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Wednesday, Dec. 11, 2024

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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:

Wordsmitty ✍️

about 6 hours ago
In response to "On the Label"

"June 25, 2024 5:40 AM" = Need time zone.

"Note to self:" = self-driving taxis

Some people definitely can be labeled, but we don't say those in polite company.

2 Like

Annette

about 6 hours ago
In response to "On the Label"

Only one label matters. Cat person or dog person. If the answer is anything except "yes" the person's life choices defy all logic analysis.

I wonder what is the difference between psychotherapist, psychologist, and psychoanalysis. Or are they like po-ta-to, po-tuh-two?

3 Like

tj-Merry Mischief Maker

Dec 9, 2024 at 2:51pm
In response to "Analog Log"

As time progresses, it amazes me how we have moved from tide clocks/analog computers to people eating tide-pods.

1 Like

Aiva Raine

Dec 9, 2024 at 2:37pm
In response to "Story of the Century"

Fantastic entry. Have I mentioned how I love your snark? Thanks once again for the grins and your awesome sarcastic responses to the articles.

1 Like

Anni Pon

Dec 8, 2024 at 10:01am
In response to "Revisited: "Millennials Killed Millennials""

It's kind of funny to me that people still use "millennials" to refer to "those darn kids" when most of them are in their 30's now with kids of their own. As an elder millennial (a Xennial, if you will), I haven't really found the generational definitions too useful for myself. I'm right on the border of generations, so I have a lot in common with both Millennials and Gen X. Growing up in silicon valley with tech savvy parents, I had earlier access to computers and technology than a lot of other people my age. But in terms of cultural milestones, I lived through and am old enough to remember things like the 90's, Y2K and 9/11. The borders are sort of arbitrary, but on a population level I can see how sometimes it can be useful to group people into generations.

2 Like

Elisa: Snowman Stik

Dec 8, 2024 at 9:40am
In response to "Revisited: "Millennials Killed Millennials""

*rubs hands together* Time for me to dive right in!

2. In this system, I'm early Generation X, which hardly anyone ever talks about, opting instead to rag on "boomers" or "millennials" or "Gen-Z." Or praise them, depending on the author's beliefs and age.

Looks like I need to change my name to "hardly anyone". Also, there has been more and more chatter about Gen X in some circles, but curiously this seems to be happening in institutions that have dropped labels (which I'll touch on in a second here).

On top of which, you'd have to convince me that our 1983-born X-er has more in common with someone born in 1966 than with someone born in 1986.

Very, very, VERY few organizations that have ever in their history used generational labels have set the Gen-X border any later than 1980. While I'm still very salty that Pew stopped this practice (one of the few things they've done wrong, IMO), I still use their Gen-X demarcation of 1965-1980. That demarcation nicely strikes the median of most demarcations. SO in this case it's not a matter of you needing to be convinced. It's a matter of the author leaning on a REALLY bad source.

Much of what sets "generations" apart, in modern terms, has to do with technological advancements and societal changes...then other people had to think that the original wearer was cool enough to start a fashion trend.

And how that message has been conveyed has drastically changed among generations, to boot.

So you know what I want to see Millennials finally kill?

Generations.

As a Millennial, I can tell you that this is probably the last thing our generation will try to kill. It's something that's persisting even as we reach middle age. And that's another thing. We're aging very strangely, namely that physically we're aging more slowly than people in Gen Z. We could have killed the concept of aging a certain way, but Gen Z's circumstances have effectively torpedoed that revolution.

Also, if anyone wants to read the original article, you can certainly try throwing the URL in the Wayback Machine. It doesn't always work, but it's worth a try. There are some other methods as well, but I haven't tried them myself yet. (Speaking of which, has anyone here tried Zette? I've been meaning to sign up for that but haven't had a chance. It's one of my goals for 2025.)

2 Like

Wordsmitty ✍️

Dec 7, 2024 at 12:41pm
In response to "Story of the Century"

Maybe it helps if you can dance - Dick Van Dyke and Coldplay - although he's just 99. (I assume everyone has read about that)

4 Like

🌖 HuntersMoon

Dec 6, 2024 at 10:07am
In response to "No Space for Time"

I think you just added clarity to the Twilight Zone...

3 Like

tj-Merry Mischief Maker

Dec 5, 2024 at 4:05pm
In response to "How To Give A Fock"

How many photons does it take to make a torpedo? Who gives a Fock! Actually, wasn't Fock Spock's half brother?

3 Like

Jayne

Dec 5, 2024 at 10:23am
In response to "How To Give A Fock"

Versatile Fock States is the name of my next thrash album.

3 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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