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Friday, Nov. 1, 2024

12:41am 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 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 25, 2020 at 12:03am

#974136

Twist In My Sobriety

PROMPT January 25

CREATION SATURDAY! Put on your creative thinking caps

You're headed down to Imagination Station to pick up your imaginary friend.

Tell us about the friend - is it human? Humanoid? Animal? Talking banana? Three-headed monster who's afraid of heating blankets? What's their story? Likes/Dislikes? What name do they answer to? Why are they in your life?

Don't forget to tell us how your friend ended up at the station in the first place!

Obviously, Imagination Station is a bar, and my imaginary friend is a beer.

Not just any beer, of course; that would be silly, because then it wouldn't be imaginary. No, this one is magical -- well, more magical than usual, if that's even possible -- so it never runs out, or away.

Beer has been around since the dawn of civilization. Arguments have been made, compelling ones, that there was a causal link there, that beer is what kick-started civilization. There were probably other factors, notably cats, but the manufacturing of beer required a level of cooperation that only cities could provide. That's what civilization is, you know: cooperation and specialization.

So Beer didn't "end up" at Imagination Station. Imagination Station was built around Beer.

Incidentally, as similar as the names are, there doesn't seem to be an etymological connection between "bar" and "beer." The former is named for the counter where drinks are poured, which in turn was named for the metal rod or bar it traditionally sported, in an example of nested synechdoche (Nested Synechdoche would be an awesome name for a band). The latter is derived from the Latin verb for "drink." "Imbibe" is another derivative thereof.

As old as Beer is -- and it is old, by human standards -- it spent much of its history ignorant of its own provenance. It wasn't until the microscope came into being that we discovered what made Beer beer instead of malted barley soup: yeast. Until then, the process of fermentation was, at best, obscured; it might as well have been magic.

Here I was setting out to craft a story and I got bogged down in history. It happens. It's all fascinating to me, though: both the history and the science, of course, but also the creative spark that I'm just not feeling tonight. Maybe someday we'll invent a tool to examine creativity and find its source, the way the microscope enabled us to discover yeast. That wouldn't end creativity, I think, just as discovering that alcohol is essentially yeast piss didn't end Beer.

For now, though, I'll just raise a glass to science, which may not always make everything better, but certainly increases our understanding -- if not our creativity. And to Beer, which made it all possible.

All God's children need traveling shoes
Drive your problems from here
All good people read good books
Now your conscience is clear
I hear you talk girl
Now your conscience is clear

In the morning I wipe my brow
Wipe the miles away
I like to think I can be so willed
And never do what you say
I'll never hear you
And never do what you say

Look my eyes are just holograms
Look your love has drawn red from my hands
From my hands you know you'll never be
More than twist in my sobriety
More than twist in my sobriety
More than twist in my sobriety

6 Like • Comment • View 7 comments

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