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Friday, Nov. 1, 2024

2:37am 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 2, 2020 at 12:06am

#972434

Livin' In The Future

PROMPT January 2nd

Yesterday, we looked to the past. Today, we’ll write about the future! (No resolutions, I promise, Robert

)

2030 sounds so futuristic, but it’s only ten years away! What do you think the world will be like ten years from now? What inventions do you think we will have by then? What are some changes you think will happen in the world in the next ten years?

I discovered science fiction young.

Between the TV shows like Star Trek, short stories (which were still a published thing at the time), novels and even comic books, I got to see what I thought were different authors' visions of The Future™.

Later, I came to understand that it is not the job of a science fiction author to foretell the future; it is his or her job to prevent it.

I don't mean the post-apocalyptic wasteland subgenre, or not just that. I mean that science fiction is, essentially, a philosophical form of writing that explores the repercussions of change on humans and their societies. "But not all science fiction is like that," one might object. "Sometimes it's just space empires and adventure stories." This is not the place to get into the fine details of what is and is not science fiction; besides, any such argument starts to wiggle perilously close to the No True Scotsman logical fallacy. Yes, I understand the objection. In rebuttal, I'll just post a link to Sturgeon's Law.

Notably, Theodore Sturgeon was a science fiction author.

Point being, every once in a while you come across a "news" story or fluff piece that explores what this or that science fiction author "got right" and what they "got wrong." While sometimes intriguing, they miss the point; again, SF authors aren't here to foretell the future. On those occasions when they do explicitly foretell the future, the only reason they might have a slightly better track record is because they are, pretty much by definition, interested in the trends of science and technology, and anyone with such interests can prognosticate some advancements to some degree of accuracy.

On the other hand, those are some of my interests as well, and yet I have no idea what things are going to look like in 10 years because it's not just about science and inventions; it's also about human interaction with them.

Let me provide a quick example. It was fairly common, in the 60s and 70s, to predict the advent of videophones. As I recall, the idea was you have the existing telephone line technology, only instead of just having an audio transmission, you also have a video screen. Some enterprising individuals even figured out how to make the things work. But people freaked out. What if someone calls when I'm getting out of the shower? What if my hair is a mess? What if my house in the background is a mess? So, even though we had the technology, in spite of science fiction "predictions," the vidphone never caught on.

At least, not until phones were basically replaced by computers, smartphones and other internet - connected devices, at which point people started Skyping and videoconferencing and whatnot. It was the vidphone, manifest at last - but in a way that I don't think anybody foresaw.

It was a failure of imagination all around. The general public couldn't conceive of a way to make a phone call without the traditional "run to the phone to answer it when it rings" routine. Would-be vidphone makers couldn't come up with a way to change that routine, or otherwise alleviate the public's distrust of the concept. It was only when a lot of other factors came together, both technological and social, that we could have the effective equivalent of the videophone.

I see similar arguments playing out around the idea of self-driving cars, right now. Lots of people are distrustful of them, in the same way lots of people are scared shitless of flying because of the possibility of a plane crash, but think little of speeding to the airport if they're a little late. The chance of death or serious injury is many orders of magnitude higher in the latter case, but people focus on the former possibility.

Right now, in the US, about 40,000 people die each year in auto accidents. That number's fuzzy, but let's use it for arguments' sake. You can also find statistics by miles driven if you look for them; I can't be arsed. Logically, then, if we can switch to self-driving cars and get that number down by at least one or two standard deviations - say to around 32,000 - then autonomous vehicles could be shown to be inherently safer than human drivers, and in a perfect world, we'd just switch over.

But an autonomous vehicle killed one pedestrian, and the consensus became "we can't have these things; they're too dangerous." We're apparently perfectly okay with killing 40,000 of ourselves every year rather than reducing that number by changing the way things work.

People, in short, are fundamentally illogical. And that is why you shouldn't trust anyone who says "this is the way things will be in 2030." Not even me. There's no telling how the public will react to a change, either from without or within.

But I will make one prediction that you should definitely take seriously: People are not going to fundamentally change.

And that's why we continue to need science fiction: to prepare us non-changing meatsacks for the things that do change, be it technology, scientific discoveries, unexpected breakthroughs, alien invasion, the zombie apocalypse, 40 foot sea level rise, nuclear annihilation, or the inevitable takeover of all forms of entertainment and government by Disney.

Don't worry, darlin'
No baby, don't you fret
We're livin' in the future
And none of this has happened yet

7 Like • Comment • View 11 comments

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