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Thursday, Oct. 31, 2024

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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 4 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 25, 2019 at 12:13am

#972005

Here's Your Sign

Merry Christmas to those who celebrate it. As for me, well, a few days ago Drunk Me got into my Amazon account and ordered the final book in a fantasy series I've been following (Brent Weeks, if you're curious, or even if you're not), so I'll be spending the day reading the massive tome. Thanks for the holiday gift, Drunk Me! You shouldn't have!

Nah, I'd have bought it sober eventually.

But then, seeing articles like this one kinda makes me want to drink:

https://www.newyorker.com/magazine/2019/10/28/astrology-in-the-age-of-uncertaint...

Astrology in the Age of Uncertainty

Millennials who see no contradiction between using astrology and believing in science are fuelling a resurgence of the practice.

Fuck your stupid generation demographical nonsense again, but still, the article has some interesting stuff in it.

“That is one of my favorite things, as a Leo and as a person—building community,” she said. It was a little before eight-thirty, and some of the fifty-two participants—who had paid between $19.99 and $39.99 each—were typing hellos; one woman, in Europe, had set her alarm for 2:30 A.M., to log in.

You know, I can't even work up outrage over people making money from astrology. Gotta keep the economy going somehow, and I don't know many astrologers with private jets (likely, the planets never told them when would be the optimal time to buy one).

In its penetration into our shared lexicon, astrology is a little like psychoanalysis once was. At mid-century, you might have heard talk of id, ego, or superego at a party; now it’s common to hear someone explain herself by way of sun, moon, and rising signs.

Psychoanalysis has had - probably still has - its problems, to be sure. Freud is all but dethroned as anything except the guy who started it all, and many closely-held beliefs of early psychology have been turned on their head - "id, ego or superego" among them. But you know, that's how science works: Make a theory. Test the theory. Revise or replace the theory. (That's an oversimplification of the scientific method, but bear with me here.) Just as medicine moved away from balancing the humors and whatnot, psychology advances, in fits and starts, as more studies are done and more data collected. They learn from their failures - most times.

There is no science to astrology. I mean, okay, there's math, but as this article points out, that's all done by computer programs now; I'd wager few of these younger astrologers could compute charts by hand as it used to be done. But computing the chart is only the first step; next up is interpreting it. And there's no science to that; only the accumulated guesswork of generations of astrologers.

Sure, sometimes it seems to be right, even scary right. There's a lot of stuff at work there, not the least of which is confirmation bias.

Back when I was genuinely interested in the practice, a friend of mine who's an accomplished astrologer wanted to do my natal chart. Thing is, I have no idea what time I was born (as the article points out, this is essential). I know the day, and the place, but not the time, and obviously over the course of the 24 hour day any one of the 12 star signs could be "rising." And supposedly the rising sign (the zodiac sign subtended by the eastern horizon) is third in importance only to sun sign and moon sign - which, in my case, are the same thing.

So. If there's any science to it at all, we ought to be able to work backwards. I had a pretty good idea of my personality and, being my friend, so did he. So, in theory, if you subtract the influence of sun-in-Aquarius and moon-in-Aquarius, the dominant aspect that remains would be my rising sign, et voilà, I'd know to within a couple of hours the time I was born.

It shouldn't come as a surprise that every one of the 12 possible rising signs had near-fits to my actual personality.

That's the thing about us Aquarians: we're highly skeptical of astrology.

Anyway, I'm not really feeling like quoting more from the article. I've never been a fan of The New Yorker's preferred highbrow, rambling style that usually circles the point like a dog about to take a nap - if it ever gets to the point in the first place. This doesn't, really; it just goes on and on about how different people approach astrology.

But, as unscientific as it is, I just can't work up to the point where I get mad about it. Energy crystals? Hogwash. Homeopathy? Dangerous hogwash. UFOlogy? Balderdash. Prosperity gospel? Fraudulent balderdash.

Can it be dangerous? Sure. As the article points out, that utter asshat Reagan was a fan; imagine consulting an astrologer to decide when would be the optimum time to launch nukes. But that's an edge case; most of us don't have access to the national weaponry. The way I see it, in the world we live in, we're overwhelmed with choices, and it can be paralyzing. Everything from which laundry detergent to buy to which restaurant to visit is fraught with possibilities that even our recent ancestors would have boggled at. If some people want to turn to the skies and those who interpret them to help them make such choices? I get it. Sometimes I roll the dice, like I do when I decide which of my many waiting articles to post here; that's as good as astrology.

I just wish more people actually looked at the stars. Maybe that'd get 'em out of the gutter.

In parting, since it's Christmas, enjoy my favorite holiday song:

2 Like • Comment • View 1 comment

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