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Sunday, Nov. 10, 2024

2:29pm 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:

Kåre เลียม Enga

a day ago
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

a day ago
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.

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

1 Like

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

JayNaNoOhNo

Nov 5, 2024 at 1:16pm
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 Like

August 1, 2024 at 9:41am

#1074643

Help Yourself

By coincidence, another Guardian link today. This one's trying to help with self-help.

Self-help was meant to make me feel better. Instead it turned toxic - and borderline dangerous

I always questioned the concept of self-help books, myself. Even putting aside the questionable credentials of some of the authors, you're not really doing self-help; you're looking to a book and an author that doesn't know you for advice. Which is fine if you're cooking and grab a recipe book.

They do, however, sometimes self-help their authors to bigger bank accounts.

I remember buying my first self-help book, which promised I could be healed of anything if only I banished my limiting beliefs.

And then if you're not healed of whatever, it's your own fault because you didn't banish hard enough!

Over the next 15 years, I bought hundreds of self-help books, courses and apps, and tracked down every self-styled personal improvement guru on TikTok and YouTube in the hope that they could teach me how to become happier, more confident and more lovable.

Apparently, the concept of "to be happier, confident, and more lovable, don't waste money on self-help books, courses, and apps; and stay away from social media" never occurred to her. Of course, none of the people involved would have given her that advice. But I can.

Look, I'm the last person who'd advise someone to "be yourself." But at some point, I realized that the way to be content with what you have is to be content with what you have.

Some approaches were gentle and perhaps even obvious: “talk kindly to yourself, get enough sleep”. Others bordered on dangerous, whether it was encouraging me to spend more money than I could afford in order to “manifest” wealth or telling me to ignore my health problems to feel healthy.

If, on the other hand, I was content with being a bigger asshole than I already am, I would totally be like, "You know the secret to happiness and eternal bliss? It's to give me all your money. Yes, all of it."

Hey, it works for preachers.

But even though I was following the guidance, nothing was helping me to feel better about myself and my brain scans still showed I was living with an incurable neurological disease. I couldn’t help but feel that not getting results was my own personal failing, rather than the industry’s with all its promises.

Yeah, that's one of the biggest problems. I mentioned it up there, too: it's easy to fall into the trap of "obviously it's my fault because I didn't pray / manifest / wish / meditate enough." Which can lead to a whole spin/rinse cycle of doom.

It took a deep conversation with a loved one to recognise that in trying to change my life, I was trying to change things that had happened to me and shaped who I was – often things that were out of my control.

And yet, she had "a loved one." I think I finally understand some of the people who are like "be grateful for what you have."

Instead of focusing on who I wanted to become, I had to quit self-help to learn and accept who I really was.

Happiness isn't having what you want; it's wanting what you have.

Since I quit my self-help crutch, I’ve realised that focusing all your energy on improving yourself can really suck the joy out of life. It makes happiness conditional: only when I have got to a certain stage can I feel contentment; only when I look that way can I be loved.

So that's your ironic self-help advice for the day. For just $19.95 a month, I can self-help you even more!

5 Like • Comment • View 3 comments

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