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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

a day 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

a day 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

a day 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

a day 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

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?

August 5, 2020 at 12:11am

#989926

Only the (not so) Lonely

I was an "only child," so this article caught my interest. So I'm sharing it. See? We can share.

https://qz.com/980226/neuroscience-shows-that-only-children-are-more-creative-mo...

Neuroscience shows that our gut instincts about only children are right

That headline can bite me. That's not the thrust of the article at all, as we shall see.

Conventional wisdom has it that only children are smarter and less sociable.

"Conventional wisdom" is almost always wrong. But flattery will get you everywhere with me.

Conversely, since those only children never have to share a toy, a bedroom, or a parent’s attention, it is assumed they miss out on that critical life skill of forever-having-to-get-along.

"Critical," my solitary ass.

But are their actual brains different?

OH COME ON.

Jiang Qiu, a professor of psychology at Southwest University in Chongqing, China and director of the Key Laboratory of Cognition and Personality in the ministry of education, led a team of Chinese researchers that sought to answer this question with more than 250 college-aged Chinese students.

FWEEEEET! Flag on the play. Minuscule sample size, representative of just one culture. 10 yard penalty, fourth down.

Hey, I just made a sportsball joke.

They used standard tests of intelligence, creativity, and personality type to measure their creativity, IQ, and agreeableness.

Fuck agreeableness.

On the behavioral tests, only children displayed no differences in terms of IQ, but higher levels of flexibility—one measure of creativity—and lower levels of agreeableness than kids with siblings.

You're also going to have to explain to me how to actually quantify creativity. I mean, I know there are issues with IQ tests, but at least some measures of intelligence can be quantified within a particular cultural and socioeconomic context.

Having worked on the 1896 study “Of Peculiar and Exceptional Children,” Hall cast only children as “oddballs” as “permanent misfits,” descriptions that have stuck over the years with remarkable persistence. “Being an only child is a disease in itself,” he claimed.

As developed countries transitioned from agrarian to industrial economies, family sizes tended to get smaller. I mean, I can't be arsed to find the data on that or anything, but I'm pretty sure it's the case. So, naturally, in the 19th century, growing up with a bunch of siblings would be considered "normal" and not doing so would be considered "abnormal." I assert that had the opposite been the case, it would be having siblings that would be considered "a disease in itself."

There is ample evidence suggesting the stereotypes of the “lonely only” are wrong.

As I'm pretty sure I've mentioned in here before, being sibling-free taught me a lot about self-reliance. I wouldn't want it any other way.

They found that only children, along with firstborns and people who have only one sibling, score higher IQ marks and achieve more, but aren’t markedly different personality-wise

Which right there contradicts the Chinese study, throwing both into question.

Jiang and his co-authors hypothesized a few reasons for their findings.

You can hypothesize all day. I mean, I do. Until you do the science, it remains opinion and educated musings.

Creativity —defined as having original ideas that have value—is strongly influenced by everything from family structure and parental views, to interactions and expectations

Okay, so you can define creativity, but again -- how do you measure it? If it can't be quantified, it's not science. And "original ideas that have value?" We share a world with seven billion other humans. I've had original ideas that, it turned out, someone else had already thought of.

The article goes on to talk about some measures of creativity: flexibility, originality, and fluency. Those sound more like general intelligence to me, but what the hell do I know?

Look, I'm not trying to argue from one datum (me), and if I hadn't been drinking wine I might seek out other sources to delve deeper into this, but so far it's not passing the bullshit test for me. Then again, I'm just not very creative, so maybe I'm just inflexible enough to provisionally reject this.

He also noted that just like IQ tests, creativity tests are not perfect measures of the thing they are measuring.

Duh.

Creativity involves spontaneity and intrinsic motivation—things which are a bit hard to assess on a test.

Pretty much by definition, you can't make a standardized test that measures creativity in a meaningful way. I mean, a truly creative person could find a way to bypass the strictures of the test, making it invalid. Right? Think about how James T. Kirk beat the Kobayashi Maru test. In either universe.

To summarize, this article panders to confirmation bias.

So back to my wine, and rewatching old episodes of Star Trek because it's been years since I actually watched them. Damn, some things were cringeworthy in the 1960s. But first...

Mini-contest results!

As is appropriate for a question about decisions, this was a tough decision for me. I appreciated all of the comments. From them I gathered that we all have different ways of making decisions, as I expected.

What clinched it for me, though, was the line: "I chart a course I want to take and weigh my decisions based on whether or not they move me along the course." I like that this implies a focus on making decisions based on achieving one's overall goals, and not just the pros and cons of an individual decision -- something that neither I nor the article's author seems to have considered, but in retrospect it seems important.

So this time, the Merit Badge goes to Elisa the Bunny Stik

-- but again, I liked all the comments and everyone will get another chance soon.

I should also note that no, I'm not taking sides on which decision-making process is "best." Whatever works for you, works. But I hope that seeing how other people approach it helps us all with our own decision-making. As always, thanks for reading and commenting!

6 Like • Comment • View 5 comments

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