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Friday, Nov. 1, 2024

12:25am EDT

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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:

tj: Tenebrous Jekyll

about 7 hours ago
In response to "Phases"

Perhaps, if the full moon drives one to madness, the half moon will only make one half-crazy.

1 Like

Battywyn🎶

Oct 29, 2024 at 12:18pm
In response to "The Numbers Don't Lie"

I hear ya. I like to think I'm discerning enough to detect fakes, but that might just be my ego talking. When it comes to local businesses, I also go to social media and request recommendations. With both reviews from strangers and recommendations from friends, I give more credence when more (anecdotal, heh) details are provided. It's more an art than science, but liars either have such flawless details that their story sounds fabricated, or they get embarrassed when they trip themselves up. Truthtellers make errors, because memories are fallible, but they get more confused than embarrassed. Ultimately, the only way to really know is to try the product/service yourself. Which is why you'll hear about my Cancun vacation next month, but you don't have to believe me.

1 Like

Robert Waltz

Oct 29, 2024 at 11:07am
In response to "The Numbers Don't Lie"

Battywyn🎶

- I, too, look at the 1-star reviews, though again, reviews aren't my sole criteria. But sometimes it's blatant fake reviewing from the competition: "Don't stay here! It has rats, bedbugs, and roaches! Stay at this other place instead!" where "this other place" is clearly owned by the reviewer.

On the other paw, five-star reviews are often salted by the establishment in question.

Used to be, you could look at the four- and two- star reviews to get more honest, nuanced opinions, but the establishments, and their competition, have figured out that trick.

Which is one reason why reviews aren't my sole criteria.

(None of this applies to WDC reviews, or to the artificially inflated Uber rating system)

Battywyn🎶

Oct 29, 2024 at 11:00am
In response to "The Numbers Don't Lie"

And I was going to conclude by saying, when evaluating Caribbean vacation destinations, even if 5,000 people gave it a 4.8 rating, if the one star reviews were from seven people who encountered rats in their rooms, I'm very likely to not choose this destination.

2 Like

Battywyn🎶

Oct 29, 2024 at 10:58am
In response to "The Numbers Don't Lie"

Well, that was annoying. I was still in the process of editing, so please excuse the multitude of errors. I also intended to italicize the quotes from your post. Stupid f****** Parkinson's.

1 Like

Battywyn🎶

Oct 29, 2024 at 10:56am
In response to "The Numbers Don't Lie"

You know what sometimes lies? Anecdotes.

Also, dogs, I've heard.

Oh, hell no.

🤣 I love a good inside joke, but my marketing guru would tell you to cross link here

The fallacy is named after Robert McNamara, the U.S. Secretary of Defense during the Vietnam War, where his over-reliance on measurable data led to several misguided strategies

Bet he's proud of his claim to fame.

What's the point in data, then?

The point in data is a decimal separator, unless here in non-english speaking countries, in which case it's more likely a thousands separator.

So, whenever I'm evaluating online reviews for pretty much anything, and for the record I check them for almost everything - I always consider three things: 1. The average rating (eg, number of stars); 2. The The number of contributors to the rating; and three. What the one star ratings say.

1 Like

Annette

Oct 28, 2024 at 2:47pm
In response to "Waste Not"

In Southern California, every single family residence has a green bin. Every trash day, three different trucks make the rounds.

1 for composting
1 for recycling
1 for garbage

Trader Joe's sells almost exclusively packaged foods, even perishables. They have contracts with college food pantries. In many colleges, there are now pantries that are open to the students 4 or 5 days a week plus 1 day when people from the community can drive up and receive a bag with a mix of fresh fruits and vegetables along with non-perishable foods and donated sundries.

Churches are huge food redistribution centers also.

The "too hard to set up" systems have created good jobs here. Instead of seeing food donations as a liability, they have created a supervised and refrigerated second market.

The cost for employees is small because, of course, many of the positions are volunteers. But the supervisors and some of the staff are full time employees with benefits.

The article has thrown up obstacles that are easy to overcome.

