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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 11 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

February 14, 2020 at 12:06am

#975488

Je Suis Content

Well, here's Valentine's Day.

My plan is to spend the evening with my one true love: beer. I'll be doing this at a taphouse (or maybe two), in hopes of eavesdropping on a horrible Valentine's Day couples breakup. I'm easily amused and have a penchant for schadenfreude. Anyway, this means I can't swear I'll do my usual early-morning update tomorrow.

Meanwhile, I found an interesting article about some differences between Anglic and French cultures. It also seems oddly appropriate for Valentine's Day.

http://www.bbc.com/travel/story/20181104-why-the-french-dont-show-excitement

Why the French don't show excitement
Not only is ‘Je suis excité’ not the appropriate way to convey excitement in French, but there seems to be no real way to express it at all.

By Emily Monaco

From the name alone, I'm just going to trust her observations of the differences in cultural approaches.

“You Americans,” he said, “live in the faire [to do]. The avoir [to have]. In France, we live in the être [to be].”

Infinitives as cultural signposts. I like it.

I knew before moving that the French word ‘excité’ was verboten. It is one of the first ‘false friends’ that a student of the language becomes aware of. Most French learners can recall the day that a classmate first uttered the phrase ‘Je suis excité’ (which literally translates as ‘I am excited’) only to have their teacher hem and haw uncomfortably before explaining that the word excité doesn’t signal emotional but rather physical excitement. A better translation of the phrase Je suis excité into English would be ‘I am aroused’.

See, that's exactly the kind of thing I need to know before I attempt to ply my halting French on someone from a Francophone country.

Anglophones, meanwhile, blessed with both words, are free to use ‘excited’ as we please – which we (particularly Americans) do with reckless abandon. We’re excited for our weekend plans, for the summer holiday, to get home after a long day of work and relax in front of our favourite Netflix show.

I'm not sure I've ever constructed the sentence "I am excited" in casual conversation. Even in English, it leaves open the possibility of a double entendre, much like "I'm coming" or "It's not hard." With the crowd I hang out with, I'm careful not to leave myself open to that sort of thing, nor to pronounce the name of the planet that orbits between Saturn and Neptune. Some jokes are just too easy; I prefer to make people work for their puns.

Sadly, this means that I have actually uttered the sentence, "I'm totally psyched." And then I wince inwardly every time.

“I usually say ‘Je suis heureuse’ [‘I’m happy’] or ‘J’ai hâte de’ [‘I’m looking forward to’],” one bilingual friend said. Neither quite captures the intensity of excitement, but it seems these are the best substitutes that French has to offer.

In the course of learning French so far, I've encountered a few synonyms, or apparent synonyms. For example (par exemple), "student" can be translated into French as, at a minimum, étudiant or élève (with variations for gender and number). I suspect that there's a difference, subtle or not, between the two, but I haven't figured out what it is, yet. Older student / younger student, maybe, as with the English "pupil?" Anyway, point is, the first word I learned for "happy" was content (pronounced in the French way with the swallowed 'n's). The second was heureux (f. heureuse as above). Again, I don't know what the actual difference is, but it seems to me that the french "Je suis content" expresses something more similar to the English "I am content," regardless of the overenthusiastic helpful illustrations on Duolingo. Being content isn't really the same as being happy, but then, as far as I know, the French never put "pursuit of contentedness" into the founding documents of their republique.

So, what I'm getting at is, I don't know why the author left that particular synonym out of her discussion.

“If you’re too happy in French, we’re kind of wondering what’s wrong with you,” he said. “But in English, that’s not true.”

I have a suspicion that many French spend their ample leisure time wondering what's wrong with Anglophones in general, even while contentedly selling us their tasty cheeses and delicious wines.

Indeed, those who are unable to show the proper emotional detachment within French society can even be perceived as being somehow deranged...

You might say that they think they're...

*puts on sunglasses*

in Seine.

When we were first dating, my husband used to watch me buzzing around like a busy bee, making plans for the future. He, meanwhile, was able to find not excitement, but contentment, in nearly everything.

There's that word - the English version, anyway.

His frequent motto, whether we were drinking rosé in the sunshine or just sitting in a park, was: “on est bien, là” – we are good, here.

You know, I might just have to steal that for myself, especially when I'm three beers into a bender. Like maybe tonight.

3 Like • Comment • View 3 comments

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