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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:

Kåre Enga in Udon Thani

about 3 hours ago
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

about 3 hours ago
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

about 3 hours ago
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

about 14 hours ago
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

a day ago
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

a day ago
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

December 7, 2018 at 12:03am

#946988

Cold Inside

Another year, another shitstorm about holiday songs.

https://www.bbc.com/news/entertainment-arts-46425160

Baby, It's Cold Outside is one of those Christmas songs that's about as traditional as mince pies.

But an American radio station's decision to pull it from playlists because it's seen as unsuitable in the #MeToo era has reignited a debate about the song, and raised questions about other potentially questionable Christmas classics.

First of all, let me state outright that my life would not be lessened in any way if I never heard another holiday song. It would, in fact, be improved. Ideally, I would never step into a store and be bombarded with "White Christmas" or "Santa Claus is Comin' To Town" or especially "I'll be Home for Christmas."

There are a few that I can tolerate, but for the most part, if I never had to hear another Christmas song, I'd be happy. Or at least a little less depressed, which for me amounts to the same thing.

Okay, now that that's out of the way, I'm going to talk about the controversial songs.

What a lot of people miss when consuming media - be it audio, video, or whatever - is historical context. The platitude about people who don't learn from history being doomed to repeat it holds true here.

Things were different in the past. That's why we call it the past. Lots of things that were created in the past couldn't be created today, not in the same way. Blazing Saddles comes to mind. That movie was a product of the 1970s just as sure as Watergate and disco were. Movies like that one were created to shine a spotlight on the stupid attitudes of the time, and played a role in eliminating them. Once these attitudes became obsolete, a lot of the context of the movie was lost. If you don't know what race relations were like in the 70s, you'll miss a lot of the subtext.

As writers, one of the greatest things we can hope for is that something that we write - be it a story or a song or whatever - helps to change things. In the process, often the writer's work becomes obsolete. People later will miss the point, unless they understand the historical context. It's a bit like doctors working to eradicate disease - once it's eradicated, people in the future will start to wonder what all the fuss was about. Hence you get some of the most egregious types of reactionary in the present, like anti-vaxxers. Lacking the historical context of polio outbreaks and measles epidemics, they just don't understand why people make a big deal out of vaccination.

The song in question - and make no mistake, I think it's just as crap as any other "holiday" song - was a product of its time, and a wish for things to be different. Well, now things are different. We're closer to social equality than ever before. We're open to different expressions of gender identity. Things that once were forbidden are now commonplace - and that's not a bad thing.

But if we forget where we came from, the road that took us to this place where we are, we risk going back to it. You can try to make this a generational thing - I'm going to save my rant about "generations" for another entry, as this one's going on long enough - but it's not so much about generations as it is about ignoring history. Yes, things were worse in many ways in the 40s. But to know exactly how they were different can only highlight how far we've come, and how far we still need to go.

And I think the bigger problem is that once-respected news organizations like the BBC are quoting Twatter. If anything needs to go away, it's not old Christmas songs; it's shallow social media.

Let's work on that one, shall we?

I'll wrap this up with one of the few holiday songs I can stand:

2 Like • Comment • View 2 comments

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