3 Like

AnotherDreamer

Oct 28, 2024 at 11:33am
In response to "Waste Not"

https://cdn.prod.website-files.com/6156cebc4c605e281289a232/6156cebc4c605eb8bc89... e%20for%20beginners%2024%2009%2018.pdf

1 Like

Robert Waltz

Oct 28, 2024 at 11:33am
In response to "Waste Not"

AnotherDreamer

- Hey, it's a replicator from Star Trek!

Now let's invent the holodeck.

2 Like

AnotherDreamer

Oct 28, 2024 at 11:27am
In response to "Waste Not"

We the people of the world could use those products before they are compost as free sources for 3D printed foods that could be used for emergency food, or if tasty enough, re sold.https://builtin.com/articles/3d-printed-food

2 Like

January 29, 2020 at 12:06am

#974473

After All

PROMPT January 29

Everyone did a great job with filling the war chest yesterday! There's so many great prompts and I'm sure Em will love every one of them.

Since today *is* War Chest Wednesday, I'm going to grab one.

What is your favorite virtue? Give a few examples like kindness, cleanliness, tact, truth, generosity. Is your favorite one you possess, or one you simply admire in other people? Do you have a strategy to develop it yourself?

Prompt is courtesy of ผีKåreEngaในMontana

Snark.

Wait, is that a virtue? No? Everyone hates it? Well, shit.

I'm glad ผีKåreEngaในMontana's other idea, the one involving a certain mouthless feline, didn't make it into the prompt. Still, I find the juxtaposition of "tact" and "truth" amusing, since those are sometimes incompatible.

Other examples of virtues? Well, I suppose there are two loosely defined kinds of virtues: directed toward the self, such as tenacity, self-control, or mental flexibility; and directed toward others, like charity, fairness, and loyalty. There might be a third kind, but it's intertwined with religion, and one does not need to be religion to be virtuous; sometimes, it seems, religion gets in the way.

But there's one virtue that, I think, influences many of these others, both inward and outward, and that is compassion. One can be compassionate to others, obviously; but it's also good to be compassionate to oneself. I know I'm harder on myself than I am on others, and I could stand to cut myself a little slack now and then.

Unfortunately, for myself, compassion isn't something that comes naturally. I have to think about it deliberately. I mean, my first reaction when someone's holding up a line at the grocery store, or cutting me off in traffic, or trying to sell me insurance, is usually annoyance. I have to reach for serenity, and I have to reach for compassion: knowing, logically, that everyone is the star of their own show, and they can each justify their own actions, and maybe they're just having a bad day. Maybe their dog just died, or their house has a leak, or they're worried about a friend.

And yet, compassion is the one thing I want to strive for. On a purely selfish level, it helps me as a writer to try to see others' points of view. But more importantly, I think that if I could crack the code of compassion, perhaps other people will appreciate it if they know someone cares about what they're going through, whatever that may be.

There was some discussion a while back about what people are "really" like. I believe that we have to practice being who we want to become. If something that you want to be isn't a part of your character, is it "fake" to try to practice that virtue until it becomes a part of you? I don't think so, myself; otherwise, how could any of us deliberately change? So, no, I'm not a compassionate person. But I'm working on it.

I'm not very good at it. It's not like I can learn it like I'm learning French, or like I learned how to do engineering. But I've seen peoples' actions that I have identified as "compassionate," and that's what I strive to emulate.

One such person that stands out for me is a lesser-known singer/songwriter named Dar Williams, who as far as I'm concerned is the Avatar of Compassion -- so it's her song I'm going to feature to tie in with this theme.

Go ahead push your luck
Find out how much love the world can hold
Once upon a time I had control and reined my soul in tight

Well the whole truth
Is like the story of a wave unfurled
But I held the evil of the world
So I stopped the tide froze it up from inside
And it felt like
A winter machine that you go through and then
You catch your breath and winter starts again
And everyone else is spring bound

And when I chose to live
There was no joy it's just a line I crossed
It wasn't worth the pain my death would cost
So I was not lost or found
And if I was to sleep

I knew my family had more truth to tell
And so I traveled down a whispering well
To know myself through them...

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