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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:

🌕 HuntersMoon

about 12 hours ago
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

1 Like

Elisa the Bunny Stik

a day ago
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Montana

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 Montana

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 Montana

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

December 28, 2018 at 12:34am

#948342

Leave

Today's linked article turns feel-good stories into feel-bad stories.

https://thinkprogress.org/do-the-impossible-never-complain-live-the-dream-the-da...

Stories like this keep popping up on Twitter like zits on a prepubescent forehead: The sunshiney announcement about the GoFundMe for the guy with leukemia who can’t pay for his own medical costs. (He is employed by an organization whose owner has a net worth of $5.2 billion.) The dad who works three jobs to support his family saving up to buy his 14-year-old daughter a dress for an eighth grade dance. The college student who ran 20 miles to work after his car broke down and whose boss rewarded him for this effort by giving him his own car.

Do you get a sinking feeling when you read these stories? This feeling like, while of course you are impressed by the tenacity and generosity on display, you still want to vomit?

Behold, the rise of the feel-good feel-bad story.

I don't disagree with the thrust of the article. Providing for others may be more rewarding to accomplish directly, rather than indirectly through mandates. But it's been obvious to me for a while that our system is broken.

And yet - and here, I'm going to venture into controversy - I'm not convinced about the value to society at large of paid parental leave.

We don’t have federally-mandated maternity leave in the United States, making us one of the only nations on the face of the Earth to deny our citizens this basic and vital thing.

Essentially, I disagree that it's "basic and vital."

Of course, it's nice. It's definitely a benefit for parents, and probably for their children. Likely, not so much for everyone else.

The above quote links to a Pew Research study from 2016: http://www.pewresearch.org/fact-tank/2016/09/26/u-s-lacks-mandated-paid-parental...

Nowhere in the article, or in the Pew study, do I see anything that explains to me how parental leave is a good thing for society. It's asserted as a given, without evidence, without even argument.

Consider this:

1) Having children is a choice. Especially in the contemporary world, virtually no one can say they brought a child into the world by accident. Pregnancy can be accidental. Birth is not.
2) While one is on leave, the employer must either do without a person's services, or find a temporary replacement. While no one is irreplaceable, this puts an undue burden on the employer.
3) As we move into a more automated workforce, the need for human workers is decreasing; therefore, it is not to the benefit of future society to encourage population growth, or even stagnation.
4) Likewise, the primary driver of many of the problems facing us today - pollution, climate change, hunger, maybe even war - is population growth. Reverse that, and some problems are mitigated.
5) Parental leave is unfair to those of us who have chosen not to reproduce. Yes, some organizations provide "family leave" for reasons other than childbirth, but we're talking about state or federally mandated leave, not a choice made by an employer.

On the other hand, I do recognize that in order to continue capitalism as we know it - profits driven by eternal growth - we need the population to increase. So you'd think more companies would be on board with this (more consumers = more profit). Again, though, I don't see how this could be a good thing overall.

Now, I can see how a policy of "no paid parental leave" affects women disproportionately. And that's not cool. But nothing I've ever seen has convinced me that mandated paid parental leave is a benefit to society in general (again, yes, it is a benefit to the individuals involved). The idea of its benefit is stated, as I've pointed out, without argument or evidence.

Thing is, I have an open mind. If you're so inclined, give me some good rationales and I could change my opinion. Not that my opinion matters either way, but at least I might understand the reasoning. (Anecdotes probably won't work; I've already acknowledged that it's a benefit for the individuals taking the leave.)

2 Like • Comment • View 4 comments

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