Complex Numbers (Book)

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Complex Numbers

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/

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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 6 hours 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

about 8 hours 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.

July 28, 2021 at 12:02am

#1014638

Wit's Beginning

Getting back to articles I found online, here's one that I need...

The secret to being witty, revealed

Finally, I can learn how to be funny!

Have you ever thought of the perfect quip or comeback after it didn’t matter—a minute, hour, or day after your conversation has ended?

Sometimes it takes years. Hell, I'm still working on one from my past life in medieval Bavaria. Unfortunately, I'd have to learn Middle German first, and then find the reincarnation of my verbal sparring partner from the time and hope they have learned it as well.

Well, there’s a name for that phenomenon. It’s called l’esprit de l’escalier, or the spirit of the staircase, and refers to the perfect retort that arises at the wrong time.

Hey, that's not German; it's its polar opposite, French.

Still, you’re not doomed to sit by as clever companions exchange sharp banter. You can practice being wittier, improving your reaction times and ability to land a jab or joke at just the right moment.

By memorizing every sit-com ever aired on TV?

In his new book, Wit’s End: What Wit Is, How It Works, and Why We Need It, released on Nov. 13, author, editor, and journalist James Geary of Harvard University’s Nieman Foundation argues that wit isn’t just for a few gifted linguists.

Hey, look, it's an ad for a book (standard disclaimer: this is a writing site so I'll allow it). Also, the author failed at being witty there. He should have said "cunning linguists."

And it’s worth trying, according to Geary, because playing with language—elevating mundane communication from mere talk into a creative process—is a form of innovation that sheds new light on old ideas. Plus, it makes life less boring and more fun for you and others.

But I've been doing something like that for years. It may make life less boring, but people still hide from me at parties after I talk to them. Back when I got invited to parties, anyway.

“[W]it consists in binding together remote and separate notions, finding similarity in dissimilar things (or dissimilarity in similar things), and drawing the mind from one word to another,” Geary explains.

So... puns. Yeah, that's why people hide from me.

“Uncensored access to associations, conscious and unconscious, is essential to wit,” Geary writes. He notes that some people who experience brain damage or have neuropsychiatric diseases lose their ability to make these associations altogether, while others suffer from witzelsucht. This German term means “wit sickness” or “wit addiction” and results in a compulsion to make jokes that are often socially inappropriate.

Ah... there's some German. And I begin to see the problem: brain damage.

Understanding the neurobiology of people who suffer witzelsucht, and those who are linguistically humorless due to brain damage, could shed light on the mechanisms of wit.

I'll take that as granted, but it is utterly perpendicular to the title of the article, which is, I remind you, "The secret to being witty, revealed." Now, true, beating one's head against the wall might be funny to the viewer, but I don't think it's guaranteed to make someone wittier.

Like other forms of creativity it is borne of knowledge. Having a rich vocabulary is a starting point. Curiosity is another important element. Appreciating language in all the places and ways it’s used—from pop music to literary fiction, scientific writing to slang—makes it easier to generate unusual combinations.

I mean, sure, but "don't be stupid" is good advice for almost everything in life.

Yet writing a book about wit was harder than the writer imagined. Geary couldn’t very well be pedantic and dull while highlighting the need for wise, fun, creative communication.

I can only wish we could say the same about this article.

He raps, rhymes, puns, quips, jives, and dialogues his way through this rich history and analysis. Each section of the book, which reveals the elements of different kinds of wit, and offers insight on developing it, is written in a distinct form.

Writing something funny is distinct from saying something funny. For the former, you have months to work on the jokes. For the latter, you need to be quick like sand. Can you really learn how to be funny by reading a book that the author has spent agonizing weeks preparing?

If we were cracking wise, rather than reacting angrily, and being wittier on Twitter, we might all have a much better time.

Or -- and hear me out here; this is blasphemy of the highest order -- we could all decide to collectively ignore Twatter.

7 Like • Comment • View 3 comments

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