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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 10 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

February 27, 2020 at 12:03am

#976432

The Original Dark Side

First, let me set the mood here.

Got that going? Good.

Now a few words about The Wizard of Oz.

http://www.bbc.com/culture/story/20190808-the-subversive-messages-hidden-in-the-...

The subversive messages hidden in The Wizard of Oz
It’s easy to mistake the 1939 classic as traditional family entertainment – but 80 years on from its release, the musical is more radical and surreal than ever, writes Nicholas Barber.

(Article is dated six months ago, near the actual 80 year anniversary)

In December 1937, Walt Disney Productions released its first feature-length cartoon, Snow White and the Seven Dwarfs. It went on to be cinema’s biggest hit of 1938, a success that not only encouraged Disney to make other fairy-tale cartoons for decades to come, but also encouraged another studio, Metro-Goldwyn-Mayer, to try its own fantasy musical about an orphaned girl and a wicked witch: The Wizard of Oz.

80 years on, Disney has clearly won that particular war. Only now they're making fairy tales about superheroes and Jedi. Whatever works.

The pig-tailed Dorothy Gale (Judy Garland) is so wholesome, the Harburg and Arlen songs are so delightful, and the Technicolor adventures are so exciting that it’s still easy to mistake The Wizard of Oz for traditional family entertainment, 80 years on from its release in August 1939. But it upends the conventions of good-v-evil storytelling in ways that would have had Walt Disney fuming.

Much has been written about the symbolism inherent in Oz. I won't belabor the point here, but there's definitely a darkness to it. The article skips the symbolism, too, opting instead to look at the movie through the lens of world events at the time, as well as the things we've experienced and learned since.

The message is that people will march behind any authority figure who makes a splash, however undeserving they may be. It’s a subversive message in 2019, and it was even more pointed in 1939, when fascist dictators were stomping across Europe.

Or, perhaps, haven't quite learned.

It’s significant, too, that the Emerald City of Oz isn’t the turreted faux-medieval Ruritania where Snow White lives, nor is it the Istanbul-ish collection of domes and spires drawn by WW Denslow in the original book’s illustrations. Instead, it is a modernist mass of neon-striped skyscrapers – and, like almost everything else in the land of Oz, it is blatantly artificial.

Yeah, that's not just an artifact of the limited capabilities of special effects in 1939. A lot of it was deliberate.

A couple of years back, someone decided that it would be a good idea to update Oz (the book and its sequels) into a series called Emerald City. It, too, was a reflection of its time, our time, dealing with modern issues of feminism, gender, and culture clashes, especially the one between science and religion. Critics were less than thrilled. Critics aren't always right, though; in my own opinion, the series started out very strong, but devolved into chaos. I maintain it's worth watching, though it was cancelled after only one season.

Notably, the showrunners knew about and exploited the popular connection between Pink Floyd's Dark Side of the Moon and The Wizard of Oz. If you don't know what I'm talking about, here: https://ultimateclassicrock.com/pink-floyd-dark-side-wizard-of-oz/

It's important, I think, to experience entertainment in the context of its time. A lot of the songs from the late 60s and early 70s, for example, are impenetrable if you don't know about the Vietnam War. But we tend to ignore history, or, worse, forget about it, so the occasional article like this one helps us to keep things in perspective.

5 Like • Comment • View 3 comments

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