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Tuesday, May. 7, 2024

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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

May 5, 2024 at 8:50am
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

May 4, 2024 at 5:42pm
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

October 25, 2022 at 12:02am

#1039671

We Named the Dog "Indy"

My introduction to archaeology wasn't Raiders of the Lost Ark. I was a teen when that came out. No, it was a book about one of the first archaeological endeavors, the excavation of Troy.

Obviously, it was a long time ago that I read that, so I don't remember much about it. I think the techniques involved in that excavation were what started modern archaeology, if I recall correctly. And I do recall that, until it happened, a lot of scholars considered the Greek stories about the Trojan War to lie entirely within the realm of mythology (this doesn't mean that there weren't mythological aspects to it).

I also read a (really quite incredibly long) book by James Michener concerning the excavation of a fictional city in Israel. Fiction though it was, the description of archaeology was consistent with Schliemann's work at Troy. (It's called The Source, if you're interested; it's the only Michener book I've ever been able to complete.)

The point is, by the time I saw Raiders, I had a pretty good idea what archaeology was, and that Indiana Jones was not it. This, of course, didn't stop me from enjoying the movie or at least one of its sequels.

The Enduring Myths of ‘Raiders of the Lost Ark’
Forty years later, archaeologists look back at what the first Indiana Jones movie got wrong about their profession

Forty years after Raiders of the Lost Ark premiered to the public on June 12, 1981, the outsized shadow of Indy still looms large over the field he ostensibly represented.

Let's be honest, here: movies rarely reflect the realities of any profession. Doctors and cops, for example, do way more paperwork than has ever been depicted on either the large or small screen (or so I've heard). Such activities don't lend themselves very well to a compelling narrative.

Even in the 21st century, several outdated myths about archaeological practice have endured thanks to the “Indiana Jones effect.” And contemporary archaeologists, many of whom harbor a love/hate relationship with the films, would like to set the record straight.

Which makes articles like these even more important. I'd like to think that Smithsonian Magazine here is making an honest effort to explore the truth, and not just cut down on their time answering questions like "Where are you storing the Ark of the Covenant?" Come on, you know they get asked that a lot.

Myth 1: Rugged, swashbuckling, fedora-wearing Indiana Jones is what most archaeologists are like.

I thought everyone knew that. Archaeologists are absolute nerds, not Han Solo in leather.

This section is mostly about how, historically, arcs (look, I get tired of typing the full name) were mostly honkies, though recently there's been more diversity. Which is probably much-needed as most historical sites aren't in Europe. Ironically, the guy they interviewed here has the surname White. Okay, that's not irony, but it's still funny.

Gender diversity within archaeology has evolved much more quickly, however. “Archaeology is dominated by women—white women have taken over archaeology,” says Alexandra Jones, founder of Archaeology in the Community, a D.C.-area nonprofit that seeks to increase community awareness of archaeology through enrichment programs and public events.

And if your name is Alexandra Jones, you were absolutely destined to go into archaeology.

Myth 2: Archaeologists work primarily in universities and museums.

At the risk of sounding smug, I knew this, too. My conception of an arc is someone who works out of a tent at some location that is currently remote, but wasn't always.

But it turns out that even my impression wasn't entirely correct. So much for being smug.

...today, up to 90 percent of American archaeologists work in a broad field known as cultural resource management (CRM). Also known as heritage management, CRM deals with the relationship between archaeology and everyday life. On its most bureaucratic level, CRM covers the broad and the specific regulations that govern historical, architectural, and archaeological interests and preservation in the U.S.

So. Also a lot of paperwork. As noted in the article:

CRM work is important and rewarding, but also involves the much-less cinematic act of filling out paperwork. Kassie Rippee, archaeologist and tribal historic preservation officer for the Coquille Indian Tribe, mentions that “archaeology-based work is only a portion of my job. I review and coordinate on laws and regulations. I monitor quite a bit of construction activity and make determinations as to how construction projects will affect tribal resources.”

Myth 3: Archaeology is largely done in exotic places.

Yeah, right. Exotic places like the land I grew up on. Yes, I've had arcs come by and do their thing.

Terry P. Brock, an archaeologist with the Montpelier Foundation, uses his research to shake up the historical record of life at President James Madison’s plantation in Virginia. Working in the local community “immediately brings relevance and importance to the work,” he says, “because the objects we are excavating together belonged to the community’s ancestors and are a direct link for the community to the people who came before them.”

I'm just including this bit because it's close to home, too. The other notable historic local, Jefferson, is also the subject of archaeology.

Myth 4: That belongs in a museum!

Yeah, see John Oliver's take on museums

if you still believe this one.

I know I've talked about this in here before, but all the artifacts we found on my land went not to a museum but to the descendants of the people who lived there.

By far, the most enduring and problematic myth to come from the Indiana Jones movies is the idea that all ancient and historic objects belong in a museum. While he’s correct that private collectors contribute to looting and other heritage crimes, “there isn’t a single object that belongs in a museum,” says Heppner. “Objects belong with their communities.”

This is, of course, not always possible. Who should the artifacts dredged up from Doggerland

go to, for example?

The last shot of Raiders, where the Ark of the Covenant is placed indiscriminately in a large government warehouse, is still a very real possibility today.

That's rich, coming from the Smithsonian.

The article wraps up with what I alluded to way back at the top: none of this means we can't enjoy the movie as a movie.

White admits that the Indiana Jones movies made him want to become an archaeologist as a child. “These movies are an escape for many of us, including archaeologists,” he says. “I want non-archaeologists to know that’s not really how archaeology is, but I don’t want them to lose the value of these movies as fantasy, action, and adventure.”

I do object to the description of such movies as an "escape," though that's part of a larger discussion about the value of popular movies vs. artsy intellectual films and beyond the scope of this entry.

But do they really have to make another Indiana Jones movie? Crystal Skull kind of sucked. Oh well. As long as Shia LaBeouf isn't in it, I'll probably see it anyway.

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