Complex Numbers (Book)

Blog Calendar

◄ October ► 2022
S	M	T	W	T	F	S
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

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:

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').

1 Like

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 28, 2022 at 12:01am

#1039836

Simulation Stimulation

No, the universe isn't a simulation (to a high degree of probability). But that doesn't stop us from simulating stuff.

With So Few Farmers, Why Are Video Games About Farming So Popular?
An archaeologist considers what farming simulators reveal about humanity’s ancient and evolving relationship with agriculture.

There's a town near me with the actual name of Farmville. No, seriously. Look on a map of Virginia and you'll see it. Nice place, actually. Not poorly animated.

“I hate when I have to harvest at night,” my husband complained the other day. Lately, he’s been trying to maximize his harvests so he can upgrade his combine.

But he’s not a farmer. He’s a practicing lawyer. He said this from his computer as he toggled between a video game and a YouTube video of someone talking about playing the same video game.

I will admit that I go to YouTube and other places sometimes when I get stuck on a game. Sometimes you miss stuff, you know? But what I don't get is people who barely play the game and just watch others play it. Computer gaming to me is active entertainment, and watching other people play is the definition of passive. I mean, I can understand people watching sportsball; we can't all be star athletes. But anyone with enough money to buy a computer or console can play a game themselves.

Not dissing anyone who does this. It's just not something I grok.

As for the lawyer thing, I bet some farmers would love to play Lawyer Simulator.

That game is Farming Simulator. At peak times, up to 90,000 players are active at once.

Never heard of it. I have, obviously, heard of Farmville. Again, not for me (after having spent my childhood on a farm, I'd rather not). But I do understand the draw of that kind of game. It's a resource management game, and I've played a few of those myself—just not with the "farming" theme.

FarmVille, Sim Farm, and many other games simulate farming and rural life with various levels of realism.

If the game doesn't include giant Trump signs, pro-forced-birth posters, a bunch of coal-rolling pickup trucks, Confederate flags, and enormous anti-Democrat billboards, the level of realism is low.

Most players who speculate on grain prices, buy fancy tractors, and rush to harvest fields before they spoil are not farmers in real life.

Well, duh. I've played Civilization, another resource management game, and I'm not a god in real life.

Across the globe, the proportion of people who make their living as farmers is lower than at any time since agriculture became widespread.

That's because it's primarily corporate now.

What do people like my husband, who lives in a city and works every day in an office, find so entertaining about tilling faux fields and tending to pixels representing wheat or sheep?

For the challenge?

And what does this game’s popularity reveal about the deep history of farming and the role of agriculture in people’s lives today?

I'd say "nothing much," but the author has her own opinion.

Much of the next section is devoted to the history of agriculture and civilization, which, perhaps counterintuitively, is the same history. That is, to summarize, it was farming that allowed some people to not be farmers but pursue other specialties, trading their goods to farmers for sustenance.

Until recently, most people lived in a society deeply tied to the rhythms and sensibilities of farming. So, is Farming Simulator a high-tech form of nostalgia for this kind of connection to the land and food?

Yeah, I'm still going with my "people like the challenge of resource management games."

Well, maybe not the challenge so much as the endorphin rush when something goes your way, which is a key element to any game.

For some Farming Simulator players, farming itself may be beside the point. Some are most excited about the machinery and equipment; the newest version of the game features digital re-creations of more than 400 real machines and tools that players can buy with profits from their farms.

That's actually pretty cool.

Farming Simulator players might thus be seeking to escape the constraints of their everyday lives and experiment with new identities.

Gosh. No other game ever does that. Remind me to tell you about the white dragon my 13th-level half-orc cleric slew, by the way. He even got its hide made into plate mail.

Some real farmers who play the game say it lets them experiment with equipment or strategies that are out of their financial reach, given the current economic realities for family farms.

Gotta say, I think that's actually pretty cool, too.

Farming has been fundamental to who we are as humans. And in a world where war, climate change, and pandemics can so easily disrupt global food supply chains, it still is fundamental—but in ways that are less and less within the reach of the average person.

That's a feature, not a bug. Not all of us are cut out to be farmers; that's why other specializations exist. As I've noted numerous times, it's entirely too much like actual work. Wait, no, it is actual work. So I want no part of it.

But again, not dissing anyone. You like to play farming games? Great. Sports games? You do you. Neither of those appeal to me. Lots of games out there for lots of different tastes.

I just think we shouldn't read too much into people's preferences for different types of games. Maybe they're not trying to reconnect with a glorious past (that never really existed anyway), but are just playing out a different kind of fantasy than the ones I prefer, which usually involve dragons, post-apocalyptic wastelands, spaceships, or all of the above—none of which worlds I would want to actually live in.

1 Like • Comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.