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Friday, Nov. 1, 2024

12:24am 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 5, 2020 at 12:04am

#972682

Ramble On

PROMPT January 5th

What music makes you want to dance?

None.

I don't use music for dancing. By which I mean, I don't use anything for dancing - my name notwithstanding, I don't dance - and music is for listening.

It took me a while to figure out that this makes me different from actual humans. I can be slow like that sometimes. When I discovered that pretty much everyone except me picks music based on some nebulously-defined quality of "danceability," I was shocked and dismayed.

I did understand that there were these events called "dances," and that only certain music was allowed at them - music, it seems to me, that has a very prominent rhythm. But to deliberately avoid meaningful music in favor of a prominent backbeat? Horror.

A musician once told me that lots of people think that's the purpose of drums in many types of popular music, but that this impression is incorrect; it's the bass line that keeps the beat, while the main purpose of drums is to back up the guitar. Admittedly, I was one of those people who made that assumption, because I was never a professional musician nor played in a band. I learned some piano when I was younger, and a piano can be a self-supporting instrument. I also learned violin, and part of that training gave me the ability to internalize the rhythm of music.

I still don't know if she was right, even though since then I've picked up some basic drumming and guitar skills. Not a lot, mind you, but some. But it changed the way I listened to pop, rock, country, blues, etc.

A while back, I took karate classes. (Wow, Waltz, that's a major nonsequitur. Shut up, I'm getting to a point here.) My sensei also taught kickboxing, so I crossed over into that, not so I could beat people up, but as a fitness thing. As part of the kickboxing classes, he'd put together a soundtrack. Now, you're probably picturing a wiry Asian guy subjecting us to K-pop or something, but no, the sensei was as pasty white Euro-American as I appear, though he'd spent years training in Japan and Okinawa, so the music was all American popular music of varied genres from the 60s, 70s and 80s.

The point I'm getting to is that kickboxing class is, I would imagine because I haven't taken dance classes, a lot like dance class. The music was there to help us stay on rhythm when doing various exercises. After one class, a young lady approached the instructor and said something like, "I don't understand this music. There's no rhythm to it. Can we have more danceable music?"

This shocked me. I hadn't had a bit of a problem picking out and sticking to the beat. But upon reflection, I realized that Led Zeppelin's "Ramble On" wasn't usually played at discos.

Which is one reason I avoided discos.

Now, if he'd played Pink Floyd, maybe that would have been another story.

So that, I think, was my moment of revelation. I'd already figured out that I was weird in that I listened to popular music more for the lyrics than anything else, but I'd never considered it to have no rhythm. To me, it did indeed have a rhythm, although sometimes a subtle one that doesn't translate well to dark rooms with mirror balls and light shows.

So, I guess I might have been hasty, there in the beginning of this entry. I do dance. I dance inside, as I do whenever music is playing. Even Led Zeppelin. Even Pink Floyd - well, except for the unlistenable experimental drug-fueled albums, maybe.

I saw a piece of sheet music lying on the piano of another professional musician once - I seem to know a disproportionate number of them, even though I can't carry a tune in a grocery bag - and looked at it out of curiosity. Another thing that makes me weird: I can read sheet music, even though I can't play an instrument with any great facility. This shouldn't surprise me, I suppose; some of my favorite musicians are just the opposite, able to play naturally, maybe not even able to read sheet music. Springsteen is one of those.

Anyway, I'm looking at this sheet music and the first thing I see is the time signature: 9/8.

Something inside of me broke.

For the uninitiated, the upper numeral is the number of beats per measure, while the lower one is the kind of note that makes up a "beat" in the notation. (For the initiated, please forgive me if I got this explanation wrong; it's been a while and like I said, I was never very good at any of this.) A more standard rhythm would be 4/4 - four beats per measure, with the beat consisting of a quarter note, or maybe 3/4, which I understand is often used for waltzes. 9/8, on first glance, just seemed to me like someone had opened a portal to the Elder Gods and let their eldritch horror into our lands.

But then I thought about it. And I realized. 9/8 is basically 3/4 time, with the basic unit being a triplet. Three sets of triplets per measure.

I can dance to that.

Leaves are falling all around
It's time I was on my way
Thanks to you I'm much obliged
For such a pleasant stay
But now it's time for me to go
The autumn moon lights my way
For now I smell the rain
And with it pain
And it's headed my way

8 Like • Comment • View 10 comments

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