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Tuesday, Dec. 17, 2024

8:55pm 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 an hour 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 3 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 11 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 12 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

November 9, 2024 at 10:50am

#1079718

It Was a Dark and Starry Night

When science meets art, are they both elevated? Or do they make each other suck worse? From CNN:

Turbulent skies of Vincent Van Gogh’s ‘The Starry Night’ align with a scientific theory, study finds

I usually groan when I see "scientific theory" in a headline, because the word "theory" means something different in science than it does in everyday speech. In this case, though, my fears proved unfounded.

Which doesn't mean I don't have some issues with the rest of the piece.

Now, a new analysis by physicists based in China and France suggests the artist had a deep, intuitive understanding of the mathematical structure of turbulent flow.

Or, and hear me out here, he was an artist and thus observed turbulent flow in, perhaps, a river or whatever, and incorporated that observation without being able to do math beyond "this paint costs 3 francs and this other one costs 4; which one is cheaper?"

As a common natural phenomenon observed in fluids — moving water, ocean currents, blood flow, billowing storm clouds and plumes of smoke — turbulent flow is chaotic, as larger swirls or eddies, form and break down into smaller ones.

"Chaotic" is another word that means something different in science than it does in everyday speech. Again, though, credit where it's due; the article uses it in the scientific sense:

It may appear random to the casual observer, but turbulence nonetheless follows a cascading pattern that can be studied and, at least partially, explained using mathematical equations.

"Partially" is doing a lot of the work in that sentence.

“The Starry Night” is an oil-on-canvas painting that, the study noted, depicts a view just before sunrise from the east-facing window of the artist’s asylum room at Saint-Rémy-de-Provence in southern France.

There are, I think, a few paintings that even the art-blind (like me) can identify at first glance. Mona Lisa. That Michelangelo thing with God and Human. The Scream. Maybe that one with the farmers. And The Starry Night. But, on the off-chance you have no idea what we're talking about, the article provides helpful illustrations.

Using a digital image of the painting, Huang and his colleagues examined the scale of its 14 main whirling shapes to understand whether they aligned with physical theories that describe the transfer of energy from large- to small-scale eddies as they collide and interact with one another.

I would love to have seen their grant proposal. "Yeah, we're going to study... art."

The atmospheric motion of the painted sky cannot be directly measured, so Huang and his colleagues precisely measured the brushstrokes and compared the size of the brushstrokes to the mathematical scales expected from turbulence theories. To gauge physical movement, they used the relative brightness or luminance of the varying paint colors.

One wonders if they already had a conclusion in mind when they picked those criteria, which would make it questionable science.

Huang and the team also found that the paint, at the smallest scale, mixes around with some background swirls and whirls in a fashion predicted by turbulence theory, following a statistical pattern known as Batchelor’s scaling. Batchelor’s scaling mathematically represents how small particles, such as drifting algae in the ocean or pieces of dust in the wind, are passively mixed around by turbulent flow.

And here's where most of the red flags appear, to me. Paint is, and you might want to sit down for this one, a fluid. Granted, that's just about the limit of my knowledge of artists' paint, but I have a high degree of confidence in my assertion, having seen paint in its fluid form. I've even seen paint mixed, and noted the swirls and eddies of turbulence. This is kind of like seeing milk added to coffee, and I don't drink coffee either.

Where I become more speculative is in thinking: well, he painted the thing with wet paint, so of course there's turbulence at the small-scale boundaries of brushstrokes.

Beattie agreed: “It’s an amazing coincidence that Van Gogh’s beautiful painting shares many of the same statistics as turbulence,” he said.

While there is, indeed, such a thing as coincidence, I don't agree that this is an example of it.

The study team performed the same analysis and detected the same phenomenon in two other images, one a painting, “Chain Pier, Brighton,” created by British artist John Constable in 1826-7, and the other a photograph of Jupiter’s Great Red Spot, taken by NASA’s Voyager 1 spacecraft on March 5, 1979.

Now, that seems a little more like what I'd expect from science. First, another painting; perhaps as a control of sorts. Hell if I know; I don't know that painting, and CNN neglected to illustrate it for us (there is, however, a link). As for Jupiter, we're pretty sure it exhibits all the hallmarks of turbulence on its visible surface, so it's a check on their modeling assumptions.

And yet, it shouldn't boggle anyone's mind that an artist noticed turbulence and tried to recreate it, or that one as brilliant as van Gogh was able to do it.

4 Like • Comment • View 2 comments

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