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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

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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:

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 18, 2024 at 9:36am

#1066490

Cookie Wars

Here's an article about an important component of life.

The curious case of the disappearing Hydrox cookies
Oreo, the Hydrox knockoff, has been accused of burying its competitor by scoring sweetheart deals with grocers. Does it wield too much power over smaller rivals?

Yes, Oreo was a Hydrox knockoff, not the other way around. But that crap happened around 1910. Maybe stop worrying about who was first?

Audrey Peard is searching for an elusive, chocolatey piece of Americana: a package of Hydrox cookies.

Come to think of it, I haven't seen them in a while, either. Can't go to the grocery store without hearing the siren call of Oreos (which I usually ignore because they produced, then yanked, my favorite ones), but haven't seen Hydrox since before I can remember.

She’s visited multiple grocery stores near her home in the Bronx, followed a Facebook group, and even talked to a manager at a production facility in El Segundo, California, about supply shortages.

El Segundo may sound like an obscure California town, but in reality, it's right next to LAX. Hardly obscure.

Hydrox was the original chocolate sandwich cookie, predating Oreo. With a mildly sweet creme and a crunchier cookie that has a darker chocolate taste than its rival, Hydrox developed a reputation as the dessert of the discerning eater. It was, according to legendary food writer Calvin Trillin, the “far superior” cookie.

Sure, but this is the US. We ignore the superior in favor of the cheap and/or flood-marketed. That's kind of our thing; we even apply it to countries.

Hydrox, meanwhile, was discontinued in 2003. It came back in 2015 thanks to Leaf Brands, a San Diego-based company that specializes in reheated nostalgia.

Well, that might explain why I haven't seen any for a while.

Like almost anything else, you can buy Hydrox on Amazon (in bulk).

Don't fucking tell me that. Dammit!

In March 1912, the first batch of Oreos produced for sale was shipped from Nabisco’s six-story Romanesque-style headquarters in Manhattan to a grocer in Hoboken, New Jersey. It would’ve been a historic moment of American innovation if not for an inconvenient fact: Nabisco totally copied the cookie.

Another US thing. See also: Thomas Edison.

A smaller rival, Sunshine Biscuits (then known as The Loose-Wiles Biscuit Company), was started by Jacob and Joseph Loose in 1902.

Now, this is where my inner linguist starts asking questions. Nabisco was originally National Biscuit Company. Obviously, they both mostly made cookies, not biscuits. Except that in British English (and also in French), what we call cookies, they call biscuits. And what we call biscuits aren't technically biscuits at all ("biscuit" comes from Latin words for something like "twice baked"), though obviously they're delicious in their own way. But these were clearly American companies, as evidenced by their locations in New York and Kansas City. So why "biscuits?" Did we only split off from British usage after the watershed moment when someone invented the first delicious creme-filled sandwich biscuit/cookie?

Apparently not.

And it looks like we can blame the Dutch for, among other things, "cookie."

To complicate matters further, some cookies are called crackers.

All of which is to gloss over the fact that it's too bad they didn't stick with Loose-Wiles.

Anyway, the article goes off on a tangent about corporations and unions in the US, before going on with:

In 1908, Sunshine created one of its most popular products, Hydrox.

If you're thinking that's a portmanteau of hydrogen and oxygen, well...

According to company lore, the name stemmed from the elements of water — hydrogen and oxygen — chosen to symbolize the cookie’s cleanliness at a time when materials like chalk and plaster of Paris routinely appeared in baked goods.

I mean, technically they should have called them Carbohydrox, but whatever. Remember, this was before some other marketing convinced people that chemicals are bad, despite everything being made of chemicals.

Sunshine bragged that chemists tested Hydrox for purity and that workers made them at “thousand window” factories with natural light.

Yeah, right.

Hydrox also stood out against Oreo by promoting its more adult taste and kosher ingredients — in advertisements that bordered on erotic.

The "kosher" thing wasn't just to grab the Jewish market, either. It had the cachet of being more "pure" back then, kind of like "all-natural" is today. Whether it was/is or not is up for debate.

The article goes on with history for a while, and I think lays out a compelling case for why Oreos ended up reigning supreme. There's also quite a bit about the anti-competitive world of grocery stores, which I find fascinating.

Usually, doing articles like these makes me hungry. Not this time. All I can think of is the abomination known as Swedish Fish Oreos,

so... no, thanks.

4 Like • Comment • View 4 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
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