Complex Numbers (Book)

Blog Calendar

◄ October ► 2023
S	M	T	W	T	F	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

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:

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.

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

October 21, 2023 at 9:29am

#1057789

The Optimism Trap

It's a five-year-old article, but what the hell; it's new to me. From GQ:

Why Your Brain is Wired for Pessimism—and What You Can Do to Fix It
We’ve evolved to expect the worst. Dr. Martin Seligman, a psychologist, explains why—and what you can do to get some optimism back.

Why in the ever-loving shit would I want to fix what ain't broken? How can I get back what I never had? And most of all, am I going to have to once again rage against the misuse of evolutionary psychology in articles?

And why do I bother with GQ if I know I'm going to rant about it? Okay, that one I can answer: because it's fun.

Ever had someone tell you to just cheer up? Did it drive you crazy? Well, turns out that someone telling you to “be happy” isn’t just annoying—it’s also wildly unhelpful.

It's especially unhelpful for people with clinical depression.

Seligman compares being happy to falling asleep: it’s not something you can actively do—in the way you can get stronger by lifting more weights. It just kind of has to happen.

Okay, sure, but unless you're tired past the point of exhaustion, the way to fall asleep is to get into a comfortable position and pretend to sleep until, at some point, you either fall asleep or say "screw this" and go play a video game.

My point is that in order to sleep, we usually first have to act like we're asleep. In that analogy, we'd have to pretend to be happy in order to be happy. So, do you still want to compare being happy to falling asleep?

Now, yes, I've said in here at least a dozen times that happiness isn't a goal, but a byproduct. So, sure, I don't completely disagree with that premise; I just had to nitpick the analogy.

And as the father of positive psychology—the study what makes a good or meaningful life—much of Seligman’s work has dealt with trying to help people figure how to make it happen.

Hurk.

“Half the world is on the low positive affective spectrum,” he says referring to positive affectivity, a trait that usually correlates with sunnier dispositions. “I'm part of it, and a lot of the justification for what I work on, and what I write, is to try to help half the world, who is not naturally positive affective, to be more positive and optimistic.”

WHY?! OH GODS WHY?!!!

What if... what if the only people who benefit from someone being mindlessly optimistic are 1) those around them who don't have to deal with someone's annoying pessimism and 2) our overlords, who will more easily control a populace who believes the best will happen?

What he has learned is that well-being can be broken into five elements: positive emotion, engagement, relationships, meaning, and accomplishment (PERMA).

Boy, shrinks love their mnemonic acronyms.

Why does it seem like we are wired for pessimism?
The species that [was] going through the Ice Ages had been bred, and selected, through pessimism.

Not only is that abysmally terrible evo-psych, but it's easily falsifiable terrible evo-psych. Not that I've disproven it, mind you; but consider: not all of humanity was directly affected by an ice age. Many populations were equatorial or near-equatorial. Are their descendants happier today, controlling for all other variables?

But the main reason why it's horrible evo-psych is that, as usual, it assumes that the only evolution that mattered to us started with humans, instead of us having ancestors dating back to the dawn of life, each of which contributed factors to evolution.

So is this at odds with something like mindfulness, which argues you should be present in the moment? If you're focusing on optimism, you're also sort of missing the present moment, right?
Well, I think, if you look at what people are doing, and what you're doing right now when we're talking, you're prospecting into the future.

But if positive psychology is at odds with mindfulness, and I also despise mindfulness, oh no! Cognitive dissonance! Wait, no, I've got it—I can hate both.

I've read a few people have said that you might be better off cultivating a sort of non-attachment to well-being: be mindful that a lot of life is going to be suffering, and if you can find contentment in that, you might be better off than seeking out happiness.
I think the good thing about meditation—mindfulness, concentrating on the present, detaching—is as good anti-anxiety, anti-anger tools.

"A few people have said," interviewer? A few people? You do know that that's Buddhism, one of the most widespread spiritual practices in the world, don't you?

Of all the things you've studied, or learned, is there one idea you constantly find yourself encountering most frequently?
I think it's hope.

Despite all my rage, I am still just a rat in a cageI do believe in hope. I'll leave off quoting the article and explain that now.

So, let me simplify things, but with a simplification that can easily be extended to our more complex lives:

You have two possible outcomes, A and B. Maybe they have predefined probabilities, like drawing a certain card from a shoe in blackjack, or maybe not, but it doesn't matter. Let's say you label A bad and B good, or at least less bad.

From what I understand of positive psychology, it tells us that you should believe that B will happen. You should manifest that B will happen. But then if A happens, which it still might because no amount of manifesting will change the fact that it can happen, you're crushed, devastated, forlorn, lost. Whereas if A happens, you might feel a fleeting jolt of accomplishment, serotonin momentarily coursing through your neural network, and then it's gone.

On the other hand... if you convince yourself that A will happen, if you predict A, if you act as if A were the only way that the universe could possibly work... when A happens, you're not nearly as devastated, because you expected it. Whereas if B happens, you're not just experiencing fleeting pleasure, but absolute joy.

In other words, being pessimistic, seemingly paradoxically, must lead to greater overall happiness. But that's probably only true if you still hold out some hope that B might occur; and that's what I mean by "I do believe in hope."

This philosophy is most usually expressed by "expect the worst, but hope for the best."

No, I'm not deliriously happy all the time. But I have something I consider far more valuable: contentment. I may not be where I envisioned myself when I was younger, but I'm doing okay.

And that's the real trap of optimism: you think you can always do better, so you strive, you make changes, you expect things to improve, and then you're discontented when they don't. You're disappointed that you don't have what you want, instead of being satisfied with wanting what you have.

Or hell, I don't know. Maybe optimism works for you. I'm not judging. I only take issue with the idea that everyone should strive for some nebulous, glorious state of "happiness" at all times.

Incidentally, this is not the last GQ article in my queue. And the other? Well, it's even worse...

4 Like • Comment • View 4 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.