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Sunday, Nov. 10, 2024

3:25pm 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

September 6, 2024 at 1:47am

#1076349

Secretion

"Blog Week Birthday Bastion 2024"

[13+] by WakeUpAndLive~doingNaNo'24

Prompt 6. Sept 6.

Nothing makes us so lonely as our secrets. Paul Tournier
Can you share a secret? Small or big, tell us. No? Tell us why not.

No.

...well, now I have to come up with at least 299 more words.

I'm pretty open in here, I think, though there are some things I edge around in an effort to avoid potential problems. This blog is public, though, so once I share something here, it can no longer be considered a "secret" in a literal sense of the word. So asking me to share a secret in here is the same as asking me to destroy it.

Some things were told to me in confidence by other people, and those aren't mine to disclose. If I'm ever in doubt about whether someone else's words to me are confidential or not, I assume they are. So those aren't getting discussed.

Ever wonder, though, why "secretary" contains the word "secret?" That's not an accident. While the word has largely fallen out of favor in the business world due to sexist connotations, replaced by "office assistant" or some similar term, a secretary is, historically, someone entrusted with secrets. The word survives in government administration, like with the Secretary of State in the US, or the UN's Secretariat. I suppose we didn't want to go with "minister" like in the UK or other countries, despite its inclusion in "administer."

How the word "secretary" got applied to desks with top shelves is still a mystery to me. Perhaps it was because secretaries tended to use such desks for organization, while a boss's desk is traditionally shelf-free, as they had secretaries to do all the filing and such. Or it might be used there in the sense not of "secret," but of "secrete," as in hiding, filing, or secreting stuff away. In yet another example of English's weirdness, "secrete" can also mean to ooze forth, like... well, you know what I'm talking about; unless you're a biologist, it's usually considered disgusting.

But the noun and verb are etymologically related.

I suppose it's no secret that when I can't think of anything else to say about a subject, I retreat into etymology. Most word origins are traced back to Latin or Greek, but even Latin and Greek built on earlier languages. It's just that the further back in time you go, the fewer written records survive, so it's tough to trace everything back to what linguists call Proto-Indo-European, or PIE, the apparent source of most Western languages.

But language probably got invented long before PIE, and it's even tougher to peer back into that ancient time. The past holds many secrets, and we will probably never expose them all.

We get to give out a free Merit Badge every day this week. Want one? Anyone who comments here before 11:30 pm WDC time today could get today's. (I'll need that extra half-hour to pick a winner and send the badge before midnight.)

To clarify:

When I say "comment," I mean comment. Not review. Though reviews are always welcome.

I also mean "here," not on the newsfeed post.

MB recipient will be chosen at random.

Maximum of one MB per commenter for the week.

If I don't get comments, I'll pick a previous commenter, and maybe not at random.

The MB will be the one I commissioned two years ago, "Complexity," which is a publicly available MB.

I appreciate all comments; this is just a little incentive.

1 Like • Comment • View 2 comments

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