Complex Numbers (Book)

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Complex Numbers

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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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 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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