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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:

Elisa the Bunny Stik

May 29, 2024 at 9:02am
In response to "Ordinary Average Guy"

I think we need to be careful about saying there's no difference in socializing between online and off. I saw the following in response to a comment about discussions of gender online and the stances taken by LGBTQ community members that are chronically online:

"Truth. I had to stop looking for queer spaces online because it was full of this and angry exclusion discourse. I found some queer spaces offline and it reminded me that most people are normal and chill."

This is a topic I will likely be visiting in my journal in July. I figured I'd at least get this response in here first as a warm-up.

1 Like

Elisa the Bunny Stik

May 28, 2024 at 1:46pm
In response to "Long in the Tooth"

I feel I was too busy as a teen to screw around in convenience stores. On the rare occasion I wasn't at school or working, I tended to hang out by myself. If I hung out with friends, it was usually at someone's house (rarely mine).

Elisa the Bunny Stik

May 27, 2024 at 11:42am
In response to "Olive It And More"

Every once in a while, someone will misread the order slip and give me green peppers, which are an abomination, instead of green olives.

They truly are an abomination. If you're going to put peppers on a pizza, make sure it's anything but those little soggy cardboard slice things. Hell, even poblanos would be a major upgrade.

1 Like

Elisa the Bunny Stik

May 27, 2024 at 11:38am
In response to "Coming Up the Pike"

Man, people on Fandom Secrets would be aghast at how much you like Strange New Worlds. Personally, I haven't seen much of it. However, I did watch an episode at the gym once and found it enjoyable. It gave me that fascinated feeling I had when watching The Next Generation as a kid.

1 Like

Elisa the Bunny Stik

May 27, 2024 at 11:13am
In response to "Burgundy"

I will admit that I'm not much of a wine drinker. I've had reds and whites but tend to prefer reds. Then again, when it comes to booze, I tend to prefer things that are more intense in flavor. White wines...tend not to be that way for me.

2 Like

Elisa the Bunny Stik

May 27, 2024 at 10:38am
In response to "Distrust the Process"

That being said, I do think that people going out of their way to demonize ultra-processed foods are causing just as many issues as lobbyists are. These folks' actions exacerbate eating disorders and nervous thinking around food insecurity in equal measure. I wish the conversation around this set of actions was louder.

3 Like

Elycia Lee ☮

May 27, 2024 at 10:31am
In response to "Distrust the Process"

To me, as long food is 100% natural, then it is healthy. Pretty much like fruits, veggies and rice. I know people have thoughts about whether rice is good or not, but it is natural food so... I shall go with that.

2 Like

Kåre Enga in Montana

May 25, 2024 at 3:13pm
In response to "Plan Solo"

I'm more introverted than extroverted, but my only apprehension involves language and cultural barriers.

I'm bi- or ambi- but... always annoying. I waver between wanting to be left alone and not wanting to be alone.

I make my adjustments as necessary.

But LANGUAGE and CULTURE: true barriers that can cause problems for some and angst for me. I love strangers but find it frustrating when I can't connect.

For Belgium: make those plans soon. Today's connectivity means booking lodging in advance. In the old days it was show-up-and-ask-if-they-have-a-room. Still possible but not recommended unless cost is not an issue.

I prefer staying in hostels but rarely join in 'events'. I have gone out with fellow travelers however.

Kåre Enga in Montana

May 25, 2024 at 2:58pm
In response to "Banned Camp"

I remember when the movie "Brokeback Mountain" received "F"s from folks who basically commented that they would never NEVER watch such filth. Even those who liked or enjoyed it missed the main theme of poverty (financial, cultural, individual...). Personally, I preferred the short story to the movie. Both made a point that America didn't/doesn't want to face: choice and lack of choice.

That said, if someone were to ban my poetry I could probably live off of the notoriety.

Burning at the stake though seems a more likely outcome.

