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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

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Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

GeminiGem of House Lannister

a day ago
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

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

November 18, 2018 at 1:07am

#945780

Thanks

With Thanksgiving just a few days away, there are three things I can be sure of:

1) A plethora of "helpful" articles on the internet about traveling over the Thanksgiving holiday;
2) Nonstop ads and news "stories" about Christmas shopping;
3) Endless talk about being grateful.

I've heard people wondering why atheists observe Thanksgiving. After all, who or what are we thanking? Well, fortunately for you, I'm here to atheixplain.

There are two distinct forms of gratitude. The first is what I talked about in my last blog entry: simply expressing gratitude to someone who has done you a service (whether or not you paid for it). Religious, or spiritual, people use God, or gods, or the Goddess, or the Universe, or whatever, as the target of their gratitude, because they feel the deity (or whatever) has done them a service, so for them, it's all this first type. I have some experience with this, because I used to be religious. Of course, there's a great deal of variation among religious/spiritual people, so I'm sure one can find counterexamples, but I'm writing about generalities.

The second form of gratitude doesn't have a target. Or, perhaps, the target can be one's younger self - which certainly doesn't qualify as a deity, but what Young You did might have set the stage for today's bounty. Either way, this kind of gratitude, I think, is more about expressing a feeling of appreciation for what one has. It's an internal thing, a kind of acknowledgement that, okay, things could always be worse, but I'm going to focus on the positive.

In a more logical language than English (should one actually exist), perhaps these two expressions might be described by different words, much as the Greeks had more than one term for "love," or (and this is probably apocryphal) some Inuit supposedly have a multitude of words for "snow."

Because of this second definition, atheists can be perfectly happy to celebrate Thanksgiving in the US. I'd argue that, either way, you're acknowledging that things could be worse - and that has certain psychological benefits. Rather than dwelling on regrets, drama, or missed opportunities, you're reflecting on all that is good and helpful in your life: family, friends, french fries, fuckbuddies, finances... whatever.

Also, there's stuffing ("dressing" for my fellow Southerners). That in itself is sufficient reason to have a traditional Thanksgiving, regardless of one's religious or political point of view.

Unfortunately for me, I'm a bit of a contrarian. Okay, I'm a lot of a contrarian. In the past, I've purposely made lists on or around Thanksgiving of the things for which I am most decidedly not grateful. Telemarketers. Ice storms. Coors Light. Autoplay videos on websites. The cancellation of Sense8. Those sorts of things.

But I... I don't think I'm that person anymore. Near-death experiences can do that, I've heard. And I've had at least four of those, so sometimes the Universe or karma or fate or whatever has to kick me in the balls a few times before I'll pay attention. I just hope that doesn't mean I'm losing my edge. When snark becomes part of your personality, you come to depend upon it.

So... I'm grateful that I almost died at least four times? Maybe? It's probably disappointing to other people, though. Just goes to show that you can't please everyone, so you might as well drink.

Thank you, scotch!

6 Like • Comment • View 3 comments

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