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Wednesday, Dec. 18, 2024

1:54am 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 6 hours 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 8 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 16 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 17 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

December 10, 2024 at 12:23pm

#1081001

Gilgamash

From aeon, a tale as old as time. Well, as old as civilization, anyway:

The fermented crescent
Ancient Mesopotamians had a profound love of beer: a beverage they found celebratory, intoxicating and strangely erotic

So, they were human.

I should note that, like many free articles, this is a stealth ad for a book. But, for once, it's a book I would buy. (I'm not going to add to the advertising; the details are there at the link.)

Hamoukar, Syria. 20 May 2010. We are midway through what will be the last excavation season at the site for some time. The following spring will see the outbreak of a long and brutal civil war.

I don't talk about them much in here, but I do keep up with current events. Still, I find it hard to follow all the ins and outs of the disturbances in Syria. Nevertheless, yes, I heard about Assad, and I remember my inner cynic (which, frankly, is just Me) going, "Oh great, what fresh hell will Assad be replaced with?"

Today, though, the archaeologist Salam Al Kuntar, balanced on tiptoe at the bottom of a tomb, has just uncovered a little green stone. It is a cylinder seal, an ancient administrative device. We roll the tiny seal in clay – just as its former owner once would have – to reveal an impression of the intricate scene carved into its surface. It may not be the finest seal ever seen, but the tableau is eye-catching: a stick-figure man and woman are having sex, the man standing behind the woman, who bends over to drink from a jug on the ground. And is that a straw emerging from the mouth of the jug?

I, of course, instantly knew the implication: chick was drinking beer, maybe because her partner was ugly. I once saw a shirt that read: "BEER: Helping ugly people have sex since 1862!" And I snorted and said, "Yeah, right. More like 6000 BCE."

It may surprise you that our ancestors had sex, until you stop and think about how they became our ancestors.

Indeed, the drinkers of ancient Mesopotamia often drank via straw – though not always, shall we say, in this particular position.

While drinking beer through a straw today is as much a social faux pas as serving warm white wine, it was kind of necessary then because, apparently, the beer had floaty things in it and the straw kept them from getting swallowed. It would filter out the biggest and grossest solids.

Yes, the Sumerians (probably) invented beer. No, it wasn't the tall, frosty Pilsener of today. For one thing, no refrigeration. For another, no hops. But it was still fermented grain, hence: beer.

Banquets were a key part of the social calendar in Mesopotamia, and beer was an essential element. But people also drank beer at home, on the job, in the tavern, in the temple, pretty much everywhere.

Before we knew shit about microbes, beer was often a better choice than water because the process requires boiling water, which we know now destroys bad microbes. Hell, a big part of beer production today involves letting the proto-beer (called wort) cool enough for the yeast (good microbes) to be able to survive and work their magic. They wouldn't have known exactly why beer was good, only that it was.

Perhaps you have encountered the notion that beer was ‘invented’ in Mesopotamia. That is a hypothesis at best.

Yeah, well, it's still better supported than other hypotheses.

And, as the global search for earlier and earlier traces of alcoholic beverages gains steam, there is at least one key takeaway: beer was invented (or discovered) many times in many different places.

I'm okay with that clarification, and will note that yes, it is one of those things where you can have a legitimate philosophical argument over "invention" vs. "discovery."

The famous ‘land between the rivers’ was also the land of Ninkasi, goddess of beer. When Ninkasi poured out the finished beer, ready to drink – a Sumerian song tells us – it was like ‘the onrush of the Tigris and the Euphrates’.

Before you rush out and claim a name, there's already Ninkasi Brewing. It's located in Oregon, so I haven't tried many of their offerings, but I seriously doubt they used the ancient Sumerian recipe. However, as the article later attests, other brewers have attempted Sumerian beer. One of them was named Gilgamash, which utterly delights me (hence the entry title today, which, now you know, wasn't an original Waltz pun). But I'm getting ahead of myself, here.

The article goes on to discuss several aspects of ancient beer culture, including a paraphrased version of when Inanna got Enki so drunk that he gave her all his prized possessions. I'm sure I've covered that in here before.

Beer was brewed at home, in neighbourhood taverns, and in breweries managed by palace and temple authorities. In some cases, we know the names of the brewers – for example, homebrewers Tarām-Kūbi and Lamassī (both women), tavern-keepers Magurre and Ishunnatu (both women), and palace brewers Qišti-Marduk and Ḫuzālu (both men).

While your image of a brewer today probably involves a very large, very bearded man, historically, beer has been either a female project or ungendered.

The most detailed account of the brewing process appears in the ‘Hymn to Ninkasi’, goddess of beer. But this lyric portrait of Ninkasi at work in the brewery is hardly a set of instructions for brewing beer.

I will defer to this author's greater experience in the historical arena, but everything else I've read does call it a recipe of sorts. Not standardized like today's recipes, with their precise measurements and somewhat detailed instructions following about 50 pages of backstory, but more like a mnemonic, which the brewers were expected to fill in with passed-down knowledge and maybe even proto-science.

I'm not sure the distinction is overly important to us. Hell, we have problems re-creating other recipes from a century or more ago, precisely because a lot of the handed-down knowledge is lost. What's more important is that beer was important enough to write hymns to the gods about.

The author has a lot more to say about this, and I can, again, provisionally defer to his greater knowledge.

In conclusion, yes, I would read that book for sure. I might wait to buy it until after the holiday season, though, just in case someone wants to give me one as a present.

No, that's definitely not a hint.

Or is it?

3 Like • Comment

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