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Friday, Nov. 1, 2024

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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 13, 2020 at 12:16am

#973273

Battle of Evermore

PROMPT January 13th

In your entry today, write about games! Board games, video games, card games, sports games, mind games, etc... Share a memorable story.

I'll skip the mind games, thanks very much. Had enough of those when I was married.

I gamble on occasion, but I've only played poker in a casino once, just to say I did it. I wasn't the first one out, and that's the best I can say about that. Mostly, I stick to blackjack; I understand the odds and strategies there. Roulette is too random, and dice games are, well, dicey. Slot machines are pretty much just vehicles to part people from money, but I sometimes play them anyway; they can be entertaining and, what the hell, sometimes I get some of the money back.

I don't like sports. Not watching, not participating. Last time I was at someone's house watching football, I was struck by just how little is actually going on, between all the penalty flags and shots of angry sideline coaches and idiotic commercial breaks. I know sports-watching is a big part of a lot of peoples' lives, though, and I'm not judging. You like what you like. The closest I get is sometimes I enjoy watching martial arts competitions.

In practice, the games I play most are single-player video games, preferably of the open-world variety. Examples are the Elder Scrolls titles and the Fallout series. I detest most multiplayer games, because there's a high percentage of assholes in the gaming "community."

But if I find a group of people who don't suck, I'll play the hell out of D&D (or other roleplaying games of its ilk). This kind of game emphasizes cooperation over competition; there are competitive board games that I play, but I have to avoid both smug winners and sore losers. As I've noted here before, I don't like winning or losing; I prefer the teamwork aspect. Also, at their core, RPGs are about storytelling, and, well... look where we are.

So, since I saw the prompt, I've been racking my gray matter trying to come up with a compelling gaming story. I know I have a lot of them - lots of memorable characters and groups over the years, and when I'm playing one of these games, often something will remind me of an epic battle or hilarious situation. Naturally, now, when I try to think of one, they disappear into the mist.

There was the time I was DMing and the party was tracking trolls. Said trolls had retreated to their lairs, which were in a series of caves in the side of a cliff. Trolls were better climbers than the party, and no one wanted to be the first one into a dark, smelly troll cave that was sure to be an ambush, so they hit on a solution: they tied the halfling to a rope and lowered him down from the top of the cliff, the idea being that if they saw a craggy troll hand swiping at the hapless thief, they knew there were trolls in that particular cave. But if they didn't, then that was probably the cave to enter so they could set up their own ambush. I mean, the halfling wasn't good for much else except picking the occasional lock and the party's pockets, so he was expendable.

Or there was the time when I was playing a halfling, myself (being sure to not be annoying to the other party members - well, not annoying enough that they'd use my character to fish for trolls). He ended up as werewolf chow, as I recall. Turns out that when you piss off a werewolf, you don't have to run faster than the werewolf; you just have to run faster than the slowest party member. Which is almost always the halfling.

And then there was the time I was playing a not-very-annoying human fighter-type with a big honkin' claymore. Our party managed to piss off not one, but two armies: the orcs caught us stealing from them, but we got away; and the human army we were supposed to be working for kicked us out because the party's bard managed to flub a Persuasion check (not easy to flub a persuasion check if you're a bard, but he managed somehow). So we spent the next two or three gaming sessions fighting off scouting parties from both sides until, having enough of that nonsense, we hit upon a plan:

First, we snuck into the orc camp at night and eliminated a few of them, being sure to "accidentally" drop a scroll of "orders" from the "human army" that read something like, "Your orders: go kill some of the orcs and make it look like the renegades [my adventuring party] did it. Signed, General Brod of [the human army]." The DM made the appropriate dice rolls, and the deception worked.

Next thing we know, we're watching from the forest as a hundred+ angry orcs descend upon the camp of our former employers. The orcs won, but only after taking heavy losses - heavy enough so that we were able to clean up the few remaining - and gave us the spoils of not one, but two, military camps.

Then, of course, the DM decided that was too easy and sicced a dragon on us, but that's another story.

The apples turn to brown and black, the tyrant's face is red.
Oh the war is common cry, pick up you swords and fly.
The sky is filled with good and bad
That mortals never know.
Oh, well, the night is long, the beads of time pass slow,
Tired eyes on the sunrise, waiting for the eastern glow.
The pain of war cannot exceed
The woe of aftermath,
The drums will shake the castle wall,
The ring wraiths ride in black, ride on.

5 Like • Comment • View 5 comments

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