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Friday, Oct. 18, 2024

1:21am EDT

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Complex Numbers

by Spirit HalloWaltz

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:

Wordsmitty ✍️

a day ago
In response to "Can We?"

"corrugated ridges add strength " - and this is so you can't use your heel to crush it like you do a beer can.

1 Like

The Ghost of Jayne's Lost Sock

a day ago
In response to "Can We?"

The top and bottom seams fail first. *As reported by a friend who used to play "can bowling" with their coworkers (overnight shelf stockers at a discount grocery chain)

2 Like

Annette

a day ago
In response to "Can We?"

By the way:

"A significant new market for the can had become apparent after 1935 when, following the development of suitable internal coatings, the first beer cans were test marketed."

Evo lution of the tin can

1 Like

Annette

a day ago
In response to "Can We?"

As much as all the modern people decry canned foods, there seems to be a fierce competition on who gets to take credit for inventing tin cans.

In a small museum in the country side in France, I learned that French scientists finally achieved to retro-engineer the exact alloy for tin cans sometime in the 18th century. They claimed to have cracked a German secret.

This article that you quote credits an English person.

Funniest part is that I was convinced it was an AmeriCAN invention.

1 Like

Mummified_Mike

Oct 15, 2024 at 10:45am
In response to "Pushing the Button"

I wonder how many of the NASA guys involved in making the Apollo 11 decision had already read Crichton's The Andromeda Strain - published about 2 months before the Moon mission - and allowed it to influence their decision-making process?

1 Like

🌕 HuntersMoon

Oct 14, 2024 at 10:13am
In response to "DeTECHtion"

I had a B.S. detector but, with the election season here, it was more like a smoke detector with a weak battery - It just went on and on and on...

2 Like

Kåre Enga in Montana

Oct 13, 2024 at 6:18pm
In response to "Spit in the Ocean"

Worthy of a long comment. Yes, I could; but, I won't.

As for your list... I'm a bag of mixed nuts.

1 Like

WakeUpAndLive️🦇Elf'sSpell

Oct 13, 2024 at 11:48am
In response to "Revisited: "I Wood Knot""

1 Like

Elisa: Stik or Treat

Oct 12, 2024 at 10:46am
In response to "A Few Observations"

Oddly enough, I've encountered similar unisex style restrooms in the US. If you wander back up to Minnesota and go to the old Schell's brewery in New Ulm, they have them. Mi amor and I joke that they're likely the most progressive bathrooms in the entire (rural) county.

1 Like

Spirit HalloWaltz

Oct 12, 2024 at 10:13am
In response to "A Few Observations"

Elisa: Stik or Treat

, oh, yeah, I'd intended to mention those things but forgot.

On accessibility: Most of the places I visited were old; in some cases, older than the US. Spiral stairs, tiny passageways, multiple levels, and those blasted cobblestones. Difficult, if not impossible, to retrofit enlightened disability access features. The few places that were more modern did it better. That's one downside to the older stuff, I think.

Restrooms: tiny, few stalls, mostly unisex. The unisex thing doesn't bother me, and I expect it better accommodates trans people... but not disabilities. I saw pay-to-poo restrooms, but I managed to avoid having to use them.

Now, some people unfamiliar with Europe might wonder how the unisex bathrooms work. There's usually one or two urinals tucked behind a corner or something, but I imagine it might be shocking for some folks from the US to peer around a corner and see some dude standing at one. But the view is from the back, and it's not like you see anything important and/or disgusting. Also, the stalls don't have those flimsy walls with big gaps and cracks; each toilet stall is usually (for the ones I used) completely enclosed, with a locking door, and private. The hand-washing facilities are shared, and sometimes not even within the restroom itself. It is entirely possible that I missed some etiquette thing, but in general, one merely needs to acknowledge that, shockingly, we're all humans and we deal with waste in much the same ways. Basically, it's just different if you're used to the US (and mostly UK) segregated style, but it's not privacy-killing.

What was more shocking to me was the near-complete absence of bidets, even in hotel rooms.

October 14, 2024 at 9:27am

#1078266

DeTECHtion

From Cracked, a countdown of the unseen:

5 Ways to Detect the Invisible Stuff Hiding From Us
Surround yourself with the right sensors, and they might just save us all

All around you are signals you have no way of perceiving on your own. For example, did you know that invisible waves travel through the air, transmitting words and images, decodable by the right device?

We only see a remarkably thin slice of the electromagnetic spectrum. There are good evolutionary reasons for this, but why interrupt a fact-comedy with pure fact?

Not everything imperceptible is on the EM spectrum, though.

5. Seismometers Spot Quakes and Save Trains

Not a single person has died in an accident aboard Japan’s bullet trains.

There was a movie a couple of years back called Bullet Train, set on a Japanese bullet train. Action/comedy, so the title is a pun. It's not much of a spoiler to say that bad things happen on the train and people die. But not in an accident caused by an earthquake. I had the opportunity to watch the movie again on a recent long flight, and it was even better than I thought it was the first time.

Even in 2011, when that 9.0 earthquake hit Japan, collapsing a bunch of bullet train stations and ripping up the track, seismometers on the ocean floor detected the first tremors and shut down the trains in time.

EM waves, including radio, travel faster than seismic waves, so these early detection systems aren't magic, but science.

4. The Mountain Pool of Ultrapure Water

Japan is also home to Super-Kamiokande, an observatory for detecting neutrinos. It’s a tank a hundred feet tall and hundred feet wide, located in a mine a thousand feet under a mountain.

Neutrinos are the second hardest things to detect, after dark matter. Well, maybe third, after dark matter and something so invisible we don't even know it exists, yet.

Also, I'm pretty sure the tank is measured in SI units, as is its depth.

Neutrinos travel at the speed of light and pass through the planet without affecting much of anything, but we still manage to detect them using Super-Kamiokande.

Far be it from me to quibble about something on a comedy site, but I'm going to do it anyway: Neutrinos have mass, and therefore don't quite travel at the speed of light. But, you know... close enough. (There was some sensationalist reporting a while back on neutrinos that appeared to exceed the speed of light, but that turned out to be a mistake.)

3. ShotSpotter, the Gunshot Detector

Sometimes, you hear a gunshot outside, and you shrug your shoulders, saying, “Eh, what can you do?”

Emigrate?

Starting in 1997, several cities in the U.S. set up a system of sensors that pick up the sounds of gunfire and relay the location of the source directly to police. In D.C., for example, the sensors picked up some 40,000 shots in a 20-square-mile area over the course of seven years.

That's the sound of freedom.

2. The Detectors that Detect Radar Detector Detectors

Naturally, such devices use waves of their own, which means they’re vulnerable to being spotted by radar detector detectors. Of course, that means you should equip your radar detector with a radar detector detector detector, which will shut your device down as soon as it realizes it’s being spotted.

And so the arms race continues.

Pretty sure my state is still the only one in the US where radar detectors are illegal, but I can't be arsed to find out for sure. Yes, I drive around a good bit. No, I don't have a radar detector.

1. The Parkinson’s Sniffer

This one may seem out of place, being a mutant superpower instead of a tech device. But if you read to the end, you see that they used the mutant's superpower to create the tech needed for a Parkinson's test.

No mention in the article of radiation and Geiger counters, but I suppose most people know about that one, anyway. In any case, all of these were known invisible things. It's the unknown invisible things you really have to worry about.

3 Like • Comment • View 1 comment

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