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Wednesday, Dec. 11, 2024

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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:

Wordsmitty ✍️

about 6 hours ago
In response to "On the Label"

"June 25, 2024 5:40 AM" = Need time zone.

"Note to self:" = self-driving taxis

Some people definitely can be labeled, but we don't say those in polite company.

2 Like

Annette

about 6 hours ago
In response to "On the Label"

Only one label matters. Cat person or dog person. If the answer is anything except "yes" the person's life choices defy all logic analysis.

I wonder what is the difference between psychotherapist, psychologist, and psychoanalysis. Or are they like po-ta-to, po-tuh-two?

3 Like

tj-Merry Mischief Maker

Dec 9, 2024 at 2:51pm
In response to "Analog Log"

As time progresses, it amazes me how we have moved from tide clocks/analog computers to people eating tide-pods.

1 Like

Aiva Raine

Dec 9, 2024 at 2:37pm
In response to "Story of the Century"

Fantastic entry. Have I mentioned how I love your snark? Thanks once again for the grins and your awesome sarcastic responses to the articles.

1 Like

Anni Pon

Dec 8, 2024 at 10:01am
In response to "Revisited: "Millennials Killed Millennials""

It's kind of funny to me that people still use "millennials" to refer to "those darn kids" when most of them are in their 30's now with kids of their own. As an elder millennial (a Xennial, if you will), I haven't really found the generational definitions too useful for myself. I'm right on the border of generations, so I have a lot in common with both Millennials and Gen X. Growing up in silicon valley with tech savvy parents, I had earlier access to computers and technology than a lot of other people my age. But in terms of cultural milestones, I lived through and am old enough to remember things like the 90's, Y2K and 9/11. The borders are sort of arbitrary, but on a population level I can see how sometimes it can be useful to group people into generations.

2 Like

Elisa: Snowman Stik

Dec 8, 2024 at 9:40am
In response to "Revisited: "Millennials Killed Millennials""

*rubs hands together* Time for me to dive right in!

2. In this system, I'm early Generation X, which hardly anyone ever talks about, opting instead to rag on "boomers" or "millennials" or "Gen-Z." Or praise them, depending on the author's beliefs and age.

Looks like I need to change my name to "hardly anyone". Also, there has been more and more chatter about Gen X in some circles, but curiously this seems to be happening in institutions that have dropped labels (which I'll touch on in a second here).

On top of which, you'd have to convince me that our 1983-born X-er has more in common with someone born in 1966 than with someone born in 1986.

Very, very, VERY few organizations that have ever in their history used generational labels have set the Gen-X border any later than 1980. While I'm still very salty that Pew stopped this practice (one of the few things they've done wrong, IMO), I still use their Gen-X demarcation of 1965-1980. That demarcation nicely strikes the median of most demarcations. SO in this case it's not a matter of you needing to be convinced. It's a matter of the author leaning on a REALLY bad source.

Much of what sets "generations" apart, in modern terms, has to do with technological advancements and societal changes...then other people had to think that the original wearer was cool enough to start a fashion trend.

And how that message has been conveyed has drastically changed among generations, to boot.

So you know what I want to see Millennials finally kill?

Generations.

As a Millennial, I can tell you that this is probably the last thing our generation will try to kill. It's something that's persisting even as we reach middle age. And that's another thing. We're aging very strangely, namely that physically we're aging more slowly than people in Gen Z. We could have killed the concept of aging a certain way, but Gen Z's circumstances have effectively torpedoed that revolution.

Also, if anyone wants to read the original article, you can certainly try throwing the URL in the Wayback Machine. It doesn't always work, but it's worth a try. There are some other methods as well, but I haven't tried them myself yet. (Speaking of which, has anyone here tried Zette? I've been meaning to sign up for that but haven't had a chance. It's one of my goals for 2025.)

2 Like

Wordsmitty ✍️

Dec 7, 2024 at 12:41pm
In response to "Story of the Century"

Maybe it helps if you can dance - Dick Van Dyke and Coldplay - although he's just 99. (I assume everyone has read about that)

4 Like

🌖 HuntersMoon

Dec 6, 2024 at 10:07am
In response to "No Space for Time"

I think you just added clarity to the Twilight Zone...

3 Like

tj-Merry Mischief Maker

Dec 5, 2024 at 4:05pm
In response to "How To Give A Fock"

How many photons does it take to make a torpedo? Who gives a Fock! Actually, wasn't Fock Spock's half brother?

3 Like

Jayne

Dec 5, 2024 at 10:23am
In response to "How To Give A Fock"

Versatile Fock States is the name of my next thrash album.

3 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.

8 Like • Comment • View 2 comments

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