2 Like

🌕 HuntersMoon

May 25, 2024 at 11:32am
In response to "Banned Camp"

"Any book worth banning is a book worth reading." Isaac Asimov

2 Like

May 9, 2019 at 1:18am

#958596

Far from Home

What is the farthest you've ever been from the place you call "home?"

Ever wonder what's meant by "halfway around the world?"

Like, there's a spot in the Indian Ocean (I looked it up on Google Earth some time ago) which is exactly 180 degrees opposite my house. If I could walk in any direction at a steady pace, it wouldn't matter which direction I went in; they all result in the same time or distance to that spot. It is the south pole to my north pole, or vice-versa.

Should we consider that spot "halfway around the world" for me? Because if I were able to walk to it, and did so, but then kept walking, eventually I'd end up back home - all the way around the world. And yet, every other spot on the Earth's surface is closer, by definition, so every other spot would be less than halfway around the world. After I passed my personal South Pole, I'd be 3/8 of the way around, then 1/4, then 1/8, and all of the infinite points in between. I'd never be 3/4 of the way around the world, even though I'll have walked that far, and more.

There's no paradox here, of course; it's purely a matter of the inconsistency and imprecision of written language. Mathematics would describe the journey with far less ambiguity. To really answer the prompt question, we'd have to define exactly what was meant by "farthest," and probably "home" also.

Even defining "farthest" simply as "greatest distance along a Great Circle route" and "home" as "the place you live most of the time," perception can be thrown off by something as simple as a map. It is impossible to accurately represent every feature of a sphere on a flat map. Something is always distorted. With the most common (Mercator) projection, it's mostly distance and size; for example, a Mercator map makes it look like Greenland is bigger than South America, when it's simply not.

Distance is affected, too. Look at a Mercator map, and it appears that the closest point in the continental US to the continent of Africa is, like, somewhere near Miami, Florida. But no - the closest point (and it's not even much of a competition) is in Maine.

It's a nice old lighthouse called Quoddy Head, not far from the little town of Lubec, which features a few comfy tourist inns, a border crossing into Canada, and the absolute worst place to eat breakfast in the entire Western Hemisphere.

I know that because I've been there. Some years ago, and I think I've mentioned this in here before, I decided to drive all the way across the country. Since it would be my first time doing so, I decided to do something special: travel from the easternmost point of the contiguous US to the westernmost point. And the easternmost point happens to be... Quoddy Head Lighthouse.

From there, the most direct route would cut across Maine, then into Canada, and then pretty much stay in Canada. I have nothing against Canada. I love Canada. But my purpose was to see the US, so I took a route that meandered around south of the Great Lakes, back up through Wisconsin, then across North Dakota and Montana - avoiding interstates the whole way. Took me about two weeks; I wasn't in any hurry. There is no such thing as destination; there are only stops along the journey.

On the off-chance anyone is interested in my chronicles of that journey, well, here's the link to my offsite travel blog. Some of the links therein are broken; time will do that on the internet. First, this

and then starting with this post

and continuing as far as you can stand.

The westernmost point, incidentally, is about a three mile hike west of a map point called Ozette, in Washington State. Ozette is little more than a ranger station; the nearest town is some miles away, and features a bed and breakfast. I stayed there the night before I hiked through the woods to the Pacific. They had a calendar on the wall. The calendar picture at the time featured... Quoddy Head Lighthouse.

Life is weird.

So you ask me what's the farthest I've ever been from home. I could pace it off on a globe; it's Bethlehem. No, not the one in Pennsylvania; the original one. But that's boring. I choose to interpret "farthest" as the most removed psychologically, and for that, I'd have to say: the empty stretch of Washington coastline, a three-mile hike west of Ozette. Hiking six miles, there and back, along a poorly-maintained trail through bear-controlled rainforest, all to fulfill a whim I'd come up with - well, it's not something I'd ever done before, and it's not something I'll ever do again.

But I'm sure glad I did it.

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