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Wednesday, Dec. 18, 2024

1:52am EST

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Complex Numbers

by Waltz Invictus

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:

Aiva Raine

about 6 hours ago
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

about 8 hours ago
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

about 16 hours ago
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

Ichabod Crane-- Mince Pie

about 17 hours ago
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

tj-Merry Mischief Maker

a day ago
In response to "Fork You Too"

Now that I know forks are the center of dining controversy, I'll have to apply this at all family gatherings where demon dining utensils are in use.

1 Like

tj-Merry Mischief Maker

Dec 15, 2024 at 1:06pm
In response to "Revisited: "Those Naughty Brits""

I don't think there's such a thing as kinky sex anymore. Why? Based on the general definition, kinky sex refers to sexual activities and preferences that fall outside standard sexual practices. Nowadays it seems anything goes and there are no norms or standards.

Oh, another thing; do you remember if the link had pictures? Asking for a friend.

1 Like

Wordsmitty ✍️

Dec 15, 2024 at 12:45pm
In response to "Revisited: "Those Naughty Brits""

Waltz Invictus - As they say, you're a more proper man than I. I may even check out the other links with those key words.

2 Like

Waltz Invictus

Dec 15, 2024 at 12:32pm
In response to "Revisited: "Those Naughty Brits""

Thanks for that, Wordsmitty ✍️

. Sometimes I make the effort to find an article from a dead link. This time, I did not.

1 Like

Wordsmitty ✍️

Dec 15, 2024 at 12:29pm
In response to "Revisited: "Those Naughty Brits""

I think we're all glad that society has advanced so far in a decade and a half. Which way is up to you.

For those interested, there's a "Search" option in the Times main page. Page 6 of the results comes up with this link: https://www.thetimes.com/article/4d5f3e63-22c9-45c0-837b-c3ad9d236ae8

2 Like

Elisa: Snowman Stik

Dec 15, 2024 at 9:35am
In response to "Revisited: "Those Naughty Brits""

Damn, another entry that has me wanting to jump in and offer tons of commentary! Let's have at it.

2008 Me: Journalism may not be dead yet, but it's starting to wander and stink.

Dead now. Mostly.

Clearly I need to highlight more non-profit outlets in my link rundowns. I'm finding lots of good reporting on that front. Perhaps I also need to add more examples of this to "Watch This Space!"

[18+]. Even 60 Minutes is still able to provide some good in the weeds reporting. Point is, journalism is struggling, but good reporting is still out there. I'm doing my damnedest to shine a light on the solid examples. I could use a bit more help in the process.

2008 Me: What happened to investigative journalism? Hell, what happened to comprehensive news stories?

Gods, 2008 Me was so young and naïve.

They still exist. Strangely, I have found that at least in my area the local stations actually put some of their most comprehensive stories online. Also, at least the NBC affiliate has a post-local news show that does more comprehensive reporting. Some pieces are fluffy, but others are not. They are more locally focused, but that's probably a good thing these days. Local news has struggled the most, and we're paying the price for that.

2008 Me: Why is this in the "women" section? Men don't want to read about kinky sex? Please.

I'm guessing men are less likely to consider it kinky, outrageous, or naughty. But what the fuck do I know (pun intended)?

Strangely, this seems almost prudish by British standards, especially in light of the fact that Time magazine reported on BDSM in one of its print issues four years prior. And as we know, Time magazine isn't exactly known for sectioning off its content by gender. The Time coverage did include a photo taken in a BDSM dungeon that wasn't too explicit but really captured the D/s component really well. Honestly, I'd expect a UK publication to do that before a US one, not the other way around.

That said, I suspect the articles may have been written for slightly different audiences. If the audience is primarily women, there is likely to be more implicit shame in the picture, as women have been historically more likely to be primed to be ashamed about their sexuality in any capacity. Don't get me wrong. I know men are also subjected to this shaming. However, it tends to be less persistent and less pervasive in terms of different facets being shamed. In a general audience, the shame element can be downplayed. In a women-focused audience, you have to address the shame angle in some capacity, reassuring them that this isn't such a bad thing. This isn't something I'm directly involved in, but given the lack of women on WDC willing to write about this sort of thing these days, I might have to take one exploring this concept in depth. Ladies, if you're thinking about writing something (journal entry, static item, whatever) about this topic, this is your sign to go ahead and do it!

