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Wednesday, Sep. 11, 2024

10:13pm EDT

Members: 933

Guests: 1,093

Total Online: 2,026

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:

Aiva Raine

about 7 hours ago
In response to "Drop and Gimme Twenty"

Happy 20th. We're glad you joined and doubly glad you've stayed this long. I look forward to reading your daily blog as part of my own daily ritual.

1 Like

Wordsmitty ✍️

about 9 hours ago
In response to "Drop and Gimme Twenty"

Wow. That sounds mature for twenty. Next year you can get some booze to celebrate.

I'm sure we're all glad you did sign up. Enjoy the day.

1 Like

Annette aka Din Djarin

about 9 hours ago
In response to "Drop and Gimme Twenty"

Happy 20th to you!

My username was octobersun2 for the same reason. My first attempt to join somehow didn't work.

1 Like

🌕 HuntersMoon

about 10 hours ago
In response to "Drop and Gimme Twenty"

Happy Anniversary, you old dog...

1 Like

Kåre Enga in Montana

Sep 9, 2024 at 10:57am
In response to "Time Out"

"As long as everyone agrees to it" is paramount.

The Polynesians navigated by the stars. No clocks needed. A different approach. Still... all relative.

1 Like

Legerdemain

Sep 9, 2024 at 10:47am
In response to "Time Out"

I'm not scientific, at all. But what about Earth's wobble? Who accounts for that?

1 Like

🌕 HuntersMoon

Sep 9, 2024 at 10:20am
In response to "Time Out"

This was so heavy... I think I lost 26 microseconds reading it.

1 Like

Elisa: Middle Aged Stik

Sep 8, 2024 at 12:04pm
In response to "Writing It Off"

I am late to the party with my comments, but here we go.

Used to be, I wanted to get published.

I used to want to be published in terms of stories. Nowadays I'd rather be published in terms of photos. And self publishing may be my only option in that regard.

but the travel writing field is crowded with young influenzas who can't write for shit, but look good in selfies.

And before that it was crowded with middle aged socialites with nothing better to do (but did have some level of writing skill).

Other people here have dealt with the limit by deleting old entries. I won't do that. Most never have to worry about the limit, and that's perfectly okay.

I admit that as of late I don't let my book items hit the entry limit. Part of it is my entries are super long (current average being *checks notes* 7.48 kb in size). Part of it is I also feel like book items should end after at most five years. I think of my old paper diaries and how they felt more meaningful when I didn't let their use drag on forever. If I stayed consistent, they'd end maybe at most after a year and a half. They often wrapped up sooner than that. Even moving to online journaling, I appreciate a journal that is finite not based on the number of entries but by time elapsed since the book started having entries added to it. My current journal may last a tad longer than my previous ones, but I imagine I'll wrap it up in late 2027, maybe early 2028. We'll see how much space I have to work with. In the old days, 1000 entries was considered a major achievement of an end point. I hope I can get that much out of it, as I think that's more reasonable. I do think 3000 entries of my kind of work in one place is a bit much.

1 Like

🌕 HuntersMoon

Sep 8, 2024 at 11:00am
In response to "Revisited: "Orange You Glad This Wasn't You?""

Maybe this would help... or at least attract your attention?

1 Like

Robert Waltz

Sep 7, 2024 at 11:39pm
In response to "Spit in the Ocean"

Both commenters today had already received MBs from me this week, so I went back to every entry this week and picked a comment at random.

The final Birthday Week MB goes to:

🌕 HuntersMoon

Thanks, everyone, for reading and participating!

1 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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