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Saturday, Dec. 21, 2024

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Complex Numbers

by Waltz Invictus

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:

tj-Merry Mischief Maker

about 13 hours ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

about 18 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 18 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

a day ago
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 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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