Complex Numbers (Book)

Blog Calendar

◄ August ► 2023
S	M	T	W	T	F	S
		1	2	3	4	5
6	7	8	9	10	11	12
13	14	15	16	17	18	19
20	21	22	23	24	25	26
27	28	29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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:

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

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

JayNaNoOhNo

Nov 5, 2024 at 1:16pm
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 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

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.