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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?

November 24, 2022 at 12:03am

#1040976

The Greatest Thing Since...

You've certainly heard the cliché, "the greatest thing since sliced bread," which implies that sliced bread was the greatest invention. This is obviously false, as beer was invented before sliced bread.

Sometimes it takes a lack of something to truly appreciated it. This was true during Prohibition, and apparently, also true during World War II.

Remembering When America Banned Sliced Bread
During World War II, the U.S. government turned to drastic rationing measures.

The year was 1943, and Americans were in crisis. Across the Atlantic, war with Germany was raging. On the home front, homemakers were facing a very different sort of challenge: a nationwide ban on sliced bread.

While it's true that there were far worse things in WWII than a lack of sliced bread, I can see how that would be frustrating.

The ban on sliced bread was just one of many resource-conserving campaigns during World War II. In May 1942, Americans received their first ration booklets and, within the year, commodities ranging from rubber tires to sugar were in short supply.

These days, of course, such measures would be "government overreach," "tyranny," "an attack on muh freedumbz," and "cause for riots in the streets."

So by January 18, 1943, when Claude R. Wickard, the secretary of agriculture and head of the War Foods Administration, declared the selling of sliced bread illegal, patience was already running thin. Since sliced bread required thicker wrapping to stay fresh, Wickard reasoned that the move would save wax paper, not to mention tons of alloyed steel used to make bread-slicing machines.

Okay, so I can see the wax paper thing (plastic wasn't much used then), but didn't the slicers already exist? Sliced bread was invented in 1928

, and pretty much everywhere five years later—ten years before the ban.

On July 7, 1928, the Chillicothe Baking Company in Missouri first put his invention to use, saying it was “the greatest forward step in the baking industry since bread was wrapped.”

So, really, the expression should be "the greatest thing since wrapped bread."

As an aside, I'm picky enough to get my bread from a local bakery rather than the supermarket. They'll slice it right there upon request, and slide it into a plastic bag with a twist tie. Since it's fresh bakery bread without preservatives, if it's not wrapped, it becomes a rock within 24 hours.

Sliced bread really took off in 1930, when the Continental Baking Company’s pre-sliced Wonder Bread made its way into American homes.

Ugh. Foul. Disgusting.

After a few years of aggressive marketing, the pillowy, preservative-laced loaves were synonymous with modernity and convenience.

They're synonymous with American lack of taste, along with American cheese and light beer.

On January 24, less than a week after the ban, the whole thing began to unravel. New York Mayor Fiorello LaGuardia made a public announcement that bakeries that already had bread-slicing machines could carry on using them.

See?

No wonder he got an airport named after him.

One baker by the name of Fink, who also happened to be a member of the New York City Bakers Advisory Committee, publicly advocated for the ban, then was fined $1,000 (more than $14,000 today) for sneakily violating it.

Tempting as it may be to claim that his name was the source of the verb "to fink," no, it wasn't.

By March 8, the government decided to abandon the wildly unpopular measure. “Housewives who have risked thumbs and tempers slicing bread at home for nearly two months will find sliced loaves back on the grocery store shelves tomorrow in most places,” noted the Associated Press.

Government overreach, tyranny, muh freedumbz.

In the end, no thumbs were severed and Americans were reunited with the sliced bread they had learned to hold so dear.

Once you get used to an invention, especially one that saves time and work, it's very, very hard to do without it. If necessity is the mother of invention, laziness is the milkman.

Also, fuck Wonder Bread.

3 Like • Comment • View 1 comment

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