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Sunday, Nov. 10, 2024

2:34pm 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 14, 2024 at 11:17am

#1075264

Cat Astrophe

No link today, just a rant.

I have a calico cat, Zoe (named after an ancient Doctor Who companion, not Zoe Saldana) who just turned 11. A while back, she got diagnosed with a thyroid issue, for which the vet prescribed medicine to be smeared inside her ear twice a day, 5 mg per dose. It's like a pen with a twisty clicky thing on the bottom that dispenses the correct dose. I can never remember the name of the medicine, but it starts with "meth," which has nothing to do with methamphetamine except the one CH₃ group I assume is in both. But I digress.

As you might imagine, Zoe isn't very pleased with having me hold her down and stick something inside her very sensitive ears. Still, it's more reliable than the alternative, which is in pill form. Ever try to pill a cat? There are whole comedy routines about it. This is definitely the lesser of two ear-vils.

Everything was fine for a few months, and then they did a blood test and, behold, her whatever-numbers were still too high, so the vet changed the prescription: 5mg twice a day plus one half-dose of 2.5mg. So, now, two separate pens are necessary, and I have to label them with permanent marker that wears off after three days.

This routine doesn't offend only the cat, but also my sense of symmetry, as it means I have to dose her twice in the morning and once in the evening. Or vice-versa; doesn't really matter; just needs to have some consistency. Still, I'm OCD enough that this bugs me. Plus, it's a pain in the ass for whoever takes care of her whenever I fuck off to some distant land.

So, two weeks ago, at their request, I took her in for a blood test (catching the cat and stuffing her into a carrier is another formidable task; she senses when a vet visit is coming up and gets creative in finding hiding spots). A week later, they call me to say that their magic numbers were fine with this higher dose, and I informed them that I was nearly out of meds. They said they'd call in new prescriptions but it would take a few days. Fine, I still had a few days left.

Last week goes by, nothing from pharmacy. I call them. "We never got a prescription from the vet."

Great. At this point, the vet's closed, so I have to wait until Monday.

Now, I should note that I've been going to this vet's office for two decades. They've been pretty reliable. I trusted them with end-of-life care for two of my previous cats (another got very sick on a weekend and had to be euthanized at an emergency vet). But this time, they dropped the ball of yarn. Monday: "We'll need her to come in for blood work."

"Um, she got the blood work two weeks ago."

"Let me call you back."

So I got a call back, not from the receptionist, but the actual vet, who usually has Mondays off. He spent the next 10 minutes reiterating the same discussion we'd had the prior week: to continue with the two 5mg doses plus one 2.5mg dose. Twitch.

I said, "Question about that. That's 12.5mg daily." (In case you've ever said, "When in my life will I ever need to know math?" that's your answer.)

The vet seemed surprised that I wasn't innumerate. "Yes, that's right."

"And we're getting this filled at the compounding pharmacy, so would it be possible to get one pen with a 6mg dose, to use twice a day, instead of the one 5 twice a day plus the one 2.5 once a day?"

(As an aside, yes, that means 12mg daily instead of 12.5 mg, but these things really aren't that precise, anyway.)

He paused. "I didn't think of that," he said.

Facepalm.

"We usually think in terms of pills, and the pills come in 5 or 10 milligrams," he continued.

And I'm thinking the pills have those little score marks for breaking in half to provide the 2.5mg dose, but whatever; it's not like I'd be able to force pills down this cat's gullet.

So that was Monday, and the pens were ominously close to empty. I get a call from the pharmacy later. "We won't be able to fill this until Thursday." (That would be tomorrow, now.)

No way will the current pens last until then. Zoe's just going to have to go with a smaller dose, I was thinking. And watch the vet blame me for not following through.

Well, yesterday, Tuesday, just before the pharmacy closed, I get the text from them that the meds are ready. Okay, great, there's probably exactly one more dose left (it's hard to tell with these things), so she got that one last night.

When I'm done posting this, I'm going to head over there (it's not far from me) and get the new prescription. It's fortunate that they were able to fill it earlier than expected, but, ever the pessimist, I fully expect the dose to be wrong.

If so, well, the vet's office is a few short, angry stomps from the pharmacy. And there's a microbrewery in between. And two more right across the street. You know, just in case.

I still get to go out there tomorrow, too. My other cat, the void named Robin, needs her annual shots. Now I gotta wonder how they'll manage to screw that up.

8 Like • Comment • View 4 comments

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