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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 2, 2024 at 6:33am

#1065370

Thought Bubble

Hope you're not prone to paranoia.

Who Controls Your Thoughts?
Our minds are being coerced in covert ways.

After yesterday's article, clearly, the answer to the headline question is "space aliens."

In 2017, Simon McCarthy-Jones wrote an article about schizophrenia for The Conversation. The piece, he jokes, got read by more than two people, which, as an academic—he’s an associate professor of clinical psychology at Trinity College Dublin—was a thrill.

Except that, when I read this lede, I thought he was making a schizophrenia joke, like the old "I'm schizophrenic and so am I" one, which perpetuates the conflation of schizophrenia with MPD. Which I might be able to get away with, but not a psych professor. Anyway, no, that wasn't the intent. As far as I can tell.

Shortly thereafter, however, he found himself “just gripped by the iron claws of Facebook,” looking over and over again to see who had liked his article, who had commented on it.

Isn't there a psych disorder where you attribute your actions to some outside force, instead of taking responsibility for them? I don't mean that in a "we have no free will" way, but in a "the Devil made me do it" way.

Was his thinking being covertly, coercively controlled by external forces (in this case, a big tech company)? The experience got him wondering just what “free thought” actually was. And so he started wading into the murky waters of the psychological, philosophical, cultural, and legal assumptions about what constitutes thought—and how it could remain truly free.

His intellectual quest has exited his head, as much thought eventually does, and now exists in the form of a new book: Freethinking: Protecting Freedom of Thought Amidst the New Battle for the Mind.

Of course it's a book ad. Everything on the internet is an ad, or it's behind a paywall. Well, except for this blog, of course.

In any case, the rest of the ad is an interview.

We might want to say: No, we’re independent, autonomous thinkers. But I think we have to recognize that in front of a persuasive AI, we are in deep trouble.

In my experience, the people who shout "I think for myself!" the loudest are the most likely to follow the herd.

The first was that the right to free thought is an absolute right, based on the United Nations’ Universal Declaration of Human Rights. In the United States, it’s as close to an absolute right as there is in the Constitution. And that’s quite exciting because it means that nobody can interfere with your freedom of thought. There are instances where you can limit someone’s speech if it’s defamatory or false advertising or fighting words. But thought is unimpeachable, you can create absolute protection for people’s minds.

Well, okay, except that it's (at least so far) easy to say "you have an absolute right to free thought" when there is no possible way to read minds. Introduce a mind-reading device, though, and watch how quickly that right disappears. Sure, we can sometimes take an educated guess as to what's in someone's mind. Like if you're a shoe clerk, and some guy is in there looking at the Nike selection, you'd probably be right in assuming the guy's thinking "I might be interested in buying athletic shoes." But only "probably." After all, he might be idly gazing at footwear while wondering how he's going to trick some lady into bed that night.

There’s a quote by Daniel Kahneman, the Nobel laureate, who said: “Human beings are to independent thinking as cats are to swimming. They can do it, but they prefer not to.”

Honestly, I mostly saved this article so I could share that quote.

Astute readers may note that a lot of this is in opposition to my assertion that we don't really have free will. And it is. But lack of free will doesn't necessarily imply that it's other people pulling on our strings. Sometimes it's just the universe conspiring to keep us complacent.

3 Like • Comment • View 2 comments

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