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Saturday, Apr. 27, 2024

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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

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Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

March 6, 2024 at 8:16am

#1065695

Les Langues d'Amour

Speaking of backing things up with science... from Big Think:

Everyone is wrong about “Love Languages.” Here’s why.
Big Think spoke to the author of "The 5 Love Languages" about the popular relationship theory — and its lack of scientific support.

I'm not immune to knee-jerk reactions. Sure, I try to reason through them later, but, as I suspect most people are, sometimes I just hear about something and react with instant rage or disgust. I'd speculate that this was an evolutionary adaptation on the part of our ancestors, who had to make survival decisions in a dangerous environment, but one of the things that sets me right off is speculation based on evolutionary psychology. So I won't.

One of the things I immediately scoffed at when first hearing about was "love languages." Then, after taking some time to find out what was meant by that, my reaction softened somewhat. After all, the concept boils down to "we all appreciate different things," which I wouldn't deny.

If you're reading this, and somehow still wondering what the hell I'm talking about, well, the précis is right there in the bullet summary at the top of the linked article: The idea, created by evangelical pastor Gary Chapman, is that to make your partner feel truly loved, you must show them affection in their preferred "language."

Birthed in a perennially best-selling book over three decades ago, the idea remains ever-present in popular media, dating apps, and social media. The book’s resonant success might make you assume that the theory was born in the lab of a superstar relationship psychologist, but the notion has humbler origins.

Actually, I immediately suspect any book, especially purported nonfiction, that achieves huge success, because I distrust the zeitgeist. And it's exceedingly rare that a book written by an actual scientist climbs to that level. The only one I can think of offhand is Hawking's A Brief History of Time, and that one had pretty pictures. (It was also worthy of the success.)

The architect of the theory is evangelical pastor Gary Chapman.

Okay, here's where I feel compelled to make an embarrassing confession: In my view, evangelicals are all guilty until proven innocent. Some of them are responsible for those grifting megachurches. Others are doing their best to turn our secular country into a theocracy. Many outright reject science in favor of superstition. The ones you hear about are always trying to make life difficult for gays, trans people, and anyone else who doesn't conform to their narrow view of what people should be like. When your ranks include the likes of the thankfully-late Jerry Falwell and Pat Robertson (and those are just the famous ones from my home state), you have a hell of a lot to answer for.

This may seem to contradict my radical acceptance of diversity. And maybe it does. But to me, there's a big difference between being born into a demographic, and choosing to align oneself with a certain philosophy. Even that difference, though, contradicts my assertion that we never really "choose" anything. So I don't know. I guess that, in this way, I've been prejudiced (even though I already had a counterexample in my cousin's evangelical wife, who's one of the kindest people I know). I should work on that.

Everyone's a hypocrite in some way. I figure at least I recognize some of my hypocrisies.

Point being, when I heard the author was an evangelical pastor, I instantly dismissed anything it might have to say. And I was (probably) accidentally right to do so... but not because of the author's affiliation.

The popularity of his book, quiz (taken more than 133 million times), and theory confirm to Chapman that love languages work.

No. No, it doesn't confirm any such thing, any more than the popularity of books on astrology confirm that astrology works.

Still, popularity and anecdotes do not prove that love languages actually work, or even exist at all. For that, science must weigh in.

You knew that was coming, because I'm writing these comments.

In a paper recently published in the journal Current Directions in Psychological Science, a trio of social psychologists specializing in relationships reviewed the science conducted on love languages and found it wanting.

And yet, one paper does not a definitive takedown make.

First off, research contradicts the notion that people have a primary love language, they write. Chapman’s quiz is fundamentally flawed, they argue, because it forces takers into binary this-or-that choices.

I'm on board with that finding, myself. As I keep saying, life is rarely binary. Not everything has to be "cool" or "sucks." Maybe it's just me being Gen-X (another labeling system I question), but to me, there's always "meh, whatever," too. In various shades.

Second, the five love languages overly simplify forms of love in relationships and are based on a homogenous sample. For example, the love languages “do not include mention of support for a partner’s autonomy or personal goals outside of the relationship, factors that have been associated with relationship satisfaction,” the authors noted. They added that Chapman formulated his ideas after counseling couples “who are all married, religious, and mixed gender and likely share traditional values.”

That is, to me, a serious problem. Like with the study I mentioned yesterday, which was all Brits. Or a lot of postdoc papers, which draw from a sample core of "American college students who want a few extra bucks."

Third, and most glaringly, the limited research that has been conducted does not support the idea that speaking someone’s preferred love language yields greater relationship satisfaction or success.

As the article admits, though, the research is scant. So though I want to agree with the conclusion, I can't quite rise to the level of "science says it's bullshit."

Chapman had a chance to respond to these issues, and this is the part where my mind gets blown because it doesn't fit in with the prejudice I stated above:

Chapman, who throughout the interview expressed intellectual humility that any scientist would admire, wanted to make clear that he appreciated researchers’ work to study love languages. “I’m not against research,” he said. “Scientific research is wonderful.”

So there you have it. I'm not changing my opinion that "love languages" are airy nonsense, but maybe I came away from this with a little less animosity to evangelicals in general.

And the world just got a little, tiny bit more tolerant.

3 Like • Comment • View 2 comments

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