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Monday, Nov. 18, 2024

12:32am 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-turkey-jobble-jobble-hard-J

about 8 hours ago
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

Turkey DrumStik

a day ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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

October 31, 2023 at 10:59am

#1058353

Punctuated

It's a 2.5-year-old article from LitHub, but it's not like style ever goes out of style, right?

The Punctuation Marks Loved (and Hated) by Famous Writers
; vs. — vs. , vs. . vs. !

Parul Sehgal once argued that style “is 90 percent punctuation.”

Sure, not like anyone grumps about word choice.

As John Mayer once apparently said, for some reason, “Ladies, if you want to know the way to my heart: good spelling and good grammar, good punctuation, capitalize only where you are supposed to capitalize, it’s done.”

Apparently, dudes could get away with anything.

After all, even among experts, there are disagreements, some of them oddly vehement. (What inner forces would compel someone to demonize or deify the semicolon?)

Oh, I don't know... search my blog for "semicolon" and you might find out. (I'm a fan of it, obviously.)

Then the article goes into the punctuation marks in general. I'll only highlight the ones I agree with:

(semicolon) In compiling the sentence, efficacy—or, more precisely, precision—is important; capacity is important; and clarity is important. This kind of writer, at least, doesn’t think in little stoppered declarative sentences. It isn’t like that. Not really ever. Perhaps for some people. But not for us. For those of us whose thoughts digress; for whom unexpected juxtapositions are exhilarating rather than tiresome; who aim, if always inadequately, to convey life’s experience in some semblance of its complexity—for such writers, the semi-colon is invaluable. -Claire Messud

I have never heard of this author before, but that makes me want to seek her work out.

(exclamation point) Keep your exclamation points under control. You are allowed no more than two or three per 100,000 words of prose. -Elmore Leonard

I think this is one of those things that's going to be different depending on what you're writing. But yeah, I believe in using bangs (easier to say than "exclamation point") sparingly so as to maintain their power. Unlike cuss words, which, as my mom's family was from New York City and my dad was a sailor, to me, are really just punctuation marks.

(em-dash) Don’t you find it annoying—and you can tell me if you do, I won’t be hurt—when a writer inserts a thought into the midst of another one that’s not yet complete? Strunk and White—who must always be mentioned in articles such as this one—counsel against overusing the dash as well: “Use a dash only when a more common mark of punctuation seems inadequate.” - "many editors"

Contrary to what I said above, I don't really agree with this, but as with the bang, sparingly is good. I can see right through this writer's ham-handed attempt to convert people to their point of view by deliberately overusing it.

(comma) [On her editor, Bob Gottlieb, who famously “was always inserting commas into Morrison’s sentences and she was always taking them out”] We read the same way. We think the same way. He is overwhelmingly aggressive about commas and all sorts of things. He does not understand that commas are for pauses and breath. He thinks commas are for grammatical things. We have come to an understanding, but it is still a fight. -Toni Morrison

Oscar Wilde rather famously once wrote: "In the morning I took out a comma, but on mature reflection, I put it back again." As the most-used punctuation mark apart from the period ("full stop" for those of you across the pond), it's subject to a great deal of wasted words and time. I admit to feeling somewhat judgemental toward people who misuse them, but I can't always articulate why they're misused in a given instance.

I'm more judgemental about apostrophe abuse.

(hyphen)

No quote here. I did a whole blog entry on it a while back: "Dashing"

. In it, I overused and misused emdashes, so take it as you will.

(period)

Do we really have to argue about full stops?

James Joyce is a good model for punctuation. -Cormac McCarthy

James Joyce is not a good model for anything, and now I have even less desire to read anything McCarthy wrote.

I mean, if you write properly you shouldn’t have to punctuate. -McCarthy again

And that sentence, folks, should be in the dictionary as a sample under "irony."

To be clear, I'm not trying to claim I'm always right. I'm aware that I overuse semicolons sometimes (as well as parentheses), and get things wrong on occasion. Especially here, where every entry is a first or second draft. But that doesn't mean I don't consider these things.

1 Like • Comment • View 1 comment

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