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Monday, Jan. 13, 2025

3:11pm 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 is ready for spring!

about 2 hours ago
In response to "Rebel Without a Clause"

It's just like this sometimes.

1 Like

🌖 HuntersMoon

a day ago
In response to "Revisited: "Squash Court""

tj is ready for spring!/Robert Waltz

Oh My God!

Now I understand the etymology of "Pun-ishment."

3 Like

Elisa: Snowman Stik

a day ago
In response to "Revisited: "Squash Court""

Ironically I'm eating scrambled eggs with zucchini as I read this entry.

As someone who has shopped for and cooked delicata squash, I can say that they're mostly seasonal. I occasionally see them in the summer, but they're far easier to locate in the cooler months. They haven't quite broken out the way zucchini has or even acorn squash. I can find acorn squash year round, although admittedly I don't eat it in the warmer months. Speaking of which, if I had to guess, I think pumpkins aren't sold year round because A. summer demand and applicability is low and B. size is a factor. Acorn squash is grown in similar areas/conditions as pumpkin, but it's a smaller size. Grocery stores can carry it year round in a smaller footprint compared to pumpkin even if fewer people are buying it in the warmer months.

4 Like

Robert Waltz

a day ago
In response to "Revisited: "Squash Court""

tj is ready for spring!

- if he has lesser relatives in the produce section, that must be why he's called Bigfood.

4 Like

tj is ready for spring!

a day ago
In response to "Revisited: "Squash Court""

Here in the north woods there are rumors of a giant squash that roams the woods; Sasquash! I've never seen him, but do, on occasion, come upon his lesser relatives in the produce section.

4 Like

tj is ready for spring!

Jan 11, 2025 at 12:48pm
In response to "Time Marses On"

I agree. When we finally get close to inhabiting Mars, I doubt anyone will be scouring through sci-fi books to find a design, asking, "How 'bout this, it looks pretty cool."

1 Like

Robert Waltz

Jan 10, 2025 at 4:24pm
In response to "Cell Mates"

Oooh, a demonstration of Waltz's First Law of the Internet: Any post criticizing someone's grammar, spelling, and/or punctuation will itself contain grammar, spelling, and/or punctuation errors.

I'm pretty sure I've read all of Heinlein's books and stories, with the exception of the naked money grabs his estate published posthumously. Some of them didn't age well, but taken in the context of their time, many of them are solid science fiction.

And I can't tell you how many times I've wanted to use "grok" in an entry but passed because I didn't want to overuse it. As the blog is nearing its end, I threw caution to the wind today.

Sum1's Home!

Jan 10, 2025 at 4:13pm
In response to "Cell Mates"

@Jayne

Should I Play Grammer Police here, and tell you that you misspelled Henlein? He's one of my favorite authors. If I had the money (I do really), and a place to keep them (I don't), I would get his entire collection from the Heinlein Society. I have read many of his books and short stories, there are also many that I haven't read too.

1 Like

🌖 HuntersMoon

Jan 10, 2025 at 2:17pm
In response to "Cell Mates"

Sum1's Home! / Jayne - You make me feel like a stranger in a strange land.

2 Like

Jayne

Jan 10, 2025 at 2:02pm
In response to "Cell Mates"

I'm charging you 85 gps for making me think of Heinlen. Feel free to ignore the invoice, my molecular makeup is too unorganized to develop a collections department

4 Like

January 13, 2025 at 9:48am

#1082307

Rebel Without a Clause

Somehow, I thought I'd covered this Mental Floss piece before, but it didn't come up in the search which probably took up more of my time than writing this entry will.

5 Ways the English Language Breaks Its Own Rules
The many ways English flouts its own rules can be confusing even to those who speak it as a first language.

As witnessed by, well, everyone, not everybody talks good.

English, the language of Shakespeare and the internet, is often touted for its flexibility and adaptability. But with great flexibility comes great inconsistency.

Perhaps the inconsistency of the language is what makes so many English-speaking people comfortable with contradictions in other areas.

1. Tenses don’t respect times.

“So this guy walks into a bar …” We know a story is coming, and it’s clearly a story about something from the past—and yet, the word walks is in the present tense.

Jokes are traditionally rendered in present tense. I can't articulate why, but it just works better. Unfortunately, people have started using it for entire novels, and I find it fatiguing in that context.

In the sentence If it rained tomorrow, I would stay home, the past tense rained is used to refer to a future event.

I'm no grammartalker, but I thought that's a conditional tense, and it just happens to be the same spelling as the past tense.

2. Definites can be indefinite.

The word this is a definite determiner: It picks out referents that are specific and identifiable. If someone says “This is the right one,” they do so because they expect the listener to know which one they mean. But in the story that starts with this guy walks into a bar, this guy doesn’t necessarily refer to any person the speaker expects you to be able to identify.

Someone really likes "walks into a bar" jokes. That's okay. So do I: Two guys walk into a bar. The third one ducks.

3. Dummy pronouns serve as subjects.

...But in weather sentences like “it’s snowing” or “it’s sunny,” it doesn’t replace any noun phrase. What is the “it” that’s snowing? The sky? The clouds? Linguists call this it a “dummy pronoun,”...

It is true that I have wondered in the past about the antecedent for the pronoun in "it's snowing," but never enough to look up the answer. Now I know, and I feel like a dummy.

4. Objects can be “raised.”

On the surface, the sentences She persuaded them to try it and She intended them to try it seem pretty similar, but they differ in syntactic structure.

This one gets a little esoteric. It's one of those things that I somehow knew intuitively, but couldn't put a name to the grammar used. Well, I guess now I can.

5. Number agreement doesn’t always agree.

I have to admit, this is one I make mistakes with on occasion. Rather than fumble around with grammar rules, though, I generally opt to rewrite the sentence to avoid the awkwardness in the first place.

Alternatively, I just don't notice when it's wrong.

Which, really, can be said for all of these rule-breakers.

6 Like • Comment • View 1 comment

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