Complex Numbers (Book)

Blog Calendar

◄ April ► 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
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

April 11, 2023 at 10:16am

#1048020

Word to the Wise

Speaking of words...

Why people hate or love the sound of certain words

We’ve all experienced how certain sounds can grate on our nerves, such as the noise made by dragging your fingernails across a blackboard or the cry of a baby...

I suspect most people don't know what their own fingernails sound like dragged across a blackboard. Partly because who uses blackboards anymore, since like the 90s, and also partly because most people aren't evil enough to do it themselves. I, however, know exactly what my fingernails sounds like dragged across a blackboard.

Certainly I was a baby, but I don't remember how annoying my cries were. Knowing me, "very."

...but it turns out that the sounds of some words (like “virus”) can also affect how we feel and even give us a clue to what they mean (something to avoid).

I'd expect it to be the other way around: the name for something you want to avoid takes on a bad connotation. But that's why I'm reading the article, isn't it?

This phenomenon, where the sound of a word triggers an emotion or a meaning, is referred to as “sound symbolism”. Yet the idea that there might be a link between the sound of words and their meaning flies against accepted linguistic thinking going back more than a century.

And? Sometimes paradigms get reversed.

In our book...

Of course it's another book ad. What else is free on the internet anymore? Apart from this blog, I mean.

...we outline a radically new perspective on how we, as humans, got language in the first place, how children can learn and use it so effortlessly, and how sound symbolism figures into this.

Okay. Well, that first part sounds like speculation, but okay.

For example, if you pick a language at random that has the concept of “red”, the corresponding word is more likely than not to have an “r” sound in it — such as “rød” in Danish, “rouge” in French, and “krasnyy” (красный) in Russian.

Um.

The way an R is pronounced can be way different in different languages, such as the trilled R of Spanish or the nearly-German-CH sound of the letter in French.

Made-up words can be sound symbolic too.

All words are made up. Some just longer ago than others. And I'd be more surprised if newly minted words didn't have sound symbolism. Like when people go "whoosh" when a joke flies over someone's head.

In a classic study from 1929, the German psychologist Wolfgang Köhler observed that when Spanish speakers were shown a rounded shape and a spiky one and asked which one they thought were called “baluba” and which “takete”, most associated baluba with roundedness and takete with spikiness.

So much for flying against "accepted linguistic thinking going back more than a century."

Computer modelling of how children learn language has revealed that, as a child’s vocabulary grows, it becomes harder and harder to have unique sounds to signal different aspects of meaning (such as that all words relating to water should start with a “w”). Indeed, in a study of English sound-meaning mappings, we found that words that tend to be acquired earlier in development were more sound symbolic than words that are acquired later.

Computer modeling is a powerful tool, but it's only part of science. Also, I'm quite surprised these authors don't go into the "m" sound widely present in words associated with motherhood. Maybe they do, in the book.

I don't have much else to say, really (except "moist"). The article is less substantive than most book ads (which, again, I don't have a problem with here on a writing site), but the little bit of speculation I saw in it doesn't make me want to delve deeper by buying the book... and I'm predisposed to appreciating books on linguistics.

Still, I feel like it's something to keep in mind while writing, especially (but not limited to) writing that's going to be spoken, like a speech or screenplay: that the sound of words matters as well as their literal meaning.

3 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.