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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:

Lazy Writer est 4/24/2008

about 21 hours ago
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

a day ago
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

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
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

Apr 25, 2024 at 3:09am
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

Apr 25, 2024 at 2:58am
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

Apr 24, 2024 at 4:26pm
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

August 19, 2019 at 6:00am

#964418

Missionary Position

http://nautil.us/blog/how-will-our-religions-handle-the-discovery-of-alien-life

How Will Our Religions Handle the Discovery of Alien Life?

Poorly, I'd imagine. Because religions are made up of people, and people will handle it poorly.

For the religious, knowing that life on Earth is not unique may demand radical new ways of thinking about ourselves: How special and sacred are we? Is Earth a privileged place? Do we have an obligation to care for beings on other planets? Should we convert ET to “my” religion? These questions point to a deeper issue about whether our religions can adapt to the idea that humans are not the only sentient beings in the universe capable of worshiping God.

And once again we have the conflation of "extraterrestrial life" with "intelligent space aliens." As I've noted before, those qualities we call "intelligence" aren't required to exist by some Law of Evolution. But... that's not the most egregious assumption made here, is it?

I approach the question of alien life from the standpoint of evolution, and science in general. This doesn't mean I'm right, of course, but I tend to ignore the religious / spiritual questions. This sometimes puts my own thoughts in sync with some of the religious thinking as described in the linked article. That is purely coincidental; when I say something like "intelligent life is probably rare in the galaxy," that does not mean the same thing as when a religious person says something like "humans are unique," even though the statements are roughly similar.

At the same time, I'm not going to conclude that humans are insignificant to be contrary, just because some religious people believe we're somehow special (as in chosen by God or whatever). We're not special, nor are we insignificant. We're just... us.

History has also shown us that many religions don’t hold back to invite or even force non-believers into the fold. The efforts by European colonists and Islamic armies to convert native peoples to Christianity and Islam have an oppressive, bloody history. A similar future could unfold in which one or more of our major religious groups attempts to convert aliens.

Just what we need - religious fanatic space aliens. Can we put some First Contact protocols in place to exclude proselytizers from meeting our new alien overlords? That would be great, thanks.

Is it possible that learning of alien life will encourage us to tolerate the religious beliefs of our fellow humans, too?

Ha ha ha ha ha! Oh, wait; you're serious. Let me laugh some more: Ha ha ha ha!

I note that this author didn't list certain religions in the link. Notably absent as far as major world religions go is Hinduism. I have no idea how Hindus might approach the idea of space aliens (unless, presumably, the aliens resemble cows.) (Is that a rude joke? I don't even know. I don't mean to be rude.)

Also absent from the list is Scientology. While I don't think we could call it a "major" religion in terms of number of adherents, the idea that there are space aliens is, as I understand it anyway, baked into the religion. I have to wonder what they'd think if sentient aliens showed up and have never heard of Xenu.

I'd also be interested in the LDS church's take on the idea.

Anyway, there are a number of problems with this kind of speculation. First one I can think of is that we have, by some measures of "intelligence," several intelligent species here on Earth. Sure, dolphins don't build spaceships, and octopodes don't have vast underwater cities (at least, none that we've found so far), but they and some other species communicate with each other with some sophistication - and yet, we humans can communicate in only the most rudimentary way with these other species. These are species with whom we share a common ancestor; how can we expect to be able to really communicate with alien life?

Another problem is about time. We haven't found evidence of intelligent ETs, or even simple life beyond our world. Finding so much as a microbe (or equivalent) would be a significant event. But will it happen next year, next century? How much longer before we encounter any flying-saucer-pilot type aliens? It's laughable to think that world religions would be the same in 1000 years, considering how different they were 1000 years ago.

Then there's the persistent idea floating around that the reason ETs haven't shown their face-equivalents around here is because we're somehow ideologically impure. Maybe they're waiting for us to outgrow this "religion" stuff, or at least the "killing in the name of" part of it. Or maybe they're waiting for all of us to convert to Scientology. I think the whole "waiting for humanity to grow up" crap is little more than self-flagellation, personally. Yeah, yeah, I get it - you think humanity sucks and you're projecting that onto the motivations of purely hypothetical life-forms the nature of which we have no way of knowing.

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