These days, I have preconceived ideas about headline questions: First, if it's a yes/no question, the answer is probably "no."

Snopes is ready to challenge that assumption.

2 Like

December 7, 2024 at 10:51am

#1080897

Story of the Century

Speaking of time, here's a Guardian article about people who had more of it than usual.

Never take health tips from world’s oldest people, say scientists
Scientists still trying to work out why some people live beyond 100, but agree it is best to avoid taking advice from centenarians themselves

No, we should definitely take health tips from people who die young, instead.

The death of the world’s oldest person, Maria Branyas Morera, at the age of 117 might cause many to ponder the secrets of an exceptionally long life, but scientists say it could be best to avoid taking advice on longevity from centenarians themselves.

Far as I can tell, the secrets to an exceptionally long life include such gems as "stay alive" and "don't die."

According to the Guinness World Records website, Branyas believed her longevity stemmed from “order, tranquility, good connection with family and friends, contact with nature, emotional stability, no worries, no regrets, lots of positivity and staying away from toxic people”.

Also, unicorns and fairies. I mean, those are probably more real than her litany.

However, Richard Faragher, a professor of biogerontology at the University of Brighton, said that in reality scientists were still trying to work out why some people lived beyond the age of 100.

Because they didn't die.

Or, in some cases, because they assumed the identity of their deceased parent so they could go on collecting the... whatever benefits.

Faragher said there were two main theories and they were not mutually exclusive.

The first, he said, was that some individuals were essentially just lucky.

At some point, though, lucky stops being "you didn't die" and starts being "you died."

The second theory, he said, was that centenarians had specific genetic features that equipped them to live a longer life

So, a different kind of luck. But still luck.

Faragher said both theories, however, resulted in the same warning: “Never, ever take health and lifestyle tips from a centenarian.”

Certainly, if I'm unlucky enough to live that long, I'd troll the hell out of anyone asking me about health tips. "See, now, the key is to kick a puppy every day. Doesn't have to be your puppy. Doesn't even have to be the same puppy. But it's gotta be a puppy, not a dog. Or a kitten or a kid. Puppy."

He added: “What you see with most centenarians most of the time – and these are generalisations – is that they don’t take much exercise. Quite often, their diets are rather unhealthy,” noting that some centenarians were also smokers.

What would amuse the hell out of me would be if no exercise, diets considered unhealthy, and smoking really were the keys to long life.

“The fact that [centenarians] do many of these unhealthy things and still just coast through [life] says they’re either lucky or typically very well endowed [genetically],” he said.

Again, both of these things are luck.

Faragher added that many of the mooted possibilities for why centenarians live longer could actually be examples of reverse causation. For example, the idea that having a positive mental outlook can help you live for a very long time might, at least in part, be rooted in people being more sanguine because they have better health.

Glad they acknowledged this. I mean, they could do studies to gain insight into it, but apparently it's more important to promote "positive mental outlooks," especially in a world falling apart all around us.

“From about 100 years ago, what we started seeing was huge advances in life expectancy driven by improvements in reducing the likelihood that children die,” said David Sinclair, the chief executive of the International Longevity Centre, noting that was largely down to the introduction of vaccinations and clean water.

Well, that lasted about a century.

“What we’ve had over the last 20 years, and we’re going to see over the next 20 years, is a similar focus in terms of old age,” Sinclair said, adding that included improvements in vaccines for flu and shingles, statins, and other medications that would help increase life expectancy among older people.

Sure, because, obviously, life expectancy is a more important metric than life quality.

But he said governments also needed to take action to help individuals to make healthier choices – choices that would ultimately help them live longer – adding that many people lived in environments where it was difficult to exercise, eat well or avoid pollution.

Ah yes. "Want to live longer? It's your fault if you don't, even though you're economically stranded in a polluted area with little access to fresh food, thanks to our policies. So instead of fixing economic disparity, despair and environmental degradation, we'll make it illegal for you to eat cheeseburgers. There, we fixed it!"

As Sinclair said, while news stories about centenarians tended to be upbeat, it often emerged that such individuals faced challenges, such as living alone for many years.

Challenges? Hell, that's probably the real reason they lived longer: not having to deal with other peoples' bullshit all the damn time.

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