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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

December 30, 2019 at 12:53am

#972221

The Peasants' English

I haven't talked about it much recently, but I'm still working on learning French on Duolingo. 123 day streak as of yesterday. I can now ask a French person what color his or her cat is, and maybe find a hotel. Yay?

I'm under no illusion that I could go to Paris tomorrow (well, I could, but that's another story) and carry on a conversation in anything but English. Still, linguistics has long been one of my interests, and I'm kicking myself that it's taken me this long to learn a useful language (Latin doesn't count, and besides, I've forgotten most of it).

So today's link is about English.

English is not normal
No, English isn’t uniquely vibrant or mighty or adaptable. But it really is weirder than pretty much every other language

https://aeon.co/essays/why-is-english-so-weirdly-different-from-other-languages

English speakers know that their language is odd. So do people saddled with learning it non-natively. The oddity that we all perceive most readily is its spelling, which is indeed a nightmare. In countries where English isn’t spoken, there is no such thing as a ‘spelling bee’ competition. For a normal language, spelling at least pretends a basic correspondence to the way people pronounce the words.

Um... have you seen French?

But English is not normal.

No, it's Norman. Get it? Norman invasion of... oh, never mind.

Our language feels ‘normal’ only until you get a sense of what normal really is.

Which generally requires learning other languages.

The closest an Anglophone can get is with the obscure Northern European language called Frisian

Some would say Scots, but others call that a dialect of English. I don't know enough to make a case either way. What I do know is that the Frisians were closely related to the Angles, and it's the Angles who gave their name to English, so, okay. Fun fact: the French word for England is Angleterre. You probably already knew that. I didn't. I do now.

Thinking about it, I'm surprised their name for England isn't much ruder, what with their history and all.

We think it’s a nuisance that so many European languages assign gender to nouns for no reason, with French having female moons and male boats and such.

Well, again, Latin training here - I'm used to words having gender. What I'm not used to is such assignations not making any damn sense. I know that language gender doesn't necessarily correlate with human gender, but still. The word for "cow" is feminine, okay. "Milk" is masculine, what? "Car?" Feminine. And don't get me started on body parts. No, get your minds out of the gutter; Duolingo didn't teach me the word for "breasts" (I figured that one out from *ahem* other sources *cough* long ago). I mean, like, arm is masculine, hand is feminine, leg is feminine, foot is masculine, mouth is feminine, head is feminine... nose is masculine. Quoi le fuck?

As an aside, the French word for "shower" is douche. (Also feminine, while "bath" is masculine.) I mean, I knew that's what the English word "douche" came from, but knowing and having to translate it are two different things. One day, I will stop reflexively snorting like a 12 year old every time that comes up on Duolingo. That day is not today. It's probably not tomorrow, either. Hopefully it will be before I'm in a hotel in Paris and have to call down to the front desk to complain that the shower isn't clean.

La Réception: "Bonjour?"
Moi: "La douche *snicker* n'est pas propre... *snort*."
LR: "Pardon, monsieur?"
Moi: "La douche- heeheeha"
LR: "Est-ce que vous êtes américain?"
Moi: snicker "Oui" snort
LR: *hangs up*

Anyway.

Why is our language so eccentric? Just what is this thing we’re speaking, and what happened to make it this way?

I saved a quote from the dark recesses of the internet once: "I always thought of English as the bastard child of an orgy of languages ending with a huge bukkake leaving German covered in the messy splooge of all the others. German is seeking a paternity test while Latin fled the scene and French is denying everything." No idea who first posted it, but I stole it fair and square.

The first thing that got us from there to here was the fact that, when the Angles, Saxons and Jutes (and also Frisians) brought their language to England, the island was already inhabited by people who spoke very different tongues.

Ah, yes, the old "We're taking over now." "Screw you and your stupid language."

The second thing that happened was that yet more Germanic-speakers came across the sea meaning business.

By "business" he means "war."

Finally, as if all this wasn’t enough, English got hit by a firehose spray of words from yet more languages. After the Norse came the French. The Normans – descended from the same Vikings, as it happens – conquered England, ruled for several centuries and, before long, English had picked up 10,000 new words. Then, starting in the 16th century, educated Anglophones developed a sense of English as a vehicle of sophisticated writing, and so it became fashionable to cherry-pick words from Latin to lend the language a more elevated tone.

"Firehose." Right. You know he wanted to use the Japanese term from the anonymous quote above.

The multiple influxes of foreign vocabulary also partly explain the striking fact that English words can trace to so many different sources – often several within the same sentence.

And that's why I've been interested in linguistics.

Thus the story of English, from when it hit British shores 1,600 years ago to today, is that of a language becoming delightfully odd.

I think actual linguists have a different definition of "delightfully" than you or I do. Or than people who have to learn English as a second (third, fourth, whatever) language do.

The article provides an interesting perspective, I think. Nothing surprising in it, no world-shattering discoveries, but an excellent overview of our sometimes-maddening language.

2 Like • Comment • View 9 comments

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