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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:

Kåre Enga in Udon Thani

a day ago
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

a day ago
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

a day ago
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

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

October 22, 2019 at 12:11am

#968243

StairMaster to Heaven

Buckle up.

https://waitbutwhy.com/2014/10/religion-for-the-nonreligious.html

Religion for the Nonreligious

Rarely has a domain name been so appropriate. "Wait but why?"

You go to school, study hard, get a degree, and you’re pleased with yourself. But are you wiser?

"Wiser" is an unmeasurable comparative.

You get a job ...[long list of career-related crap]... But are you happier?

Other things matter besides happiness. Take care of those and the happiness emerges naturally.

You do all kinds of life things—you buy groceries, read articles, get haircuts, chew things, take out the trash, buy a car, brush your teeth, shit, sneeze, shave, stretch, get drunk, put salt on things, have sex with someone^{[citation needed]}, charge your laptop...

Yes. We get it. We all do stuff. If we don't, we sit around and do nothing. While that's nice from time to time, even my cats get bored if they're not chasing something for at least a few minutes a day.

But as you do these things day after day and year after year, are you improving as a human in a meaningful way?

Going back to my cats, I don't see them being concerned about improving as a cat in a meaningful way. But okay, I'm human, and I think things and have some concern about the future beyond when someone is going to give me my next bowl of kibble, so I'll play along.

In the last post, I described the way my own path had led me to be an atheist—but how in my satisfaction with being proudly nonreligious, I never gave serious thought to an active approach to internal improvement—hindering my own evolution in the process.

That sounds like a personal problem to me. Even when I realized I was an atheist, I never stopped trying to improve myself (though I slowed down a lot when I was depressed). In fact, I worked harder at it because I realized that without accepting a higher power, it's all the more important to improve oneself. Also, stop confusing people with the "evolution" thing; it's distracting.

Society at large focuses on shallow things...^{[citation needed]}

Considering that the human mind is an ocean of complexity that creates every part of our reality...^{[citation nee- oh, hell, there's going to be more of these assertions without evidence, isn't there?]}

And then the author gets into some really weird and possibly misleading graphics about consciousness and enlightenment or whatever. Obviously, I can't reproduce them here; you're just going to have to go to the link to see what I'm talking about.

Suffice it to say that atheism in itself isn't any guarantee of intelligence or understanding. Neither, of course, is religion. Or spirituality. And this seems to be a weird kind of spiritual atheism, which is fine, but then they talk about "truth" and present speculation as fact.

I have to admit, I started skimming and looking at the MS Paint drawings. It seems to delve into New Age-y etheria, though, with all kinds of metaphors presented as fact.

Remember a few days ago when I found an article that asserted that the thing that most differentiates us from other animals is our ability to dive deep into metaphor? This is the dark side of that.

Thing is, though, I think the author makes some decent points. I'm sure you can find them yourself if you're up for it. But then he comes up with stuff like:

There are really two options when thinking about the big, big picture: be humble or be absurd.

Bit limiting, isn't it? I'd pick "be curious" or "be open-minded" as alternatives; neither are absurd or require particular humility. I mean, maybe in the sense that to realize you don't know everything is a kind of humility, I guess? Or it's just a facing of reality.

To me, complete rational logic tells me to be atheist about all of the Earth’s religions and utterly agnostic about the nature of our existence or the possible existence of a higher being. I don’t arrive there via any form of faith, just by logic.

Then you're not atheist; you're agnostic. By most accepted definitions of those two words. You even said the word. I mean, I don't care, either way, but this is confusing to people.

Labels sometimes just get in the way. So do bad MS Paint drawings.

2 Like • Comment

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