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Monday, Oct. 28, 2024

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Complex Numbers

by Spirit HalloWaltz

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:

Elisa: Stik or Treat

about 20 hours ago
In response to "Revisited: "Stylish""

I admit I don't even hear the "like/comment subscribe" verbiage anymore, although it helps that I follow several channels that don't include it. That said, having heard directly from some YouTubers, they say that because it works much better than we like to admit. I'll be touching on this a bit in today's Watch This Space entry (which I'm trying to write in a way that soesn't require watching the video to understand without being too full of spoilers for those who want to watch it).

As for drama, I think there is an overlooked middle ground: interacting with people in a meaningful context and having conflict stemming from a drive to achieve a common goal. I get this from my job and my PAC work, and it helps me maintain conflict resolution skills,

1 Like

tj: Tenebrous Jekyll

a day ago
In response to "Moon Illusion"

I've witnessed this as the moon, and sun have risen and set. I've also heard many of the wrong explanations.

1 Like

Spirit HalloWaltz

a day ago
In response to "But What I Want Is Cheesecake"

Good points, Elisa: Stik or Treat

. I hadn't known about the influenza thing, because I don't follow that sort of content.

Elisa: Stik or Treat

a day ago
In response to "But What I Want Is Cheesecake"

I've been mulling over this for a bit, and I've come to the conclusion that I think both the original post and you miss a few points on this concept. The term "intuitive eating" is being both actively and passively pushed as a way to try to counterbalance influencers that are straight up promoting disordered eating. (Yes, I would consider long term adherence to some protein-heavy diets to be disordered eating, as it promotes an incomplete picture of nutrition and contributes to forms of body dysmorphia that emphasize muscle size and visibility.) The discussion of intuitive eating is done the way it is to try to get a lot of bullshit out of algorithms, and I can appreciate that kind of move.

There are also a few things I'd like to offer comment on from the entry.

Given how emotional this work can be, experts recommend working with a professional when possible.

Again... this kind of nullifies the "intuitive" part.

Not necessarily. I've talked with my counselor about intuition. Honestly, I'm starting to believe that intuition is different from instinct (i.e. a behavior programmed prior to birth/hatching). Intuition is more of an unconscious expression of past experience. Since experience is different from person to person, how one experiences hunger on an intuitive level is actually externally learned first THEN internally programmed. Since intuitive eating is essentially a reprogramming exercise, working with a professional is useful. It's especially needed for those recovering from disordered eating.

Recently, there has been renewed interest in an approach called “intuitive eating”, based on the idea that your body already knows exactly what it needs.

Yes, it absolutely does, and apparently, it "needs" to be overweight.

Going back to the intuition development principle I mentioned earlier, if you are introduced to and eat vegetables regularly, it's definitely possible to come to crave them. And this can happen for those on assistance programs, but again there are a lot of cultural factors involved. I remember reading an article years ago where for a lot of low income people vegetables needed to be introduced to them in a somewhat structured way in order for them to more actively take donated produce of any kind. And yes, there is more active work being done to get fresh produce being donated to food banks. The point is, it takes time and practice, but a person can come around to picking produce or prepared veggies over a baked good. I'm not sure how I managed to reach this point as a toddler, but let's just say after I threw a fit to get an orange over a donut my mom stopped complaining about peeling oranges.

Giving yourself permission to eat what you want may involve wrestling with how your culture’s foods might have been villainized by mainstream, white American culture, Johnson explains.

Oh, give me a fucking break. I get that it's fashionable to turn mainstream white American culture into the Bad Guy, but how about doing it by ragging on deep-fried butter with mayonnaise, or whatever culinary abomination came out of some Midwestern state fair this year?

Because the worst food demonization isn't coming out of the Midwest? I mean, at least with those food-like things we all kind of know it's meant to be a joke. Unfortunately, I think the worst of this demonization is coming from the coasts. Feel free to fight me on that one.

1 Like

Fearlycia Lee ☮

Oct 25, 2024 at 12:24pm
In response to "Pass da Pasta"

Eh? No. I don't put it in the boiling water. I drizzle them on the pasta itself.

