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Friday, Feb. 7, 2025

4:25pm 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:

tj wanderlust-words-in-motion

a day ago
In response to "So Much Energy"

I always thought electroweak{i/} was a bad choice of terminology. It sounds like the batteries in you flashlight are almost dead! They should have used a term like "electronuke" which sounds like some super-hero stuff. There's no need to fear, Electronuke is here!"

Also, when crossing Higg's field, beware of Higg's boson (cross between a boar and a bison) or you may get killed; unless of course, Electonuke shows up and saves your ass.

Alright, maybe I should be writing a story instead of leaving a comment...

1 Like

Graham B.

a day ago
In response to "So Much Energy"

The only energy-carrying particle that concerns me is the Joeson, as in "I need my morning cup of Joeson to get me up." It's responsible for the strong nootropic force (for me, anyway).

3 Like

Lazy Writer est 4/24/2008

a day ago
In response to "So Much Energy"

I need to find some of that energy..because mine is worn out!

2 Like

tj wanderlust-words-in-motion

a day ago
In response to "That Healthy Glow"

Yes, they do still make black lights, most are LED. We have one above my wife's plants, it helps them survive through the winter with our lack of sunlight. They seem to be more purple than the black lights from days gone by. Interestingly, they make our Australian Shepard glow purple (her black areas) and they make our Husky's blue eyes glow, but not the black on his fur.

1 Like

tj wanderlust-words-in-motion

Feb 5, 2025 at 1:38pm
In response to "The Fault in Our Stars"

I knew you (or someone) was going to write this; it was in my horrorscope.

2 Like

🌖 HuntersMoon

Feb 5, 2025 at 10:22am
In response to "The Fault in Our Stars"

I don't care what this article says... My psychic told me that Astrology is 100% accurate!

1 Like

tj wanderlust-words-in-motion

Feb 3, 2025 at 4:32pm
In response to "Look! Up In the Sky!"

Beware anyone wearing a black suit waving a pen looking device in front of you. Actually, they likely dress as regular people, and the device is hidden in an actual pen. Maybe they've even put the device in the pens we use! Clearly, that's because there's a government agency tasked with removing our memories of certain encounters.{i/}

2 Like

🌖 HuntersMoon

Feb 3, 2025 at 9:22am
In response to "Look! Up In the Sky!"

2 Like

Lazy Writer est 4/24/2008

Feb 2, 2025 at 10:54pm
In response to "Revisited: "Friend""

Christ is coming back...no one knows when...Only God himself...we are told to be ready...by that, the Bible means giving your heart and soul to Christ. It is a free gift. He does not force you to believe. I am not a member of any end of the world group but I do believe my Bible.

tj wanderlust-words-in-motion

Feb 2, 2025 at 11:10am
In response to "Revisited: "Friend""

I had an employee that requested some time off the week leading up to December 21, 2012 to be with his family. They had prepped and prepared for over a year and wanted to be together, in shelter, for the end of the world. On December 22 he came into work looking like he had not slept all night, head hung low, and not a word to say about the rest of us still hanging around. In March, he and his family all moved to Florida, probably to start prepping for the next end of the world.

2 Like

February 7, 2025 at 9:51am

#1083463

Roll Model

Here's a Vox article about Down Under. No, not Australia. The other Down Under.

How Big Toilet Paper dupes us all
The wild, nonsensical world of toilet paper math, explained.

I'll try to make that the only arse joke in this entry. I'll fail.

It’s a truism that everything’s bigger in America — just look at the cars and houses.

And people.

But perhaps nowhere is the virtue of bigger is better more bizarrely apparent than how toilet paper is sold.

Oh, I don't know. Have you seen the latest Ford pickups? That's relevant because both are designed for assholes.

A pack of 18 mega toilet paper rolls, for example, magically transforms into 90 “regular” ones. The labeling emphasizes this greater number in large font, lest you foolishly think 18 simply equals 18. Another pack might insist that 12 even-thicker rolls of toilet paper are the equivalent of 96 normal rolls.

Basic marketing: change what "normal" is, then compare everything else to the new normal.

Americans’ enormous vehicles and palatial abodes may in fact exist in service of conveying and storing gigantic bulk packs of this bathroom essential.

Suddenly, everything makes more sense. Still not a lot. But more.

There’s some irony, then, that for all the trumpeting of gargantuan sizes, toilet paper rolls are generally getting smaller. It’s a key example of the trend of manufacturers charging the same price (or even slightly more) for less product that’s been dubbed “shrinkflation.”

Stop.

It makes it more difficult than ever to figure out if you’re getting ripped off.

Eh, not really. Are you buying something in the US? Then you're getting ripped off.

With dubious numerical claims about how much a “mega” roll is really worth, brands can promote the perception of value without actually having to show their work.

It's worse than that.

I get my bumwad from one or two sources: the local grocery store, or Amazon (I don't want to hear it). Either way, the company presents a truly dizzying array of options, from 4-packs to giant, bulky megapacks, and of course from myriad different suppliers.

A long time ago, grocery stores, in a rare consumer-aiding move, instituted unit prices. Like, they'll put the price of the package in big numbers, but if you look closely, you'll see a price per unit. This could be price per pound, per ounce (this is the US, after all), or, in the case of loo roll, usually per 100 sheets. It makes comparison shopping easier if you can see that one package offers a lower per-unit cost than a different package of the same product; less math is involved.

But lately, I've been seeing inconsistencies in the unit pricing for several items, including buttwipe. Sometimes, it's price per sheet. Usually, it's price per 100 sheets. But sometimes, the unit price has magically disappeared (also, sheet sizes can vary between manufacturers). Or maybe they give it in price per ounce, which makes no sense at all.

This makes comparison shopping nearly impossible without a calculator. I mean, sure, I can do most simple math in my head, but that doesn't mean I can be arsed when I just want to get the shopping over with.

Unsurprisingly, the so-called standard size has no consistency, either. Charmin’s regular roll has 55 two-ply sheets, for example, but it’s often hard to even find the regular size of a brand’s toilet paper in stores.

And that's the other problem: "standard" has lost meaning.

The sheets-per-roll ratio is also subject to change depending on whether you’re looking at single-ply, two-ply, or three-ply.

Honestly, I didn't even know they made three-ply.

It’s no wonder people have taken matters into their own hands.

I feel like that could have been a butt joke.

The cost of making toilet paper may have gone up in recent years, according to the Los Angeles Times, due to a slowdown in lumber production (there’s less available wood pulp, which is what most toilet paper is made of).

You'd think they could make "bathroom tissue" (possibly the stupidest euphemism ever) out of recycled paper, but I don't know.

It’s something meant to be quickly disposed of, literally flushed away, yet commercials for toilet paper are almost always focusing on its delightful, cushiony softness or a special “quilted” or “diamond weave” texture that adds a premium feel to the product.

This. This is one reason I avoid commercials like the cliché.

One could switch to commercial-grade toilet paper, which is much cheaper but is of (ahem) crappier quality.

Ah! There it is!

In any case, the article (which I've resisted the urge to call crack reporting until just now) waits until the end (pun absolutely intended) to propose the optimal solution for wiping away all this confusion: a bidet.

4 Like • Comment

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