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Thursday, Oct. 17, 2024

11:31pm 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/

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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 11, 2024 at 7:33am

#1078100

Beersday

As expected, my sleep schedule is all screwed up now, and it might take me a few days to get back to my normally-screwed-up Eastern Time schedule.

Fortunately, I don't have a lot of requirements for being at certain places at certain times, so I'll take as long as I need to recover. I do have a role-playing game scheduled for tomorrow evening, as is the case for most Saturdays when I'm not traveling, but that's about it.

One of my cats remembered me right away. The other remembered me after I gave her some food. "Oh, yeah, you're that human."

The true miracle of the trip, though:

When I did the Bosteels tour, as part of it, they gave me a Tripel Karmeliet boxed set—a bottle of that delicious beer, packed with two glasses (remember, most Belgian beers have dedicated glassware). There's nothing extra-special about the TK glasses; they're fairly normal tulip chalices, but with the beer logo printed on them.

The problem is, they're somewhat fragile.

My suitcases were already stuffed, so I spent the rest of the trip wondering how I was gong to get this boxed set home without everything breaking. Maybe I could mail back some clothes, so I'd have room? Mailing the beer to myself was right out, because of stupid laws. US Customs allows up to one liter of alcoholic beverage in checked luggage, and this bottle is under that limit, though of course you can't bring that quantity of any liquid in a carrion bag.

Well, I spent some time over there creatively rearranging stuff in my bags, and trying to ensure that the box containing the fragile, precious cargo was well-padded with dirty clothes on all sides (look, I wasn't about to waste time in Belgium looking for a laundromat). Still, I've done similar things before, a bottle of beer from England several years ago, and it came back all shattered. The beer soaked into the clothes, but I'm used to that and I was going to have to wash them upon returning, anyway.

So I wasn't holding out much hope. Between the rough handling of the bags, and the pressure and temperature differentials at flight altitude, I mentally prepared myself for returning home with a box of shattered glass and beer-soaked clothing.

But, somehow, the beer, and even the glasses, survived intact.

I should make a holiday of this, like how Hanukkah celebrates the miracle of the lamp oil lasting longer than it should have. October 10 will be Beersday for me from now on. It's even easy to remember, since it's 10/10 in both US and Euro formats, and it's also the birthday of one of my best friends.

Really, it's not even that big a deal, except that this was my only physical souvenir of the trip (like I said, suitcases were already stuffed, so no room for plastic Eiffel Towers or Manneken Pisses). Tripel Karmeliet is generally available in my area, albeit at exorbitant import pricing, and the glassware can be ordered online. I'm just glad my luck held out.

7 Like • Comment • View 6 comments

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