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Wednesday, Nov. 6, 2024

2:42pm EST

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Complex Numbers

by Robert Waltz

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.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Turkey DrumStik

about 4 hours ago
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

about 24 hours ago
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

about 24 hours ago
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

JayNaNoOhNo

a day ago
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 Like

tj-turkey-jobble-jobble-hard-J

a day ago
In response to "It's Hard Not To Scare"

Smarter mice? Just what we need!

1 Like

Wordsmitty ✍️

Nov 4, 2024 at 12:22pm
In response to "It's Hard Not To Scare"

"Friendly neighborhood spider-goat." Isn't Marvel working on that for release in '26. - "Yes, it's cute, MJ, but you shouldn't ..."

2 Like

tj-turkey-jobble-jobble-hard-J

Nov 3, 2024 at 3:52pm
In response to "Revisied: "Inevitable""

I can think of far more absurd ways to die, but most of them involve alcohol and maybe prostitutes... This statement reminded me of the passing of a friends grandfather; he died of a heart attack while intoxicated and with a prostitute, Viagra also aided in his heart failure.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:46am
In response to "She Said Spatchcock"

You can spatchcock, or butterfly, any bird.

That bit might only be funny if you're familiar with British slang.

It's really a pity that the British national team's mascot is a lion and not a rooster. Ironically, that's the French national team's mascot, which did make for a pretty good joke during the Olympics.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:31am
In response to "Cave In"

tj-turkey-jobble-jobble-hard-J

-Yeah, those instigators from Illinois and Texas would really degrade the standards of Hell.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:30am
In response to "Revisied: "Inevitable""

Though I clicked on it to check, I no longer follow that site and want nothing to do with them, which is why we haven't had any LitHub links in over a year.

Well, now my curiosity is piqued. What happened on this front?

2 Like

November 6, 2024 at 9:03am

#1079566

Lo!

Well, that's finally over. Now I just get to grump at holiday season chatter.

Today's article, from BBC, has nothing to do with politics or seasons, and everything to do with the invention you're using right now.

'We were just trying to get it to work': The failure that started the internet

There have been differences of opinion concerning the actual beginning of the internet. It's not like a human birth, or Armstrong's boot on the moon: a clear and obvious transition point. In my view, this article is more about a precursor technology, but a vital one for what the internet became.

On 29 October 1969, two scientists established a connection between computers some 350 miles away and started typing a message. Halfway through, it crashed.

1969 would have been long before "try rebooting and reinstalling all your drivers" would become tech support's second suggestion, after "make sure it's plugged in."

At the height of the Cold War, Charley Kline and Bill Duvall were two bright-eyed engineers on the front lines of one of technology's most ambitious experiments.

I should note, for context, that this was the same year as the aforementioned moon landing. Unlike NASA's stated mission, though, this early attempt at remote networking was in service of more military pursuits.

Funded by the US Department of Defense, the project aimed to create a network that could directly share data without relying on telephone lines. Instead, this system used a method of data delivery called "packet switching" that would later form the basis for the modern internet.

Like I said, not the actual invention of the internet, and military.

It was the first test of a technology that would change almost every facet of human life. But before it could work, you had to log in.

Some things don't change.

But Kline didn't even make it all the way through the word "L-O-G-I-N" before Duvall told him over the phone that his system crashed. Thanks to that error, the first "message" that Kline sent Duvall on that autumn day in 1969 was simply the letters "L-O".

And that's what I find amusing about the story: it's very Biblical. "Lo!" As in "Lo and behold."

On the other talon, I want to think that once they got it working (which, as the article notes, they did, after about an hour), the second message sent over this proto-internet was "Send nudes."

The BBC spoke to Kline and Duvall for the 55th anniversary of the occasion.

The rest is a transcript of that interview. It goes into more depth over what happened (or didn't happen) at the time, but there's no reason to repeat it here.

As compelling as this origin story is, I had this vague memory of a different origin story for the internet, one which took place some years later. In a rare case of me actually looking something up, I found this entry from 2019: "Birthed in Beer"

So if I had to choose which one was the actual invention of the internet, I'd pick the 1970s one, because it involved beer.

7 Like • Comment • View 1 comment

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