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Friday, Nov. 15, 2024

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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:

Write_Mikey_Write!

a day ago
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

a day ago
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

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.

March 14, 2022 at 12:02am

#1028892

Grammar Police

I have mixed feelings about this one.

This Is Why; You Should Always Properly—Punctuate Your Social Media Posts’
An incorrectly punctuated Facebook post has brought on a potentially high-priced defamation suit.

Mixed, because on one side, I want to incentivize proper grammar, spelling and punctuation; on the other, I don't think the Grammar Police should use their power to screw the little people.

An Australian judge may make an example of sloppy punctuation, to the tune of over $117,000 USD in legal fees.

This article is from back in October, so it may have been settled by now, one way or the other, but that's irrelevant to the larger discussion. Also, it wasn't punctuation that was at issue.

Several outlets have reported that real estate agent Anthony Zadravic is now being sued for defamation for typing “employees” rather than “employee’s” in a Facebook post last year.

The original quote:

“Oh Stuart Gan!! Selling multi million $ homes in Pearl Beach but can’t pay his employees superannuation,” meaning an employer-subsidized pension fund. “Shame on you Stuart!!! 2 yrs and still waiting!!!”

There are, of course, several other problems with this post: there should be a comma after 'Oh.' Multi-million should be hyphenated. The $ should be written out as 'dollar.' There's another comma missing between 'you' and 'Stuart.' Starting a sentence with a digit is questionable, but most style guides specify that anything less than 11 should be written out; in this case, as 'Two.' How hard is it to spell out 'years?' This is Failbook, not Twatter. I'd be willing to excuse the triple bangs (two instances) as a casual stylistic thing meant to convey extreme shock.

But the actual point of contention, 'employees,' could be: employees, employee's, or employees'.

Each has a different meaning in the sentence.

As written, it implies that he can't pay his employees their superannuation. Awkward, and it's pretty clear on a casual reading that it's meant to be a possessive. But there are two possibilities for the possessive:

The second option asserts only a lack of funding for a single employee, presumably the author but that's not as clear as it could be.

And the third projects the idea that he couldn't pay the fund for ALL his employees.

So the grammar police are right: something needs to be done.

Last week, Judge Judith Gibson reportedly ruled that Zadravic’s employer Stuart Gan would be allowed to proceed with the suit because “employees” could suggest a “systematic pattern of conduct” of shortchanging staff, whereas Zadravic claimed he was only speaking for himself. Gibson also reportedly said that the suit might cost Zadravic up to $250,000 AUD, or roughly $180,000.

However, I'm not sure that even the most hardcore Grammar Cylon would consider $180K to be a reasonable penalty for even the most egregious error in forming a possessive.

Well, maybe the most hardcore. There is the temptation to also string the offender up by his toenails until he learns the difference between it's and its; there, their, and they're; and you're, your, and yore.

Temptation, but still, probably too far. After all, you can't practice your grammar if you're hanging upside-down. You'd be too busy howling in agony. Though the pooling of blood in the brain could cause you to lapse into a comma.

Another Australian court has lately gone off the rails with social media defamation policy.

Is it really "going off the rails?" Or is it enforcing some level of needed accountability?

Last month, the High Court of Australia upheld a ruling in favor of a former teen detainee who sued media companies over commenters’ ridicule under news posts showing him hooded and strapped to a chair in a detention center. The court found that media companies (or anyone who so much as runs a Facebook page) for commenters’ speech; as a result, some outlets and the Tasmanian premier have restricted comments, and CNN has blocked Australian readers from its Facebook page.

Bit of both?

Seems more reasonable to hold the people making the speech accountable, and not those merely providing a platform. But maybe it'd be too much work to search out the true identity of OzMan69, only to find that they're hiding behind seven proxies and besides, they live on a troll farm in Kazakhstan.

Amusingly, that last quoted paragraph contains a grammatical error; it's missing a phrase. Sue them in Australia! Props for correct use of the semicolon, however.

And now, maybe some unfortunate soul goes to apostrophe jail.

Where they'll be mercilessly teased by a whole gang of purveyors of fine fresh produce.

Now, Waltz's First Rule of the Internet states that any post correcting someone's spelling, grammar, and/or punctuation will itself contain spelling, grammar, and/or punctuation errors. So I've tried to go through and proofread this entry, eliminating any of my own mistakes. Did I succeed?

Well see.

4 Like • Comment • View 4 comments

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