Complex Numbers (Book)

Blog Calendar

◄ June ►
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
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:

Brandiwyn🎶

a day ago
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

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

June 19, 2024 at 11:40am

#1072895

Matters of the Heart

Way back before the solar eclipse, I saved this Atlas Obscura article to my queue. But the topic itself is timeless, so there wasn't any rush, and the Random Number Gods saw fit to wait until today to bring it forth.

‘Total Eclipse of the Heart’ Was Almost a Meat Loaf Song
Bonnie Tyler’s classic rock epic nearly got the ‘Bat Out of Hell’ treatment.

Hardly the usual AO fare; they usually concentrate on place oddities (hence the name) or food. They were doing special "eclipse" articles, and this was one of them. Everything here tracks with stuff I already knew, but I didn't fact-check it further.

When Bonnie Tyler’s husky, powerful “Total Eclipse of the Heart” hit the radio in 1983, rock ballad fans around the world fell in love.

Well, some did. Some hated it. Still do. I can always tell if someone is worth hanging out with based on their feelings about that song alone.

But for one musician, the history of the tune, which was written by composer Jim Steinman, is as torn as the dark love ballad’s lyrics. Meat Loaf was the one who was supposed to have sung that song.

Confession time: I possess, and have read, a copy of Meat Loaf's autobiography (unsigned, unfortunately). But I can't remember whether I knew the above from that or through other sources over the years. But the way I see it, ML was famous anyway, still one of the best-selling performers in history; and it boosted Bonnie Tyler, so no real losers here. As the article notes later, ML didn't seem to hold any of this against Tyler.

Meat Loaf had long worked with songwriter Jim Steinman, including on his hit 1977 album Bat Out of Hell.

What I did get from the book, I think, was that that album was supposed to be a collaboration between singer and songwriter, not purely Meat Loaf with the writing credit added as an afterthought. (Many of the session musicians on it were also members of the E Street Band, adding to its awesomeness.)

Meat Loaf’s next planned album, the never-made Renegade Angel was poised for recording, and was supposed to include the track “Total Eclipse of the Heart.”

There are at least two things in music history that almost happened that I wish had happened, and that's one of them. The other also involves Jim Steinman—he was meant to collaborate with Andrew Lloyd Webber on a stage production. Just as well that the latter didn't happen; Broadway would have been sucked into a black hole of melodrama.

Amid mysterious and abrupt problems with his voice and a psychologically damaging aversion to fame, Meat Loaf’s success and partnership with Steinman began to slowly unravel, forever changing the sound and trajectory of the ballad “Total Eclipse of the Heart.”

It changed a lot of trajectories, really. And that sentence glosses over a lot of drama. The article dips into this a bit, then:

Meat Loaf, under contractual obligation, went ahead with his next record, Midnight at the Lost and Found, a collection of songs written by various songwriters, which Meat Loaf later came to regret. (Steinman meanwhile released songs that he initially thought up for Meat Loaf on his own solo album, Bad for Good.)

I bought that Steinman album on LP when it came out. I also acquired the CD several years later. I like it. It's not for everyone. Steinman's voice just didn't work in the same way Meat Loaf's did. Most of the tracks on it later showed up on different Meat Loaf albums, after they reconciled, and the difference is plain if you hear both versions of a song.

But that's kind of a sidebar; the point is, Steinman was a prolific songwriter, but lacked the performance talents needed to turn his ideas into popular music. For that, he needed other talent. Preferably people who could pull off melodrama, like Meat Loaf... or Bonnie Tyler.

This Rolling Stone article

has more on that.

So back to the actual topic of the article (and this entry):

The song’s music video, which featured prep school boys with glowing eyes, gymnasts, dancing men in leather jackets, and lots of floating fabric, also spawned a Literal Video spoof in the early 2000s that highlights the super weirdness of the visuals.

I've posted that Literal Video in here before, so I don't want to do it again. It's still up on YouTube, attesting to not only the power of the original song and video, but to the wonder of parody. Yes, I can like an original and also appreciate the parody.

Despite the song's title, though, it wasn't really part of my eclipse soundtrack. No, that was mostly Pink Floyd.

1 Like • Comment • View 2 comments

© 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.