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Monday, May. 6, 2024

1:27am EDT

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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 17 hours ago
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

a day ago
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

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

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
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

April 11, 2022 at 12:02am

#1030515

Asking Persimmon

I'd never heard of this before reading the article, so here it is:

For Enslaved Cooks, Persimmon Beer Combined Ingenuity and Joy
A conversation with Michael Twitty about the powerful history behind a centuries-old beverage.

When I was a kid, we had a persimmon tree. Apparently, the trick to persimmons is you have to wait for first frost (usually around October 15 in my area) to pick them, because they only ripen with extreme bitter cold (I consider anything below 45F "extreme bitter cold"). Never did appreciate the taste of them, but all kids have weirdnesses about food.

Michael Twitty, the James Beard Award–winning culinary historian, estimates he has brewed his grandmother’s persimmon beer about a dozen times. Made by fermenting Diospyros virginiana, the diminutive North American persimmon, with sugar, honey, and yeast, persimmon beer is more akin to fruit wine or liqueur than anything brewed with barley, malt, and hops.

In general, beer is fermented grain, while wine is fermented fruit. However, exceptions abound. Cider, usually from apples or pears, is its own category. Japanese sake is most often known as "rice wine" in English, probably because its alcohol content is higher than most beer and it's generally not bubbly. For example. So if someone wants to call this "persimmon beer," well, they don't need my permission.

For generations of Black families across the American South in the 18th and 19th centuries, persimmon beer played an integral role in daily life. In his quest to uncover more about the foodways of his ancestors, Twitty learned that American persimmon trees are a genetic echo of fruit trees in West Africa, and that both the plant and the beverage provide a thread across the history and geography of the African diaspora.

Now, that is interesting. Of course, humans also all have genetic roots in Africa, just some more recent than others.

Persimmon beer was really important for the people working in the fields. That was a typical thing to be brought to them in a gourd or a bottle or a crock. Remember, they didn’t have Gatorade.

I can't imagine Gatorade would have been better. Or permitted.

Some of these foraged foods that are the grandeur of younger white folks that are into this now, quite frankly, this is not white people food. One of the best quotes I’ve ever seen in reference to pawpaws was “The food fit for Negros and Indians.”

We had pawpaw trees too, growing wild.

The article delves into some cultural issues that I think are relevant. It does not, however, provide an actual method for preparing persimmon beer -- but the mere fact of its existence should be enough, and probably it's in the book the guy is trying to promote.

4 Like • Comment • View 2 comments

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