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Monday, Oct. 28, 2024

6:33am EDT

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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 21 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 18, 2024 at 11:02am

#1078516

Lithium

It's science, not magic; and it's not secret anymore, thanks to Noemi. Fair warning, this is a long read:

The Secret, Magical Life Of Lithium
One of the oldest, scarcest elements in the universe has given us treatments for mental illness, ovenproof casserole dishes and electric cars. But how much do we really know about lithium?

It may surprise some people to know that I don't have the Periodic Table memorized. I go, "Hydrogen, helium, lithium..." and then I have to look it up. Fortunately, I live in the 21st century, and it's easy to look things up rather than commit them to long-term memory.

(Beryllium's next, by the way, followed by boron and carbon.)

The universe was born small, unimaginably dense and furiously hot. At first, it was all energy contained in a volume of space that exploded in size by a factor of 100 septillion in a fraction of a second.

This view of universal origin may be in need of revision, thanks to JWST observations. It does not change the material (pun intended) facts of the piece.

Quarks and gluons had congealed to make the first protons and neutrons, which collided over the course of a few minutes and stuck in different configurations, forming the nuclei of the first three elements: two gases and one light metal.

Those would be the ones I mentioned above.

For the next 100 million years or so, these would be the only elements in the vast, unblemished fabric of space before the first stars ignited like furnaces in the dark to forge all other matter.

"Unblemished" is surely poetic license. Also, again, details subject to change pending study of recent observations.

Almost 14 billion years later, on the third rocky planet orbiting a young star in a distal arm of a spiral galaxy, intelligent lifeforms would give names to those first three elements.

"More than" 14 billion, and they need to be careful about calling us "intelligent," as doing so invites self-contradictory jokes about intelligence. (Self-contradictory, because one needs to be intelligent to make such a joke, but it's still stupid.)

“Lithium has one of the most complex stories,” Fields said. “The oxygen you’re breathing, the carbon in your DNA, the iron in your blood — that came later, out of stars. But lithium comes straight out of the Big Bang.”

This is misleading, as lithium can also be produced post-Bang, but the article does mention that later.

But the sources of lithium in the universe have, since the late 1980s, presented astronomers with an odd problem. As Fields told me, astronomers studying the abundance of elements after the Big Bang have created complex calculations that account for the expansion of the universe, nuclear reactions and the behavior of subatomic particles like photons and neutrinos. The math pencils out for hydrogen and helium — the measurements match the predictions. Not so with lithium — only a third or less of the expected amount of lithium is observable in the universe.

This sort of thing is exactly why we do science.

The story of how humans discovered lithium goes back to the late 18th century and a Brazilian scientist, statesman and poet named José Bonifácio de Andrada e Silva who was hopscotching around Europe on a sort of early study abroad program.

I'm betting he studied more than "a" broad.

Because the element was discovered in a mineral, Arfwedson and Berzelius named it “lithia,” after the Greek word “lithos,” for stone.

It should surprise no one that I find the origins of element names fascinating. Apart from obvious ones like iron and gold, known from antiquity, their names tend to reflect how we discovered them. Hydrogen, made from water. Helium, first detected in the sun. Beryllium, found in the mineral beryl (emeralds, e.g.) That sort of thing.

Finally, in 1855, two chemists — Robert Bunsen and Augustus Matthiessen — were able to isolate lithium in a quantity large enough to study its properties.

Yes, that Bunsen, namesake of every chemistry student's favorite flame source.

The article goes on to describe the beginnings of what might be lithium's most famous application: treating mental disorders. Don't read it if you like guinea pigs.

Research in Texas, Greece, Lithuania and elsewhere has found that naturally occurring lithium in drinking water is associated with lower rates of suicide and violent crime, prompting some scientists to advocate adding it to municipal water supplies, much like fluoride is sometimes added to strengthen teeth.

1) I want to take this opportunity to point out that Lithuania and lithium are not etymologically related.
2) Oh, adding elements to drinking water is sure to be uncontroversial.

The article then turns to what's probably the second most famous application of lithium (and might have already claimed the #1 spot): batteries.

Thomas Edison died in 1931 with a tin of lithium on his desk. One of the final projects in the great inventor’s life was experimenting with new chemistries in what he called “storage batteries.”

Yeah, right. "Great inventor," my fat ass. Edison was a hack with a flair for marketing and melodrama, who coasted to most of his patents on the writhing backs of his underpaid servants. Could be he invented a thing or two by himself along the way, but he was a massive dick. Muskmelon reminds me of him.

Anyway, the article ends with a section highlighting lithium's ubiquitous role in today's technological life. As I expected, nothing magical about it, but it is interesting to read about.

5 Like • Comment • View 1 comment

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