the Saga of the Greenlanders. These are collectively known as the Vinland Sagas, as they describe the Viking exploration and attempted settlement of North America—part of which the explorers called “Vinland,” after the wild grapes that grew there.

A few entries ago, some article said that meant "Land of Wine," which may be inaccurate, but I like it better anyway.

Also, they freely mix fact with fiction. Their pages crawl with dragons, trolls, and other things supernatural.

How else are you going to scare the kiddies into behaving?

But the central tenet of the sagas has been proven by archaeology: In the 1960s, the remains of a Viking outpost were dug up at L’Anse aux Meadows, on the northern tip of Newfoundland.

I wouldn't say "proven." "Supported," maybe. It's not news anymore that Scandinavians made it to North America long before Italians did.

Among the rubble was found a spindle, used for spinning yarn, which was typical women’s work and thus possibly handled by Gudrid herself.

Right, because Gudrid sounds like the kind of chick who would do "typical women's work."

And in the Saga of the Greenlanders, Gudrid is called “a woman of striking appearance and wise as well, who knew how to behave among strangers.” That’s a trait that may have come in handy when dealing with the Native tribes of North America, whom the other Vikings dismissively called skrælings (“weaklings,” “barbarians”).

As I've noted before, who's the "barbarian" depends on who you're asking.

The article continues with a summary of the sagas involving Gudrid, and while I'm sure the originals (well, the original written-down versions, I mean) would be fascinating, the Cliff's Notes here seem to provide the pertinent details.

Another story from the sagas that has mystified readers for centuries because it mentions two “Gudrids” and has traditionally been dismissed as a ghost story could in fact be the earliest recorded conversation between a European and an American.

And no, they didn't discuss trade agreements or war. Or much of anything, considering they apparently didn't have time to learn each other's languages.

There's a lot more at the article, but as it notes, her relatives Erik and Leif got all the PR, but they didn't travel alone.


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