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Monday, Oct. 28, 2024

8:17am 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 22 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 26, 2024 at 9:26am

#1078956

Moon Illusion

From SciAm, and an author I hung out with for a week a few years ago:

Why Does the Moon Look Bigger Near the Horizon?
The rising moon looks huge on the horizon, but it’s all in your head

I can smugly assert that this is something I'd already figured out.

I remember watching the full moon rise one early evening a while back.

You'd think astronomers would spend more time watching moonrises.

As it cleared the horizon, the moon looked huge!

Eastern Colorado, where this occurred, is basically a continuation of Kansas: Flat as the proverbial pancake. There's an actual horizon there.

Anyone who is capable of seeing the moon (or the sun) near the horizon has experienced this effect.

I don't have an unobstructed view of the horizon here, but I've spent time on the coasts, so yes.

But it’s not real. Simple measurements of the moon show it’s essentially the same size on the horizon as when it’s overhead. This really is an illusion.

As opposed to time, which really is not (yes, another time article is in the queue).

Attempts to explain it are as old as the illusion itself, and most come up short. Aristotle wrote about it, for example, attributing it to the effects of mist.

As smart as Aristotle was, he got lots of stuff wrong. This was one of those things.

A related idea, still common today, is that Earth’s air acts like a lens, refracting (bending) the light from the moon and magnifying it.

The "simple measurements" noted in an earlier quote refute that bit instantly. Refraction does make it appear redder than usual, though, just like it does with the rising or setting sun.

Another common but mistaken explanation is that when the moon’s on the horizon, you’re subconsciously comparing it with nearby objects such as trees and buildings, making it look bigger. But that can’t be right; the illusion still occurs when the horizon is empty, such as at sea or on the plains.

But, see, coming up with explanations like that, even when they can be disproven... that's part of science.

So what’s the cause? Like so many things in science, there are two effects at play here.

Phil indeed goes on to explain the cause, but no need for me to quote it word-for-word. The first part of the answer is related to this well-known optical illusion.

The second part is devoted to showing that we don't see the sky as a hemisphere, but as a nearly-flat surface. This is the harder part to accept, I think, but next time you're out on the plains or the ocean on a partly cloudy day, note how the bottoms of the clouds make the sky seem flat. This is for the same reason that the Earth itself appears (but only appears, dammit) flat in such locations.

So you've got two (nearly) planes, earth and sky (the temptation exists to make a plains/planes pun, but I'm not in the mood), but only one moon. Still, presumably, you've seen the moon high in the sky quite often, so then when you see it near the horizon, your brain goes back to remembering seeing that.

Moon illusion misconceptions still abound, and like so many myths, they likely won’t go away no matter how much someone like me writes about them.

Yes, this is, indeed, the curse of fact-checkers.

1 Like • Comment • View 1 comment

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