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Monday, Nov. 18, 2024

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Complex Numbers

by Robert Waltz

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:

tj-turkey-jobble-jobble-hard-J

about 13 hours ago
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

Turkey DrumStik

a day ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

August 23, 2023 at 8:11am

#1054477

Sumer Time

Nothing is forever, but some things endure for quite some time.

Poet of impermanence
Enheduana is the first known named author. Her poems of strife and upheaval resonate in our own unstable times

Ironic, then, that works about societal change have survived over 4,000 years.

About 4,200 years ago, the area we now call southern Iraq was rocked by revolts.

History doesn't repeat itself. It echoes.

The once-independent Sumerian city states had been brought under one rule by the legendary king Sargon of Akkad.

For comparison's sake, I tried to figure out when Sumer became, well, Sumer. There's a pretty wide range of possible founding times. Seems like the Sumerian civilization had been around for at least 1000 years before the time of this poet, and possibly even 3000. That's a pretty long time for a civilization.

One such revolt is depicted in a fascinating poem known as ‘The Exaltation of Inana’. Besides being a poetic masterpiece in its own right, ‘The Exaltation’ bears the distinction of being the first known work of literature that was attributed to an author whom we can identify in the historical record, rather than to an anonymous tradition or a fictional narrator. The narrator of the poem is Enheduana, the high priestess of the city of Ur and the daughter of Sargon. According to ‘The Exaltation’, she was cast into exile by one of the many revolts that plagued the Old Akkadian Empire.

Regular readers might also recognize ancient Sumer as the source of the world's oldest known joke. It is a fart joke. I'm just reminding us of this so we don't start thinking that all Sumerian literature was highbrow.

We do not know for sure whether the poem was written by the historical Enheduana herself, as a literary retelling of a real event, or by a later poet writing in her name, in the ancient version of a historical fiction that was meant to celebrate the famous high priestess.

I think this is important to note, also. Whatever the provenance, though, it exists. The clay cuneiform tablets shown at the link are also remarkably well-preserved.

The poems do not merely register the reality of an historic upheaval – they go one step further by turning that instability into a cosmic insight, an occasion to reflect on what the world is really like. They contain, compressed within their often-cryptic verses, the germ of an ancient philosophy of change.

An ancient philosophy of change, sunk into clay to preserve it for a very, very long time. Like I said... irony.

The article presents excerpts of translations of some of the writing (it was only a couple of days ago that I did an entry about translation). It's fairly long, but I found the whole thing intriguing, even the way the author related the upheavals of ancient Sumer to some of the changes we're going through today. I'm not saying I agree, but having the perspective of history can be useful.

I just wanted to make one more observation here, relevant to writers in general. It's not complacency and peace that generates lasting works of literature, but upheaval, change, and tragedy. Something to keep in mind if you want your works to last over 4,000 years.

4 Like • Comment • View 1 comment

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