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Monday, Nov. 18, 2024

6:27am 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:

tj-turkey-jobble-jobble-hard-J

about 14 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

July 8, 2023 at 7:27am

#1052318

Unsung

Despite what airy nonsense your life coach may have spouted, it is not possible for one person to change the world.

5 People Who Changed the World and Got Jack Squat for It

And even if it were possible (which it's not), there's always the chance that no one would notice.

Link is from Cracked, so don't try to use this in any world-changing scholarly papers.

5. Rosalind Franklin

I agree she got dicked over (pun intended), but I suspect more people recognize her contribution now.

Before 1953, though, the structure of DNA was unknown, until the now ubiquitous double-helix structure was modeled by James Watson and Francis Crick. If you know any names related to the study of DNA, it’s most likely theirs.

To the best of my knowledge, Watson was unrelated to A.G. Bell's Watson, or Sherlock's.

Watson and Crick did admit that solving DNA’s structure without the Franklin data would have been “unlikely, if not impossible,” but apparently putting her name at the top of the paper was a step too far.

In case you're wondering, this is one reason I say it's impossible for one person to change the world: everyone has been influenced by others, and, in many cases, others have to let themselves be influenced by that person.

4. Ignaz Semmelweis

I didn't recognize the name at first, but the thing he did was something I'd heard of.

So what was Semmelweis’ incredible, world-changing medical discovery? It was that doctors should maybe start washing their hands.

This really was tantamount to heresy at one point.

3. Michael Delligatti

When you think of a central figure related to McDonald’s, you might think of the founder, Ray Kroc, or more likely, a fictional and mildly unsettling clown.

Kroc founded McDonald's like Musk founded Tesla Motors: in mythology only.

You may have assumed the Big Mac was cooked up in some secret burger laboratory deep beneath McDonald’s HQ. In reality, it was Delligatti who suggested a two-patty burger and developed the special sauce, an idea that McDonald’s hated at first.

This may be heresy, too, but I've never really liked the Big Mac. I do miss the McDLT, so it's all for the best that it's no longer available.

So what did Delligatti get for forever changing the cholesterol levels of the human race? The ultimate bare minimum: a plaque.

We all get plaque from eating at McDonald's.

2. Philo Farnsworth

If you’re born with a name like Philo Farnsworth, you basically have two viable career paths: some sort of strange preacher, or a brilliant inventor.

You forgot "supervillain."

I don't feel like copying much of this section; basically, he invented the television. Which, come to think of it, may have caused as much suffering as the Big Mac. (The part that was surprising, to me, was that said invention was nearly 100 years ago.)

1. Henrietta Lacks

As with Franklin above, she's more widely known, these days. Unlike Rosalind Franklin, though, it wasn't what she did that was significant (which in no way should diminish her significance).

For whatever reason, her cells reproduced at an unbelievable rate, and “HeLa” cells have been used in research ever since. She did finally get a book and a movie in which she was played by Oprah, but she and her relatives got a whole lot of absolutely nothing for years after her death.

Played by Oprah? Talk about adding insult to injury.

Moral of these stories: sometimes it just doesn't pay to be influential.

3 Like • Comment • View 3 comments

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