Complex Numbers (Book)

Blog Calendar

◄ January ► 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

Comments ·

10 Most Recent Blog Comments:

🌝 HuntersMoon

Sep 20, 2025 at 12:12am
In response to "Numbers End"

Boy, am I behind thee times. I thought you just put this on hiatus. Of course, in March I wasn't a complete devotee of your brilliance yet.

I'm more than happy with Carrion Luggage, however.

1 Like

Elisa the Bunny Stik

May 1, 2025 at 7:09pm
In response to "Shhhhhhh"

Anytime I hear/read about the Quiet Zone, I am always reminded of this video.

TJ: one day closer to camping

Mar 12, 2025 at 8:16pm
In response to "Penultimatum"

As my Grandmother used to say, "Everything changes except that which stays the same." I never did understand why she said it, but it sounds good.

1 Like

TJ: one day closer to camping

Mar 12, 2025 at 8:13pm
In response to "Numbers End"

Looking forward to the new book and hoping you don't encounter a meteor.

1 Like

Lazy Writer est 4/24/2008

Mar 12, 2025 at 4:19pm
In response to "Numbers End"

Sorry this one is closing..I will look for the new one tomorrow! Looking forward to it.

2 Like

Aiva Raine

Mar 12, 2025 at 3:45pm
In response to "Numbers End"

Thanks for a great 3000 entries.

Looking forward to the new blog, whatever it might be.

2 Like

Wordsmitty ✍️

Mar 12, 2025 at 1:36pm
In response to "Numbers End"

OK. What have you done with the real Robert Waltz?

Also, for the scientist engineer in me, have you actually tried to make entry 3001 and been rejected. Until there's proof, it's not real.

Thank you for your indulgence and sharing of wisdom.

R.I.P. "Complex Numbers"

3 Like

Ѧͷͷΐ

Mar 12, 2025 at 11:20am
In response to "Numbers End"

Sorry that this one is coming to an end, but I'm excited to see what you have in store for the new one!

2 Like

Wordsmitty ✍️

Mar 11, 2025 at 1:42pm
In response to "Penultimatum"

It's been an enlightening run. We wish you well in your next adventure.

It will be interesting to see if after the next entry that WDC actually does stop you from adding another.

We're all waiting on pens and pencils for the unveiling of the new blog and to discover what it will be called.

1 Like

BIG BAD WOLF is Lucky

Mar 11, 2025 at 10:46am
In response to "Penultimatum"

I'm reminded of this scene from The Princess Bride.

(Vizzini has just cut the rope The Dread Pirate Roberts is climbing up)
Vizzini: HE DIDN'T FALL? INCONCEIVABLE.
Inigo Montoya: You keep using that word. I do not think it means what you think it means.

3 Like

January 14, 2023 at 12:03am

#1043102

Inspire

Periodically, as I've noted before, I find articles bloviating about things that science fiction authors have "predicted." This is misleading, because unless it was a sealed prediction opened some years later, it's more like they dreamed it up, or someone invented something based on an idea they saw in SF.

Today's article is a refreshing change from that because of how the headline is worded.

11 Scientific Advancements Inspired by Sci-Fi Stories

Ideas can come from all sorts of places, and inspiration can hit in a flash—think of Archimedes supposedly yelling “Eureka! Eureka!” in the bath when he realized that irregular items could be accurately measured through water displacement.

Probably apocryphal, but for whatever reason, we love our narratives about inspirational flashes. Like that one, or Newton's apple.

But sometimes, it’s fiction, not reality, that provides the spark of inspiration. There are sci-fi tales, for example, that have gone beyond predicting technological advancements to directly inspiring scientific progress, from robotics to rocketry and everything in between.

And they just lost my good will from the headline by using "predicting" here.

In any case, I'm not going to copy all of them here, just the ones I want to comment on.

