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!

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.

October 31, 2019 at 12:07am

#968682

Funny Business

https://theconversation.com/the-mystery-of-what-makes-a-joke-funny-but-only-to-s...

I thought about running this in one of my Comedy newsletters. Hell, I still might.

The mystery of what makes a joke funny – but only to some people

It's a fixed law of comedy that explaining what makes a joke (or any joke) funny makes it not funny. This, I think, is the central paradox of existence.

Also, don't post pictures of mimes.

How do you like the following joke from Sumeria in about 1900BC? “Something which has never occurred since time immemorial; a young woman did not fart in her husband’s lap.”

I've mentioned before that the oldest known joke in the world is a fart joke. This would be that one.

One consistent finding in scientific studies is that laughter is universal and predates humans, while humour seems to appear alongside modern humans – wherever there is a record of modern humans, one finds jokes.

That's because we are jokes. Keep throwing me softballs.

These themes also confirm some of the scientific theories of jokes and humour. For example, humour often involves the realisation of incongruity (mismatch) between a concept and a situation, violations of social taboos or expectations, the resolution of tension or mocking and a sense of superiority

See? Not funny. And it's not like someone who doesn't have a sense of humor (or, per this article, humour) would be able to craft a joke based on the scientific evidence. I bet they couldn't even tell us how many scientists it takes to screw in a lightbulb

(None - that's the grad student's job)

Even worse, one of the most successful comedians inspired by Chaplin, Benny Hill, is considered cringeworthy in the UK, despite him being one of the few UK comedians to break through in the USA. That’s because Brits like to think that they are a bit more sophisticated in their humour than a man being chased around by naughtily-dressed ladies.

It is true that a lot of people in the US love Benny Hill. I never did find it all that amusing, even though I enjoy British humour in general. Still, Brits... no, you're not actually more sophisticated; thinking don't make it so.

So what does make a joke funny? We have made great strides in understanding the scientific bases on laughter and humour processing – but until we can incorporate the social and cultural complexities of humour fully, we will remain mystified by how people can enjoy comedy we find lame.

And thus endeth the article without it having told a single worthy joke. Still, some of the insights are useful, if not amusing, and I'm left with the same thoughts I had going in; that is, something is either funny or it's not, and once you explain why it's funny, it's also not.

Or, in the immortal words of Dug: "I know a joke! A squirrel walks up to a tree and says, 'I forgot to store acorns for the winter and now I am dead.' It's funny because the squirrel gets dead."

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