1 Like

Spirit HalloWaltz

Oct 25, 2024 at 11:00am
In response to "Pass da Pasta"

Fearlycia Lee ☮

- maybe it is true. At worst, you just waste olive oil; I don't think oil in the water can do any real harm to anything but your wallet.

1 Like

Fearlycia Lee ☮

Oct 25, 2024 at 10:57am
In response to "Pass da Pasta"

I think #2 is true though. I had only started drizzling olive oil on my pasta two attempts ago and it's true. I never put olive oil on pasta and they stick all the time. Also, it doesn't help that I forgetful and forget to try this method until two attempts ago. Took me years to remember. Yup.

1 Like

Elisa: Stik or Treat

Oct 24, 2024 at 10:57am
In response to "A Winner's Tale"

I'm just glad to see reporting showing young adults can exercise responsibility and restraint.

2 Like

🌕 HuntersMoon

Oct 24, 2024 at 10:43am
In response to "A Winner's Tale"

No, Lilli Munster 🧿 ☕ 🎃, WINNING is the first step.

2 Like

Lilli Munster 🧿 ☕ 🎃

Oct 24, 2024 at 9:59am
In response to "A Winner's Tale"

Remaining anonymous is the first step.

4 Like

October 21, 2024 at 10:16am

#1078678

Mything the Point

From the BBC, an article at the intersection of science and mythology.

The myths that hint at past disasters
Myths and fables passed down over thousands of years are full of fantastic creatures and warring gods. But they also might contain evidence of environmental disasters of the past.

It's long been assumed that many, if not all, myths contain some elements of fact. (Like the article, I'm using "myth" in the sense of a passed-down story, not the more modern meaning of falsehood.) The tough part is teasing out the fact from the fiction.

The article opens with a bit about expected sea level rise, comparing it to past sea level rise. This might add fuel to the "climate's changed before and we're still here" campfire of climate change deniers, but so be it.

With the possibility of a catastrophic global sea level rise of 3ft (1m) by 2050 which could force millions of people to leave their homes, researchers have now started to look at ancient stories about land lost to the sea and downed cities in a new way.

Hell, it might have looked like the whole world was flooding, leading to one extraordinarily popular myth (though that one might have been due to its Mesopotamian origins).

Some researchers argue that tales of hot boulders thrown into the sea or the building of sea walls comprise factual information, albeit exaggerated and distorted to some extent.

Well, okay, argue all you want, but how about some science to back it up? I have this hypothesis that the "nephilim" mentioned exactly once in the Bible, in Genesis, are actually a passed-down memory of Neanderthals. There's no definitive translation to it, and the KJV muddled the waters by rendering the word as "giants," with even less evidence (we didn't know about Neanderthals at the time). Like I said, it's my hypothesis. I have literally no way of supporting or disproving it.

These researchers are geomythologists.

As good a name as any, and better than most.

“Geomyths represent the earliest inklings of the scientific impulse,” says Adrienne Mayor, folklorist, historian of ancient science and research scholar at Stanford University, California, and author of the important The First Fossil Hunters, “showing that people of antiquity were keen observers and applied the best rational, cohesive thinking of their place and time to explain remarkable natural forces they experienced.”

I suppose, for various definitions of "rational" and "cohesive," if such words can be applied to deciding that floods are due to gods yeeting boulders and whatnot.

There's a lot more at the article, including specifics; I won't quote much more.

Back when the glaciers retreated, humanity was already infesting the European lands (I'm including Neanderthals in that group). In that era, Britain wasn't an island; it was connected to the mainland by a low-lying chunk of land now called Doggerland. This wasn't particularly ancient, in geological terms; apparently, it flooded out about 6,000 years ago, around the time civilization was flourishing in Mesopotamia, thanks to beer.

I'd often wondered about undersea archaeology in that region, and what it might find in terms of artifacts. It's often called a land bridge, but that implies that humans mostly lived in Britain or Nederland, only crossing the "bridge," but there's no reason why people wouldn't have lived there.

Turns out, of course, that actual scientists were way ahead of me.

The whole thing's fascinating to me, though I doubt the article's thesis that there's much practical use in terms of dealing with catastrophic modern climate change in an era when there are billions of people, not hundreds or thousands, living near a coast. But finding more truth about ancient humans is practical enough for me.

4 Like • Comment • View 1 comment

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