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Friday, Nov. 1, 2024

2:23am 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 9 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 12, 2020 at 12:30am

#973200

Tougher Than the Rest

PROMPT January 12th

Describe a time when you exhibited bravery.

Well, one time I touched a cat's belly fur...

Or... no, I shouldn't talk about it.

Okay, fine; I've been drinking, so I'll talk about it.

Long, long ago, when I was young and stupid (as opposed to now, when I am old and stupid), I was banging this married chick. She lived a couple hours away, right on the edge of the state, and sometimes I'd go over there on Friday nights and stay the weekend. The alternative was staying home and dealing with my first ex-wife, who hadn't yet moved out.

The woman's husband, a long-distance trucker, was never home.

One time I went over there, on invitation, and he was home.

So I played it cool. Just friends. Hanging out. No big deal.

Until he brought out the guns.

"Hey, Bob, let's go target shootin' in the woods."

Gulp.

Oh well. I'd recently been in bed with two hot redheads (the wife in question was one of them), so I figured this was as good a time as any to slip the bonds of this mortal coil. I just hoped he would make it quick. So I agreed, and he handed me one of the rifles.

A bit more background: as I've noted here before, I spent my childhood in rural Virginia. Rifles and shotguns were just tools to me - like tractors or scythes, things with a purpose that also happened to be dangerous, so my dad had instilled in me safety procedures for the various farm implements, including guns. Some of these procedures actually stuck. There wasn't any of the modern-day abject fear of the weapons themselves in me; I'd been shooting rifles, shotguns and even pistols since I was old enough to stay upright after the recoil.

Fear of jealous husbands, now, that's another story. I'd always said that I wanted to die by being shot in the back by one whilst trying to escape out a window, but what I meant was it should happen when I was 100 years old.

Not 30.

Besides, the guns, as it turned out, were old-fashioned single-shot muzzle-loaders. I'd never fired one, and I was curious. As I recall - this was, of course, some time ago - you stood the weapon upright, packed in a charge of black powder in a little sack, and then packed the lead ball on top of that. After, you didn't want to point the gun down, lest the bullet fall out. All of this, The Husband explained to me as we stood out back of their house, a paper target tacked to a tree just over the property line on National Park land (this was probably illegal, but that was the absolute least of my worries at the time).

Spoiler alert: he didn't shoot me. In fact, I think that either he believed that I was just some random friend she'd found on the then-nascent internet, or - more likely - he knew that his job kept him away from home for extended periods, and he didn't begrudge his wife the occasional dalliance.

(I should further note, here, that I was between wives at the time. My first wife had just asked for a divorce, harsh things were said, and she finished with "I hope you get what you deserve." She'd said it in a way that implied that she thought I deserved getting my nuts stuck in a paper shredder. So we officially separated. It was that weekend that I found myself between two hot redheads. Later, after we'd divorced and gotten on speaking terms again, we had a good laugh about that.)

So, in retrospect, I think The Husband just wanted to see if the dude his wife was banging had the stones to go out back with a larger guy who was holding a gun. Whatever the reason, I learned my lesson. No more married chicks for me. Well, except for the one other time, but my excuse there is she was married to me.

Oh, and for the record? I was a much better shot.

Some girls they want a handsome Dan
Or some good-lookin' Joe
On their arm some girls like a sweet-talkin' Romeo
Well 'round here baby
I learned you get what you can get
So if you're rough enough for love
Honey I'm tougher than the rest

6 Like • Comment • View 9 comments

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