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Saturday, Nov. 23, 2024

11:41am 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:

Robert Waltz

Nov 20, 2024 at 2:54pm
In response to "Powers of Three"

🌕 HuntersMoon

- that's pretty much what quantum computing is, from what I've read.

2 Like

Brandiwyn🎶

Nov 20, 2024 at 2:32pm
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

Nov 20, 2024 at 1:20pm
In response to "Powers of Three"

With binary, it's either on or off. Wouldn't ternary introduce Schodenger's Cat? On, off, or both?

2 Like

Turkey DrumStik

Nov 19, 2024 at 7:43pm
In response to "Paramount Purpose"

I suspect old web filter attempts

would have combusted when confronted with this article.

1 Like

tj-turkey-jobble-jobble-hard-J

Nov 19, 2024 at 4:04pm
In response to "Losing Weight Is Easy"

Some of them break out in hives if you ask them to add 10% to something.

Yesterday I purchased an item that cost $6.42 after tax was affixed by the register. I handed the cashier a ten dollar bill and watched as she placed it in the cash register, which like most now days, showed her how much change to return. She had to try three times to count out the proper amount, and as I was leaving commented to the bagger, "Why do people have to pay with cash, don't they know how hard it makes my job?"

I didn't say anything, but was trying desperately not to break out in hysterical laughter.

1 Like

🌕 HuntersMoon

Nov 19, 2024 at 9:28am
In response to "Paramount Purpose"

At your age, Bob, take heart in the fact that it can be restored...

2 Like

Wordsmitty ✍️

Nov 18, 2024 at 12:34pm
In response to "Losing Weight Is Easy"

This brings up the old question of whether your weight changes when you inhale a helium balloon to make your voice higher.

Maybe this has to do with the difference of a mug of beer vs a tankard of ale.

The universe has so many weighty/massive questions.

3 Like

Brandiwyn🎶

Nov 18, 2024 at 11:27am
In response to "That's the Spirit"

Maybe you’d go with “Thunder” because that one’s so terrible that only divine intervention can explain its success. Wow. Missed opportunity, here. How could you let this go without a shoutout to mighty Thor, son of the Allfather, wielder of Mjolnir, He with the Long Forehead? (Said in the voice of the Soup Nazi): "No Valhalla for YOU!"

Brandiwyn🎶

Nov 18, 2024 at 11:19am
In response to "Losing Weight Is Easy"

Has anyone ever told you how annoyingly pedantic you are?

Damn your pedantic ways. I was hoping to justify a vacation to Venus (which I still argue would be a much better holiday destination than fr-fr-freezing Mars, Elon. Ugh.) Now I guess I'll have to settle for the Cancun plans we already made, since my mass (and waist diameter, and thigh diameter) will be exactly the same regardless.

3 Like

tj-turkey-jobble-jobble-hard-J

Nov 17, 2024 at 4:04pm
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

November 23, 2024 at 9:09am

#1080374

Pursuit

Here's something sure to brighten everyone's day, if for no other reason than this Time article is shorter than some of the others that have popped up lately.

Obsessing Over Your Own Happiness Makes You Less Happy

Well, I'm not sure that's true for everyone. You never know what'll make someone happy, sometimes. Like, I've known people who were only happy after they made everyone around them miserable. So it's not a stretch to believe that obsessing over... whatever... might be pleasing to someone. Given all the obsessing people tend to do, I'd almost guarantee it.

Happiness is a worthy pursuit.

Is it, though? Is it really? Or are other things worthy of pursuit, and happiness is a byproduct of that?

But fixating too much on achieving it often leads to bad feelings when you fall short—which ultimately makes you less happy.

Especially if you expect not to fall short.

That’s the finding of a new study published in the journal Emotion.

For once, I actually clicked on the link provided to the study. I didn't read it too closely, but I'd take it with the same level of skepticism as any other psych study, even if it does speak to my biases.

In the study, people who said they were worried about achieving and maintaining happiness tended to have more depressive symptoms, worse well-being, and less life satisfaction than those who simply held happiness as a goal—and didn’t fret about whether they were meeting it.

Which is, honestly, exactly the result I'd expect. Which doesn't mean it's right. Or wrong. But to me it's like a study that investigated whether cumulus clouds look soft and fluffy.

What’s the secret, then? Take the pressure off and stop taking your own happiness temperature so often, Zerwas says.

Okay.

Embrace all of your feelings—both happy and sad ones—since all emotions can be informative, providing us insights into our psychic makeup.

Okay.

And practice cognitive-behavioral strategies such as mindfulness—being present in one’s emotions and aware of what those feelings are—to truly tune in.

Aaaaand you lost me.

I feel like this "pursuit of happiness" thing is mostly an American phenomenon, thanks to the famous words in the Declaration of Independence. There's some discussion

over what exactly was meant by "happiness" therein, but I'm pretty sure the connotation of the word has changed in the last 250 years. It probably didn't mean a feeling of unbridled joy, but something closer to security.

And in my experience, living without fear is happiness enough.

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