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Thursday, Nov. 21, 2024

2:13pm 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:

Robert Waltz

about 23 hours ago
In response to "Powers of Three"

🌕 HuntersMoon

- that's pretty much what quantum computing is, from what I've read.

2 Like

Brandiwyn🎶

about 24 hours ago
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

a day ago
In response to "Powers of Three"

With binary, it's either on or off. Wouldn't ternary introduce Schodenger's Cat? On, off, or both?

2 Like

Turkey DrumStik

a day ago
In response to "Paramount Purpose"

I suspect old web filter attempts

would have combusted when confronted with this article.

1 Like

tj-turkey-jobble-jobble-hard-J

a day ago
In response to "Losing Weight Is Easy"

Some of them break out in hives if you ask them to add 10% to something.

Yesterday I purchased an item that cost $6.42 after tax was affixed by the register. I handed the cashier a ten dollar bill and watched as she placed it in the cash register, which like most now days, showed her how much change to return. She had to try three times to count out the proper amount, and as I was leaving commented to the bagger, "Why do people have to pay with cash, don't they know how hard it makes my job?"

I didn't say anything, but was trying desperately not to break out in hysterical laughter.

1 Like

🌕 HuntersMoon

Nov 19, 2024 at 9:28am
In response to "Paramount Purpose"

At your age, Bob, take heart in the fact that it can be restored...

2 Like

Wordsmitty ✍️

Nov 18, 2024 at 12:34pm
In response to "Losing Weight Is Easy"

This brings up the old question of whether your weight changes when you inhale a helium balloon to make your voice higher.

Maybe this has to do with the difference of a mug of beer vs a tankard of ale.

The universe has so many weighty/massive questions.

3 Like

Brandiwyn🎶

Nov 18, 2024 at 11:27am
In response to "That's the Spirit"

Maybe you’d go with “Thunder” because that one’s so terrible that only divine intervention can explain its success. Wow. Missed opportunity, here. How could you let this go without a shoutout to mighty Thor, son of the Allfather, wielder of Mjolnir, He with the Long Forehead? (Said in the voice of the Soup Nazi): "No Valhalla for YOU!"

Brandiwyn🎶

Nov 18, 2024 at 11:19am
In response to "Losing Weight Is Easy"

Has anyone ever told you how annoyingly pedantic you are?

Damn your pedantic ways. I was hoping to justify a vacation to Venus (which I still argue would be a much better holiday destination than fr-fr-freezing Mars, Elon. Ugh.) Now I guess I'll have to settle for the Cancun plans we already made, since my mass (and waist diameter, and thigh diameter) will be exactly the same regardless.

3 Like

tj-turkey-jobble-jobble-hard-J

Nov 17, 2024 at 4:04pm
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

October 5, 2024 at 12:55am

#1077785

It Was Just Waffle

Even on the TGV, it takes a while to get from Lyon to Brussels. Worst, Brussels wasn't my actual destination; I had to hop on an intercity train to Bruges. Those trains are open seating and run frequently; they're more like NYC subways than what I'd expect from intercity (IC) trains, only without the piss, buskers, and giant Saks sacks.

Well, I guess technically, they're more like NJT trains, but more people know the subway.

Anyway, I was concerned about time, because I had to be at a certain statue at 6:30 pm or I'd miss a beer tour (and of course I couldn't let that happen under any circumstances). So I ran to catch an earlier IC train, which I barely did because the TGV was late getting to Brussels. Then, once in Bruges, I had to get to the hotel even though the meeting place was kind of between the station and the hotel, because who schleps travel bags on a beer tour?

You'd think I'd have learned my lesson back in Tours, but, apparently, we ugly Americans just won't take a hint. Once again, the hotel was 1600 meters from the train station. Once again, the terrain between was mostly flat. And once again, I cursed every single goddamn cobblestone in Europe.

I got to the hotel at 6, exhausted. My left knee is still wonky, and so is my right ankle. Of course it can't be one leg; it's gotta be both so I can limp with every step instead of just half of them.

Now, the hotel is older than European colonization of America (unless you count the Norse incursion, which I don't because they didn't make a lasting colony), so it has a few... interesting features. One of them is an abundance of stairs. Another is that, in order to get to my room, I had to take an elevator up one floor (or carry bags up a spiral staircase, which, well, no) then walk down a hallway, up a ramp, bounce up two steps, take a few twists and turns, and then get on a separate elevator to take me up half a floor.

At least the hotel has been retrofitted with electricity.

I barely had time to throw the bags in my room before I had to turn around and make my way to the statue. One of the streets on the way was called Steenstraat. Now, I don't know very much Dutch, I'm afraid, but "steen" and "straat" are two words that I am familiar with: Stone Street.

Even without bags, cobblestones are a pain in the ass.

When I got there, the guide was waiting impatiently, tapping his foot. Apparently, he'd messaged me to meet at 6 instead of 6:30. I'd never gotten any such message. Fortunately, his English was excellent, and I showed him that no, I'd received nothing. Unfortunately, the reason he'd wanted to meet earlier was that the best beer places closed at 7, and now we wouldn't have enough time.

All that running and stumbling on cobblestones... all of that... for nothing.

Well, not completely nothing. We agreed to try again for Sunday at 2:30. And the guide pointed me at a nearby restaurant which he said was good. Now, I'm pretty sure it's the law in Belgium for every restaurant to be good, but in this case, he was definitely right. I managed to hit the entire Belgian flag

in one dinner: Beer, chocolate, and waffles. And meatballs for the main course, but meatballs aren't on the flag. All, incidentally, delivered to the table by a Japanese nekorobot . No, seriously. This thing had cat ears and a screen with an animated cat face. I felt like I was in a Black Mirror episode. Or at least Doctor Who. I should write a book: Cobblestones and Advanced Robotics: A Study In Contrasts.

Oddly enough, even though the beer I had was very local to Bruges, I'd had it before; somehow, a keg had made its way to my hometown in 2021, and, as I keep meticulous beer-drinking records (okay, it's an app), I was able to determine that I'd sampled it back then. Of course, I didn't mind drinking it again, and there are plenty of other beers here that never make it out of the EU, so it's not like I wasted the trip.

I could have done without all the quaint fucking cobblestones, though.

9 Like • Comment • View 5 comments

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