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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 16 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

about 19 hours ago
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

a day ago
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 20, 2019 at 1:01am

#964457

Idle Ideals

https://www.theguardian.com/technology/2017/may/08/virtual-reality-religion-robo...

The meaning of life in a world without work

Okay, I'm thinking, this should be good. I haven't done "work" in about a decade, and I almost never miss it.

As technology renders jobs obsolete, what will keep us busy? Sapiens author Yuval Noah Harari examines ‘the useless class’ and a new quest for purpose

"Usefulness" is overrated, anyway. So is "purpose."

The same technology that renders humans useless might also make it feasible to feed and support the unemployable masses through some scheme of universal basic income. The real problem will then be to keep the masses occupied and content.

I'm not going to turn this post into a discussion of UBI. Just know that I'm sure that it has positives and negatives, and I'm even more sure that here in the US, we will fuck it up royally.

People must engage in purposeful activities, or they go crazy. So what will the useless class do all day?

Must we? Must we, really? I guess if that's true, then I'm officially crazy. Well, that shouldn't come as any surprise.

One answer might be computer games. Economically redundant people might spend increasing amounts of time within 3D virtual reality worlds, which would provide them with far more excitement and emotional engagement than the “real world” outside.

Ah. Well, that explains me.

This, in fact, is a very old solution. For thousands of years, billions of people have found meaning in playing virtual reality games. In the past, we have called these virtual reality games “religions”.

Ooooooh! BURN.

Muslims and Christians go through life trying to gain points in their favorite virtual reality game. If you pray every day, you get points. If you forget to pray, you lose points. If by the end of your life you gain enough points, then after you die you go to the next level of the game (aka heaven).

Okay, look, I'm no fan of organized religion, but even I think this may be taking things a bit too far.

The idea of finding meaning in life by playing virtual reality games is of course common not just to religions, but also to secular ideologies and lifestyles. Consumerism too is a virtual reality game. You gain points by acquiring new cars, buying expensive brands and taking vacations abroad, and if you have more points than everybody else, you tell yourself you won the game.

Okay, now you're stretching. Fine, I can see that some people think of things this way, but I'm not convinced.

In the end, the real action always takes place inside the human brain. Does it matter whether the neurons are stimulated by observing pixels on a computer screen, by looking outside the windows of a Caribbean resort, or by seeing heaven in our mind’s eyes? In all cases, the meaning we ascribe to what we see is generated by our own minds.

Saved. Now the author has come back around to what I've been saying for a long time: there is no meaning to life, save that which we impose upon it.

In any case, the end of work will not necessarily mean the end of meaning, because meaning is generated by imagining rather than by working. Work is essential for meaning only according to some ideologies and lifestyles. Eighteenth-century English country squires, present-day ultra-orthodox Jews, and children in all cultures and eras have found a lot of interest and meaning in life even without working. People in 2050 will probably be able to play deeper games and to construct more complex virtual worlds than in any previous time in history.

And that is an interesting point. I've never been on board with the Protestant work ethic, partly because I've never been Protestant, and partly because to me, the only purpose of work is to accumulate enough money to live with all the basic necessities and a few luxuries (with the luxuries becoming more and more important with time).

Problem is this: Back in the 1970s, when computers started to insert themselves into our daily lives, promises were made. These promises took the form of something like: "As computers become more prevalent, our productivity will increase. Paperwork will become a thing of the past, and we could work for no more than 10 hours a week."

Oh, you sweet summer disco children... how wrong you were. Okay, maybe paperwork has become more electronic, but instead of maintaining our 1970s productivity with a reduction in time spent working, we've expected greater and greater productivity... and, worse, we're expected to work more than the standard 40 hours a week to get shit done.

So I take projections like this with a grain of salt. Society, especially a society as rooted in Puritanism and work-worship as ours is, won't let its members have significant downtime. "Idle hands do the devil's work," as the saying goes. No, this utopian vision of the future will never pan out.

Besides, we probably won't be around long enough to give it a chance to do so.

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