1. The Taser // Victor Appleton’s Tom Swift and His Electric Rifle

Written under a pen name and published in 1911 by the Stratemeyer Syndicate (which also published the Nancy Drew and Hardy Boys novels), Tom Swift and His Electric Rifle sees the titular character invent a weapon that looks like an ordinary rifle but fires bolts of electricity. The book was a childhood favorite of Jack Cover and partly inspired the creation of his own electroshock weapon: The Taser.

That might have been the ultimate origin; I don't know of any stun devices in SF before that (the genre hadn't been around for even 100 years at that point, anyway). But the idea took off in a big way in SF and, especially, space operas; the ray gun, or zapper, or whatever, became a staple. Perhaps the most famous version was Star Trek's phaser. Now, this article goes on to note that "TASER" stands for "Thomas A. Swift’s Electric Rifle," and other sources back that up—but it was invented starting in 1969, three years after the first Star Trek episode featuring phasers. And phasers, of course, took their name inspiration from the laser.

My only point here being that many inventions have more than just one inspiration.

2. Helicopters // Jules Verne’s Robur the Conqueror

Leonardo came up with a helicopter concept first. In fairness, though, his wouldn't have flown.

3. The World Wide Web // Arthur C. Clarke’s “Dial F for Frankenstein”

Without Arthur C. Clarke’s 1960s-era short story “Dial F for Frankenstein,” there might be no World Wide Web as we know it. The sci-fi story is about a global, interconnected telephone network that gains sentience—and it served as one of Tim Berners-Lee’s inspirations when he created the Web while working at CERN in the 1980s.

I'm always amazed at the number of people who, after reading a science fiction story that warns "under no circumstances should we invent this thing," go on to invent that thing.

7. Investigating the Habitability of Mars // Ray Bradbury’s The Martian Chronicles and The Illustrated Man

Physicist Peter H. Smith, professor emeritus at the Lunar and Planetary Laboratory of the University of Arizona, attributes his initial interest in extraterrestrial worlds to Ray Bradbury’s sci-fi stories, including those in The Martian Chronicles (1950) and The Illustrated Man (1951).

Okay, fine, but let's remember that Bradbury himself was inspired by earlier Mars stories, which in turn were inspired by even earlier Mars stories, etc. Not all of them were science fiction. Hell, Bradbury is only marginally science fiction; he was more interested in poetic prose than in the science behind things. Nothing wrong with that—he was certainly awesome and inspiring; this isn't meant to rag on him at all.

11. Remote Manipulators // Robert Heinlein’s “Waldo”

Published under the pseudonym Anson MacDonald, Robert Heinlein’s short story “Waldo” is about a scientist named Waldo Farthingwaite-Jones who invents a device to help him manage his degenerative muscle disease. His machine can perfectly mimic his hand movements, but with greater strength and from a distance. This device is essentially a remote manipulator, also known as a telefactor. Because of Heinlein’s story, some call the mechanism—which, according to Fundamentals of Robot Mechanics, “usher[ed] in the era of teleoperators”—a “waldo.”

I'm mostly including this one because the term "waldo" is a legitimate word for this technology, and I get the impression many people don't know where it comes from. Heinlein didn't actually come up with the idea for the remote manipulator; he in turn was inspired by earlier writings. But the name is all Heinlein.

If I had to take a stab at which science fiction author was most influential in terms of real-life invention, Heinlein would be in the top 5. He's often credited with the ideas behind the waterbed (Stranger in a Strange Land), and computer-aided design (The Door into Summer), just to name two other examples.

It would be wrong to say that any of these writers "invented" the technology they inspired. Invention requires far more detailed design work than most SF writers need to go into, especially in their stories; that would get really boring really quickly, like Melville's detailed descriptions of whaling in Moby Dick. But this is the way things get invented in the first place: it always starts with an idea (or, some might say, a Platonic ideal) which only gradually makes its way through mind and sweat to consensus reality. Who gets the credit? Well, in my personal opinion, the inventor gets the bulk of the credit because they're the one who made it work. But there's good reason to acknowledge the source of one's inspiration.

Comment • View 3 comments

© Copyright 2025 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.