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Wednesday, Feb. 19, 2025

3:27pm 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:

Adherennium - Maybe Writing?

about 2 hours ago
In response to "Fail to Succeed"

Having drunk soda on both sides of the Atlantic, I have to say that Mountain Dew with HFCS in America tastes a lot better than the 'same' drink made with sugar here in the UK. The experience is smoother and so is the taste.

1 Like

tj wanderlust-words-in-motion

about 21 hours ago
In response to "Tater Tales"

Instant potatoes? Yes, I enjoy them, too. We also use them for thickening up soups and stews.

1 Like

Robert Waltz

a day ago
In response to "Linguistic"

Annette

- I appreciate the recommendations, but I canceled Netflix when the choice was to put up with ads for a lower price or pay a shitload of money. If it were free with ads, I'd manage like I did in the days of broadcast TV, but I flat-out refuse to both pay money and watch commercials, which is why I never had cable TV.

The price for the ad-free experience also went up to the point where it wasn't worth it with the amount I watched.

Annette

a day ago
In response to "Linguistic"

I refer to my three languages as three different brains. In France, I activate my French brain. Which made for some funny turns of phrase when I was speaking to my son in English with English words, but in French syntax.

Netflix has some really good multilingual TV series. I recommend

Monsieur Spade

Black Spot

Capitani

1 Like

Robert Waltz

Feb 17, 2025 at 12:00pm
In response to "Linguistic"

Kåre เลียม Enga

- yeah, I edited out the duplication, because it could be seen as a refutation of itself.

1 Like

Kåre เลียม Enga

Feb 17, 2025 at 11:32am
In response to "Linguistic"

I use translation tools all the time... and subtitles on youtube.

My French pronunciation is okay because I learned it as a child; my Spanish is okay because I practiced it. I slip into both with one key exception. French is easier when I'm depressed and Spanish can draw me out of depression.

Speaking multiple languages has also been linked to delayed onset of dementia symptoms.

Yes, I saw that you repeated that. It bears repeating.

Speaking multiple languages has also been linked to delayed onset of dementia symptoms. Or so I hope.

1 Like

Lazy Writer est 4/24/2008

Feb 16, 2025 at 3:18pm
In response to "Revisited: "Hush""

Well as someone who only hears out if one ear..I prefer to be able to hear completely any sound or noise or whatever. There are sounds you never would miss until you can't hear them anymore.

Anyway each to their own..I also prefer silence at times too.

Keep writing.

1 Like

Robert Waltz

Feb 15, 2025 at 2:57pm
In response to "Ignorance is the Opposite of Bliss"

Kåre เลียม Enga

- While competition is often touted as the driving force of progress or evolution, it's actually cooperation that's most important. Even opposing sportsball teams, while seeming to be in competition, have agreed on a set of rules, the enforcers of these rules (referees or umpires or whatever), and the penalties for breaking the rules.

The Space Race is another example. On the surface, it was a dick-measuring contest between US and USSR. Each country relied on internal cooperation, obviously, but they also cooperated with each other—if only through things like weapons treaties and promises not to go to war over it.

Competition is a factor, of course. But survival depends on cooperation.

1 Like

Kåre เลียม Enga

Feb 15, 2025 at 12:46pm
In response to "Ignorance is the Opposite of Bliss"

Denver Broncos beat the Cleveland Browns... just saying. No, I didn't know. I looked it up! And although I know a thing or two I rely on the experts behind google to find out for me.

Is this blog entry pertinent? As Our Dear Leader fires experts left and right (but mostly left, because he's always right), we're left with loyalists who may or may not be experts or have any knowledge of the field at all.

You delineate the weakness of competitiveness. One ring to rule them all negates the contribution of millions. In the case of reaching the Moon or Mars, the crew cannot be competitive and even the technicians have to be a competent expert in what may be a detail (like proper heat shielding for any shuttle). China, USA and India can compete on getting to Mars; but, it will be a cooperative crew of experts that gets there.

I loved reading my poetry to a group of writers who could pick it apart. I miss that. Since I am the boss, I don't have to change one comma and I can ignore their suggestions... but I'm better off doing that than submitting to an AI program that reduces everything to General American for an audience of 12 year old Vacation Bible School students (a.k.a. the education system of Southern Baptist Confederacy of Oklahoma).

2 Like

tj wanderlust-words-in-motion

Feb 14, 2025 at 3:35pm
In response to "Steaming Ship"

Thanks for clearing that up. On a side note, if I have a 16 foot fishing boat and stick my kayak in it, is it now a ship?

Speaking of space "ships", I've often wondered why the termed the craft used to shuttle people/beings between the planet and ship, or even between ships, shuttle-crafts.

In sticking with terminology, if the larger vessel is a spaceship and carries smaller crafts, shouldn't it be a spaceboat?

1 Like

February 16, 2025 at 8:43am

#1083940

Revisited: "Hush"

Back in November of 2019, as part of a round of 30 Day Blogging Challenge, I answered the call of a prompt ("Besides music, what are some of your favorite sounds?") with a loud silence: "Hush"

When I dig into the past on these weekly adventures, I try not to repeat myself. This one came up at random, today, and I got the feeling that I'd Revisited it before. But, searching around, I didn't find any evidence that I'd done that. Perhaps I'd simply come across this one in another search. When a blog spans 18 years (albeit with a long hiatus in there) and nearly three thousand entries, I suspect it would tax anyone's memory, and mine more than most.

As for the entry itself, it's short and contains no external quotes.

A while back, I vaguely recall, there was a 30DBC prompt that asked the old question: would you rather be deaf or blind? And I said something like, I despise 75% of all sounds, but the other 25% is music, and I wouldn't want to live without music.

While true, I do prefer to be able to hear.

If someone has the dedication to swing back and look at what I actually wrote, and finds that it's something different from that, and calls me on it, well, congratulations.

This is a universal bit of sarcasm. I don't doubt that I've contradicted myself before, or remembered different details.

I don't really mind the little sounds that accompany everyday existence: the hooting birds, the rustling leaves, that sort of thing, but I can't say they're my favorite sounds.

Bird chirping, especially, can really get on my nerves. At first, I thought Silent Spring was aspirational.

I've been known to reject potential romantic partners if they're the kind of people who leave the TV on all day for "background noise."

Seems like this is less an issue now, with more people doing deliberate streaming. I also have no problem with (most) music being used as background noise. At this point, though, and even back when I wrote this, I was done with the whole "romantic partner" nonsense.

Not to mention that a non-trivial reason why I never wanted kids is because children noises make me meshuggah.

It wasn't the deciding factor (that was, well, look around), but it was definitely on my list.

If I can't listen to music, I prefer silence, or as close to it as I can get.

Still true.

Not that I'd want to be deaf; not just because of music but because I like to have some advance warning that someone is trying to sneak up on me - less likely to have such warning if there were a lot of background noise.

No one's successfully snuck up on me in over 20 years, so this must be working.

So, between yesterday's prompt and today's, I suppose I've been outed as someone who prefers both silence and darkness.

Hello darkness, my old friend.

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