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Sunday, Jan. 19, 2025

3:38pm 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:

🌖 HuntersMoon

about 5 hours ago
In response to "Revisited: "Science Is Almost Always Wrong...""

I feel for you, Bob. "Kiss my Pythagoras" never really caught on either.

1 Like

tj wanderlust-words-in-motion

about 22 hours ago
In response to "Bon Voyage"

Who knows, maybe they'll like the record, swap it out with one of their own and ship it back in the original container(Voyager), starting an intergalactic record exchange.

2 Like

🌖 HuntersMoon

a day ago
In response to "Bon Voyage"

It's not exactly like having your credit cards hacked.

For those interested...

2 Like

Elisa: Snowman Stik

a day ago
In response to "Bon Voyage"

"People like a happy-ending success story, I hear."

Now to see if this one gets a good response here or if it needs to be further shared.

2 Like

🌖 HuntersMoon

Jan 17, 2025 at 2:51pm
In response to "Up In Re-Volt"

Interesting... but the puns

@ Jayne: One of my all-time favorite scenes.

1 Like

tj wanderlust-words-in-motion

Jan 17, 2025 at 12:21pm
In response to "Up In Re-Volt"

After reading this I realized that most of what I know about electricity is that if you get a shock, it Hertz!

4 Like

Jayne

Jan 17, 2025 at 11:18am
In response to "Up In Re-Volt"

If only there was some way to milk cows with without electricity...

I know what they're referring to, but I still think it sounds dumb lol

3 Like

🐕GeminiGem🎁

Jan 16, 2025 at 6:15pm
In response to "Meat Me In the Lab"

I am a vegetarian for animal-rights reasons. I eat plant based meat, some are pretty good. The rest are an acquired taste. They can call cultivated meat "slaughter free" if they call the real thing "slaughter house delights" or something ridiculous like that.

2 Like

tj wanderlust-words-in-motion

Jan 16, 2025 at 4:18pm
In response to "Meat Me In the Lab"

In time, and once the bugs (possibly literal) are worked out, I think it's a great idea. Of course, twenty-five to fifty years down the road it's likely they'll find some kind of adverse health problems related to eating bio-meats, but if it's not that it would be something else. Life is like that and the answer isn't to not try, it's to push forward and overcome.

Will we (you and I) ever see the day every home has a food replicator in it instead of a microwave? Probably not, but it would not only solve a lot of food related issues, it would also solve a lot of problems of what to do with our waste products...

2 Like

🌖 HuntersMoon

Jan 16, 2025 at 10:11am
In response to "Meat Me In the Lab"

Congratulations, Bob! You managed to get through the whole subject without once mentioning Soylent Green.

Mmmmmm. Real meat!

2 Like

January 19, 2025 at 9:25am

#1082544

Revisited: "Science Is Almost Always Wrong..."

Our delve into the past today takes us back to just before the beginning of my still-going blogging streak, early December of 2019, when I saved this entry: "Science Is Almost Always Wrong, And That's A Good Thing"

Other than noting that maybe—just maybe—being the longest entry title I've ever typed, there's not a lot to say about the entry itself. The article featured is from Quanta, and it's still available.

There are a few things I see now from a different, older, wiser perspective:

I mean, seriously, how hard is it to get the damn science right? I personally know a guy who works as a science consultant to certain TV shows, and the problem is they don't listen to him.

Turns out it's kinda hard to "get the damn science right." Sometimes the necessities of plot just get in the way.

That's going to be my new curse. "Hey, Waltz, someone keyed your car." "Galileo's balls!"

Unsurprisingly, I promptly forgot about that expletive, and I don't think I ever actually used it in speech or writing.

What that entry is, then, is probably a good representation of my postings here, but that's about all.

2 Like • Comment • View 1 comment

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