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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

Apr 25, 2024 at 3:16am
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

Apr 25, 2024 at 3:09am
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

Apr 25, 2024 at 2:58am
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

Apr 24, 2024 at 4:26pm
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

Apr 23, 2024 at 6:51pm
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

Apr 23, 2024 at 3:31pm
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

Apr 23, 2024 at 3:14pm
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

Apr 23, 2024 at 3:11pm
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

Apr 23, 2024 at 3:04pm
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

Apr 23, 2024 at 2:58pm
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?

March 9, 2024 at 9:27am

#1065919

Daydream Believer

Like to daydream? Well, consider this article from The Conversation. Author is British, so there are some weird-to-Americans spellings:

Daydreaming’s dark side: the compulsive, complex fantasy disorder that dominates some people’s daily lives

If daydreaming has a dark side, wouldn't that be a daymare?

Despite what we’re often taught to believe, daydreaming can be immensely useful.

Especially when you're approaching a deadline.

Daydreaming, when defined as thoughts that aren’t tied to what you’re currently doing, occupies a good chunk of our waking lives – an average of around 30% of the time if you randomly probe people.

Hopefully not while you're at work. Because that would be time theft. You'd be stealing from the Company. You're not stealing from the Company, are you, Janice?

But it’s estimated 2.5% of adults experience a type of excessive daydreaming which is defined as the disorder “maladaptive daydreaming”. So-called maladaptive daydreamers compulsively engage in vivid fantasies and daydreaming plots so excessively that it interferes with their ability to function in daily life.

I suppose there is no activity (or, in this case, usually inactivity) that someone, somewhere, can't find a downside to.

Unlike typical daydreams which can be fleeting (lasting seconds), maladaptive daydreamers can spend several hours at a time in a single daydream.

Okay, fine. That does seem a bit excessive.

These invented worlds are often rich and fantastical, with complex plots and intricate storylines that evolve over many years.

You've just defined fiction writers. Except for the, you know... writing it all down part.

With maladaptive daydreaming, there’s a strong urge to daydream and annoyance when this is not possible or interrupted. Most also find it difficult to stop or even reduce the amount of time they spend daydreaming.

I'm no expert, but isn't that pretty much the classic definition of addiction?

It’s important to note that immersive daydreaming and vivid fantasy activity isn’t by default maladaptive.

I'm just leaving that quote here in case you can't be arsed to read the article (perhaps because you're too busy daydreaming), and are wondering if you should be concerned about yourself. Chances are, no. I think the article is about making the rest of us aware that people like this exist, not, for once, trying to tell us that we're doing something wrong.

There seems to be a strong relationship between OCD and maladaptive daydreaming. One study found that over half of participants with maladaptive daydreaming also exhibited signs of OCD. This may suggest possible shared mechanisms between the two disorders, including intrusive thoughts, dissociation and a lack of cognitive control.

Again, far from expert here, but I'm pretty sure that by OCD, they mean diagnosed by a professional, not just someone being coy about their cleaning and/or organizational habits.

The fact that maladaptive daydreaming is not recognised as a psychiatric condition also means we know little about treatment options. There is one documented case study published in a peer-reviewed journal showing a 25-year-old man was able to cut the time he spent daydreaming in half – from nearly three hours daily to under an hour and a half. This was done over the course of six months using a combination of psychological treatments such as cognitive behavioural therapy and mindfulness.

At last, a practical use for cognitive behavioral therapy and mindfulness. Maybe. As always, one data point does not a scientific study make. Somehow, "directing the patient to become a writer" doesn't seem to appear in the list of treatments.

Finally, I can't do a title like that without posting the song I cribbed it from, which was written by John Stewart, but not that John Stewart:

4 Like • Comment • View 6 comments

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