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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:

Annette

about 9 hours ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day 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

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

a day 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

Dec 19, 2024 at 3:43pm
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

Dec 19, 2024 at 8:53am
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

July 27, 2024 at 8:33am

#1074446

Still Planning

Time for a travel plan update, though it's probably going to be short. But maybe I have some other things to write about.

The travel agent I'm going with has a subcontractor for local knowledge. In this case, a French woman. And I'm completely on board with that, but the sub didn't get back to her before Wednesday of this week. And that matters because the agent took off for vacation on Wednesday, so that means no further information until, at least, Thursday of next week. Probably later, because she's the owner of the agency, so she'll be coming back to utter chaos that she'll have to deal with first.

Or, you know, maybe she's a better business owner than I was, and everything will run smoothly in her absence.

Must be nice to go on vacation when you're a travel agent. You can get yourself the best deals.

And there's not much else I can do until I at least know when I'll be leaving, which I don't yet. I tried searching for fun things to do in France, but Google keeps pointing me at the Olympics, and I don't give a shit about that.

Which, it occurred to me, may be hypocritical of me, as I've harped in here again and again about how there's no such thing as useless knowledge or experiences. And I do believe that. My rationale (or at least rationalization to make me feel better about myself) is that I also tend to avoid anything that's too popular. Like Taylor Swift (who I acknowledge has talent) or "reality" shows.

But yeah, I do have an aversion to sports. You know how kids sit bored in math class wondering how they're ever going to use this? You ever notice no one says that about gym class, even though the vast majority of the kids aren't going to go on to be professional athletes? "But, Coach, when will I ever use sit-ups in my career as a veterinary technician?" "Well, um, strong abs will help you lift big dogs onto examining tables."

My argument is that you never know when the stuff they teach you in school will be useful or necessary. Was it "necessary" for me to spend high school in orchestra and drama class, let alone Latin? No, probably not. And I didn't know I was going into engineering until like senior year, so even math was questionable. But I learned all that shit anyway (and promptly forgot most of it).

The point being that just as strong abs are generally a good thing (something even I can acknowledge) even if you're not a pro athlete, so it is with a strong mind.

Now if only schools would emphasize that sort of thing instead of being all about the football team, we might actually get somewhere.

What does this have to do with travel? Well, nothing, except that maybe I can stretch (another good exercise) and claim that travel broadens one's perspective, so it's the same sort of thing. But, mostly, I'm rambling because I didn't accomplish anything else in terms of travel planning this week.

Next week, I'm going to look into relatively cheap laptops so I can bring one on the trip. Like a Chromebook or something, so I don't have to use my phone to make blog entries. I don't want to take my expensive gaming laptop with me (the one I'm typing on now), so this seems like a reasonable thing to do. Besides, it never hurts to have a backup here at home in case this thing blows a circuit one day.

And then I have to see about getting internet there. I'm well aware that they're ahead of the US in that regard, but that doesn't mean the systems are compatible, kind of like how I have a plug adapter to handle the different electrical outlet configurations.

5 Like • Comment • View 4 comments

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