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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 26, 2023 at 11:34am
May 26, 2023 at 11:34am
#1050116
Feeling much better today, thanks.



This article, from NPR, is dated April 30 of this year, the actual anniversary in question.

"Imagine being able to communicate at-will with 10 million people all over the world," NPR's Neal Conan said...

9,999,990 of whom are idiots, trolls, bots, or some combination thereof.

..."Imagine having direct access to catalogs of hundreds of libraries as well as the most up-to-date news, business and weather reports...

Mostly fake, and/or stuck behind paywalls.

...Imagine being able to get medical advice or gardening advice immediately from any number of experts...

And having it turn out to be (sometimes dangerously) wrong.

"This is not a dream," he continued. "It's internet."

And it was fun for a couple of years.

On April 30, 1993, something called the World Wide Web launched into the public domain.

The web made it simple for anyone to navigate the internet. All users had to do was launch a new program called a "browser," type in a URL and hit return.

And then troubleshoot the url typed in, because most people can't spell, and were hopelessly confused by the // thing.

This began the internet's transformation into the vibrant online canvas we use today.

Jackson Pollock's paintings can also be described as vibrant canvases. And any attempts to make sense of those are doomed to failure, or at least false success.

Anyone could build their own "web site" with pictures, video and sound.

And malware.

They could even send visitors to other sites using hyperlinked words or phrases underlined in blue.

Such as this one.  Open in new Window.

Okay. I'm being deliberately cynical. There's a lot to like about the internet, not the least of which is this website. But the web certainly has its downsides... just like everything else. Later, the article goes into some of these downsides.

CERN owned Berners-Lee's invention, and the lab had the option to license out the World Wide Web for profit. But Berners-Lee believed that keeping the web as open as possible would help it grow.

Well... he wasn't wrong. Fortunately for all of us, CERN was—and is—an international government science research organization, not a private company like ExxonMobil, AT&T, or Apple.

Today, nearly two-thirds of the world's population uses the web to visit hundreds of millions of active websites. Some of those pages belong to companies that are among the most valuable in history like Facebook, Amazon and Google.

None of which would exist without the internet as we know it.

With all of its problems, it's still one of the most influential inventions in history, if not the most. It's difficult to put an exact date on "this is when the internet was born," because there were all sorts of remote networks available before 1993, with many different individual inventors (none of whom were Al Gore), and of course the internet continues to evolve.

But the beginning of the World Wide Web is as good a milestone as any to commemorate.


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