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Thursday, Oct. 31, 2024

2:16pm EDT

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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:

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.

1 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

Elisa: Stik or Treat

Oct 28, 2024 at 10:29am
In response to "Waste Not"

When looking at the article, I did notice that they discussed compostings' pros and cons. I recognize the initial cost would go up, but I do think increasing composting infrastructure could be a productive way to address surplus perishables. I know in somd municipalities that have composting the pickup for that is handled by the local authorities, so enforcement can be built in. It can be one of a few strategies implemented simultaneously (such as donating food that's still safe for consumption but composting items that have already reached an inedible stage).

3 Like

October 31, 2024 at 9:44am

#1079221

Phases

Samhain, and the temperature is supposed to get up into the 80s (Freedom Units) today. Not that I'm unhappy about that, but it is somewhat unnerving for the end of October.

This Halloween night coincides closely with a new moon (8:47 Eastern tomorrow), so it's not nearly as cool as when it coincides with a full moon.

So I'm doing... absolutely nothing for the occasion. Except, of course, trying to keep both of the black cats indoors, because some people are idiots.

Speaking of the moon, though, here's a lunar mythology article from Discover:

Myths of the Moon Shaped Ancient Cultures and Modern Cultures of Today
From ancient myths to modern superstitions, all cultures — even modern ones — tell stories about the moon.

The moon is something all people on Earth, no matter where or when they’ve lived, have in common.

Unless, I suppose, you spend your entire life underground.

That we all share the moon does not mean that we imagine it the same way, however. In our myths and stories, the moon plays many different roles.

We know more about the moon than ever before, and we continue to learn more. That dead hunk of rock in the sky still has secrets to give up. Myths and legends don't tell us much about the moon, but they do reveal a lot about us.

The relationship between the moon and the tides, for example, was clear to early peoples who lived near the sea, explains Tok Thompson, an anthropologist at the University of Southern California who specializes in folklore and mythology.

That's probably an example of noticing a correlation without understanding the deeper effects (in this case, gravity) behind the correlation. In other words, the "observation" part of the scientific method.

The moon, with its regular phases, also functioned as a calendar. You could track the days by the sun, but for longer periods, the moon was useful. The English word moon comes from mensis, the Latin word for month, which is also the origin of the word ‘menstruation.’

Much as I enjoy a good etymology, I'm not sure this is right. Wiktionary

traces the word back through Proto-Germanic, all the way to PIE. This suggests to me that, rather than having its origin in Latin, the Latin and the Germanic words share a root.

I'm not an expert, by any means, but this is enough to make me question the "comes from Latin" assertion.

Pretty sure Luna is from Latin, though; that was the name of a moon goddess.

All that aside, let's stop pretending that Gregorian calendar months are related to lunar cycles.

So yes, ancient cultures knew a lot about the moon, and they wanted to share that knowledge to keep a record of it.

I also question the qualifier "a lot" in that sentence.

Thompson’s favorite myth involving the moon is a creation story from the Tlingit people of the northwest coast of North America. In this story, an old man keeps all the light in the world stashed away in a box. Through wiles that vary from telling to telling, the trickster Raven steals the box and releases the Sun, the moon, and all the stars, bringing light to the world.

One could be forgiven for wondering how Raven was able to see the box, considering there was no light at the time, but myths follow their own, dreamlike, rules.

In Chinese mythology, a woman named Chang E drank a magic elixir, whereupon she floated all the way to the moon, and there she lives still — with, in some versions, a rabbit.

Radical feminists: "Hey, gimme some of that elixir!"

We still have some fascinating myths about our favorite satellite. Probably the most persistent is that the moon can drive us mad.

I find that it's necessary to separate the two meanings of "myth." A foundational story, like the ones about Raven or Chang E, is not the same thing as a persistent falsehood. I don't think this article draws the distinction.

Many people — including some healthcare workers and police officers — believe that crime, traffic accidents, psychiatric hospital admissions, and even suicides spike during a full moon.

Or that could be cognitive bias. You notice things more when they fit your pre-existing worldview. Like when you're frustrated by machines and bureaucracy, and think "Mercury must be in retrograde."

These days, we don’t blame the effect on moon goddesses or magic elixirs but on something at least quasi-scientific: the moon’s gravitational effect on the water in our bodies. On its surface, that makes a lot of sense.

No. No, it does not.

After all, the moon creates tides, and roughly half our body weight is water.

Okay, but have they ever observed tides in a mudpuddle?

And indeed, though a few small studies have found some possible effects of the moon on mental health, research over the past decades has not borne this out. For example, a Swiss study published in 2019 looked at almost 18,000 cases of in-patient psychiatric admissions over ten years and found no correlation between the phase of the moon and psychiatric admissions or length of stay.

There's some nuance there, but basically, the "moon causes madness" bit is the second definition of myth.

Pausing to gaze at the moon can create an intense feeling of both awe and peace. Rather than making us mad, the moon might just make us a little bit more sane.

Nice to think, but there's little evidence for that, too.

Still... go look at the moon. Might want to wait a few days, though; it's too close to the sun right now.

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