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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Brandiwyn🎶

a day ago
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.

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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.

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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').

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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.

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Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

October 9, 2020 at 12:09am

#995429

The Pleasure Principle

Today's story is kind of parent-focused, but it illustrates some things that I've been harping on for a while.

https://theconversation.com/pleasure-is-good-how-french-children-acquire-a-taste...

Pleasure is good: How French children acquire a taste for life

The article discusses the idea of pleasure from different cultural perspectives. Well... not too different. European and American. But it's still worth noting some of the ideas in here.

In the US, we tend to compartmentalize pleasure, separating it from our daily chores and relegating it to special times. We have happy hours, not happy days. We have guilty pleasures, as if enjoying chocolate or a favorite movie is a moral failing.

To too many people, it is a moral failing. Whereas in France...

Pleasure, in fact, takes the weight of a moral value, because according to the French, pleasure serves as a compass guiding people in their actions.

Pleasure, then, is the goal. The purpose. Not a meaningless distraction on the way to some other goal.

Stimulating practices included reading to children, playing music and giving them massages. The ultimate goal of stimulating children is to develop their understanding of what gives them pleasure.

Some in the US would find this "creepy." The whole point is that it's not.

The moment that tied it all together for me was when I asked a mother in my research study why it was important to train her children to behave properly in public. She simply replied, “Because if they know how to behave properly, they will know how to adapt and get along with people. And that will give them pleasure.” Adhering to social rules is a means to greater pleasure. You have to give up something to gain something greater.

Pick an activity, any activity. Ask "why do we do this." Ask "why" to the answer. Keep doing this and eventually you come to the root causes. If the root cause is "to increase pleasure," I'd say you're on the right track.

As Americans, we are taught to deny pleasure and venerate self-sacrifice and hard work. And when we finally take time off to have fun, we often do things in excess. We party hard. We eat and drink too much. And then we feel guilty. When we enjoy food too much, we say we’ve been “bad.” Maybe if we didn’t deprive ourselves of simple pleasures all day every day, we wouldn’t feel so compelled to overdo it on weekends.

I'm just going to leave that right there. Personally, I've never been on board with that ethic. Hard work just leads to more work. If, as our cultural myth goes, hard work leads inevitably to financial success, then sharecroppers would be millionaires. So that myth is debunked right there.

I only ever worked with the goal in mind to one day not have to work anymore.

The rest of the article delves more into the family aspect of things, which I skipped, because it gives me great pleasure to have never had to deal with offspring.

Now, I understand others' ideas of pleasure are different from mine. Maybe work gives you pleasure. Not the results of the work, but the work itself. Or maybe raising kids was a challenge you willingly embraced, and it gives you joy. That's great My point is those things aren't universal.

Maybe if people chased things because it would genuinely improve their level of happiness instead of adhering to someone else's idea of happiness, people's lives would be better.

Or maybe we all just need more money.

Hell if I know. I just thought it was an interesting article.

3 Like • Comment • View 4 comments

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