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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/

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Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Aiva Raine

about 3 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?

Aennaytte: Free & Wild in GoT

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

I have never been to New York, but it seems that my assessment years ago that Berlin, Germany and New York have some similarities. Both cities are known for being inhabited by rude people. And both places, as I now found out, are dog obsessed. And they have high rents.
Berliners though, have a habit of letting their dogs run off leash. Maybe New York is a little better than Berlin in that regard.

1 Like

Robert Waltz

Apr 21, 2024 at 1:48pm
In response to "Revisited: "Hack This""

Wordsmitty ✍️, far be it from me to speculate on the motivations of space aliens, but why in Xenu's name would they do such a thing to the universe?

1 Like

Wordsmitty ✍️

Apr 21, 2024 at 1:39pm
In response to "Revisited: "Hack This""

I thought humans got bigger brains because extraterrestrials affected our evolution, and we eat processed chicken and eggs.

1 Like

December 1, 2021 at 12:01am

#1022595

You Have Nothing to Lose But Your Chains

It's December now (ugh) and my participation in 30DBC last month gave me a chance to restock my Blog Fodder folder. I've got enough now for this month, and then some... assuming I'm able to blog every day this month.

If I can just make it to the 13th, that will be two years of blogging every day. As my first surgery isn't until the 16th, that should be possible, though my vision has deteriorated to the point where it's hard to see what I'm typing. So if I do make it, it is likely that there will be more typos than usual.

For now, though, randomly picked from the Fodder Folder, a rare (for me) hot-button issue to kick off the month:

A worker in Florida applied to 60 entry-level jobs in September and got one interview

Joey Holz recalled first hearing complaints about a labor shortage last year when he called to donate convalescent plasma at a clinic near Fort Myers, Florida.

Okay, I know what plasma is (it's not the same thing as the plasma I talked about a few days ago in "Life, The Universe, and Everything"

), but "convalescent plasma" is new to me. Apparently it's used as treatment for the 'rona -- blood plasma from people who survived their encounter with the virus. I mean, I knew they were using antibody treatments, but that's the first time I encountered that particular phrase. Great; I love learning new things, even though it turns out that does jack shit

.

However, that really has nothing to do with the story. Have the writers at Business Insider been taking lessons from The New Yorker?

"The guy went on this rant about how he can't find help and he can't keep anybody in his medical facility because they all quit over the stimulus checks," Holz told Insider. "And I'm like, 'Your medical professionals quit over $1,200 checks? That's weird.'"

As a former business owner, I would like to cordially invite any business owner to try to live off of stimulus checks and see if it makes you want to never work again. Hell, I'll even make it "stimulus checks plus your lowest-paid former worker's unemployment benefits."

Over the next several months, the 37-year-old watched as a growing chorus of businesses said they couldn't find anyone to hire because of government stimulus money.

I'm reminded of an old proverb: If you run into an asshole, you've run into an asshole. If everyone you run into is an asshole, you're the asshole. These business owners are assholes.

He said he found it hard to believe that government money was keeping people out of the labor force, especially when the end of expanded federal unemployment benefits did not seem to trigger a surge in employment. All expanded benefits ended in September, but 26 states – including Florida – ended them early in June and July.

"If this extra money that everyone's supposedly living off of stopped in June and it's now September, obviously, that's not what's stopping them," he said.

Yeah, I remember some of these assholes going, "Boy, when the government turns off the firehose, them workers are gonna come begging." Well, the firegardenhose is turned off, and that didn't happen.

Two weeks and 28 applications later, he had just nine email responses, one follow-up phone call, and one interview with a construction company that advertised a full-time job focused on site cleanup paying $10 an hour.

When I was a kid, $10 an hour was above poverty level. This was about the same time when Cokes were a quarter each. Now? Now, it's a fucking joke.

But Holz said the construction company instead tried to offer Florida's minimum wage of $8.65 to start, even though the wage was scheduled to increase to $10 an hour on September 30. He added that it wanted full-time availability, while scheduling only part time until Holz gained seniority.

And that's an even funnier joke. I've been seeing a lot of reports of bait-and-switch like this, too: companies advertising like $20 an hour but then after the interview you find out that it's actually like $12 until some nebulous future time when you're off probation or whatever. Maybe. If they're not lying about that, too.

In a Facebook post on September 29, which went viral on Twitter and Reddit as well, Holz said, "58 applications says y'all aren't desperate for workers, you just miss your slaves."

Truer words cannot be written.

By the end of September, Holz had sent out 60 applications, received 16 email responses, four follow-up phone calls, and the solitary interview.

There might be any number of reasons for this, and it's hardly a scientific study (despite the inclusion of pie charts). But the guy in the story understands the limitations of his "experiment:"

Holz acknowledged that his results may not be representative of the larger labor challenges in the country, since his search was local and targeted the most vocal critics of stimulus spending.

Honestly, I'm just surprised that an outlet like Business Insider ran an article like this one instead of kissing business owner ass.

And now, of course, people are freaking out about inflation. I don't want to delve too deeply into that quagmire, because I'm not actually an economist -- and even if I were, economists can't agree on inflation policies, either. The economic system, like the weather, is inherently chaotic: unpredictable past a certain point, and subject to wild swings based on the tiniest of inputs. But I will say this: anyone who didn't expect some inflation was fooling themselves.

One other thing I'll say, though. I've been waiting for this. For too long, employers have had the bulk of the power in the working world. They got to dictate working conditions, salaries, benefits... all of which have been deteriorating for some time. I've been hoping to see more bargaining power returned to the employees and potential employees, and I feel like it's finally happening.

In other words...

7 Like • Comment • View 4 comments

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