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Complex Numbers

by Spirit HalloWaltz

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 5 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

Spirit HalloWaltz

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

Spirit HalloWaltz

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

December 2, 2019 at 12:12am

#970837

Pure Imagination

https://www.vox.com/science-and-health/2017/10/18/15995478/chocolate-health-bene...

Dark chocolate is now a health food. Here’s how that happened.

Let me guess - Willy Wonka paid for "scientific" studies.

The Mars company has sponsored hundreds of scientific studies to show cocoa is good for you.

See? Cynics are usually right. Shunned and ignored, but right.

A year after James Cadbury, the 30-something great-great-great-grandson of the British chocolatier John Cadbury, launched his luxury cocoa startup in 2016, he introduced an avocado chocolate bar.

Way to destroy both avocado and chocolate, Jim.

The company promised to deliver the nutrition of avocados — in a chocolate bar. Journalists were dazzled.

Journalists shouldn't be dazzled. Journalists should be even more cynical - and skeptical - than I am. But we live in the 21st Century and, clearly, in Bizarro World.

Big Chocolate’s investment in health science was a marketing masterstroke, catapulting dark chocolate into the superfood realm along with red wine, blueberries, and avocados — and helping to sell more candy.

I'm a big fan of science. I'm also a big fan of chocolate. But science mixed with chocolate is like... M&Ms mixed with Skittles. I had a chaotic evil Dungeon Master who did that once. Once.

Point is, science, especially when it comes to food and nutrition, is largely statistical. And you know what Twain said about statistics.

Actually, Twain said (or, more accurately, wrote), "There are three kinds of lies: lies, damned lies, and statistics," but he didn't come up with it. So that's a lie too. It's lies all the way down!

Which brings me back to healthy chocolate.

Such overwhelmingly positive findings suggest this area of industry-funded nutrition science may be biased.

YA THINK?!

Fawning cocoa coverage is so pervasive, one journalist even created a bad chocolate study, suggesting the candy promotes weight loss. His goal was to fool the media into picking it up and make a point about how easy it is to do so. (It worked.)

I find that hilarious. And sad. Sadlarious.

“I don’t want to be cynical — a lot of their science is good; it’s put in peer-reviewed journals,” Coe added. “But just keep in mind that too much of anything is not really good. If you’re hooked on chocolate, you’re hooked on sugar.”

Funny you should mention sugar. Turns out a whole bunch of studies have been done on sugar as well, and it appears that added sugars are Really Fucking Bad For You. There might well be bias in that science as well, but you don't hear as much about it. Now, me, I prefer chocolate that's as bitter as my ex-wife and as dark as her lawyer's heart, but the vast majority of people? "Oh, I hear chocolate is good for you so I'mma eat this whole bag of M&Ms." Like one guy I knew who heard that red wine was good for you so he chugged a gallon of it every day. Pretty sure he's dead now. Liver and pancreas got into a fight and he exploded.

Still, most nutritional studies that you hear about are touting the health benefits of foods that taste like ass. Kale, for example. I was shocked to learn recently, by the way, that there was supposedly a time when no one had heard of kale. Shocked, because my family grew that by the bushel in the garden and sold it at farmers' markets when I was a kid. Always hated that stuff. It's only recently that I figured out how to make it palatable.

And that's one problem with "health" foods - the Puritan undertones of American society steer us away from believing that anything can be good for you if it's not like doing penance. Which is probably why so many people are eager to believe the chocolate stories - they reverse the narrative.

My personal opinion? Eat chocolate. Don't make it a "guilty pleasure." Don't pretend it's a health food. Just enjoy it for what it is - limit yourself if you have to (I certainly do), but god DAMN I'm tired of all the anxiety and neuroses surrounding food and drink these days.

1 Like • Comment • View 3 comments

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