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Saturday, Nov. 16, 2024

5:39am EST

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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:

Write_Mikey_Write!

a day ago
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

a day ago
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

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.

July 11, 2022 at 7:06am

#1035020

Speakers for the Dead

Here's another one from Atlas Obscura, shedding some light on our wonderful American history.

The Quest to Honor Disabled Patients Buried in Anonymous Graves
Historically, institutions often interred their dead with simple markers. In Massachusetts, researchers are learning about the patients’ lives and the facilities’ fraught legacies.

It's fairly long and involved, but worth it for a glimpse of how attitudes have changed (and not).

Between 1947 and 1979, these institutions buried 296 of their patients in simple, anonymous graves on a plot of former marshland now called the MetFern Cemetery, a portmanteau of the two institutions’ names. The grave markers are sunken and toppled, and have only two things etched onto their concrete slabs: “C” or “P,” for Catholic and Protestant (though records indicate that a Muslim man and two Jewish patients may have been buried there as well), and a number that denotes the order in which the patient was interred.

It's hard to say who was less valued to them: the differently abled, or the differently religious.

The Walter E. Fernald Developmental Center, also referred to as the Fernald School, was originally called the Massachusetts School for Idiotic and Feeble-Minded Youth.

But doesn't that describe all youth?

Founded in South Boston in 1848 by Samuel Gridley Howe, it opened as a small experimental school to teach children and teens with intellectual disabilities life skills so they could live independently. Due to the popular perception that children with disabilities couldn’t learn, it proved to be the most progressive and radical institution of its era, says Green.

I suppose they had to start somewhere.

As conditions declined, an increasing number of patients suffered premature deaths, leading the institutions to open a shared cemetery, says Green.

Easier than hiring more people.

The unnamed gravestones were likely a measure taken to protect a family’s reputation in an era of overwhelming social stigma surrounding disabilities.

I guess it doesn't much matter to someone who's dead, but what about protecting their reputation?

Rosenblatt says there’s now “a lot of energy” around unearthing information and restoring dignity to deceased people who have long been overlooked.

Again, it's a start.

I'm just hitting some lowlights here. There's much more to the article. As maddening as it is to hear about how some people were dehumanized, it's also rather gratifying to see that the trend is now toward some restoration.

6 Like • Comment • View 3 comments

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