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Tuesday, Feb. 4, 2025

3:52pm 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

about 23 hours ago
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

a day ago
In response to "Look! Up In the Sky!"

2 Like

Lazy Writer est 4/24/2008

a day ago
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

Elisa, Stik of Clubs

Feb 2, 2025 at 10:41am
In response to "Revisited: "Friend""

🌖 HuntersMoon

, that emoticon use is top notch! I have feelings like that on a regular basis.

2 Like

🌖 HuntersMoon

Feb 2, 2025 at 10:40am
In response to "Revisited: "Friend""

@ Elisa, Stik of Clubs - Cognitive Distortions: It seems to apply equally to our current Pumpkin Prophet.

3 Like

Elisa, Stik of Clubs

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

for a country that claims to love freedom and individuality, some of us are remarkably susceptible to following prophets of the End Times.

I wonder how much of that stems from a large portion of the population not being aware of how cognitive distortions work. (Luckily there are some advances

in making that kind of learning a bit easier.)

3 Like

tj wanderlust-words-in-motion

Feb 1, 2025 at 5:26pm
In response to "This Is the Whey"

Years back there was a dairy farm just outside of Anoka Minnesota that specialized in old-world cheeses; I loved that place. It's too bad we don't have craft cheeseries like we do craft breweries.

1 Like

tj wanderlust-words-in-motion

Jan 31, 2025 at 5:01pm
In response to "Unscheduled"

I would have to add fear to this as well: "Only by making us feel guilty can they sell us stuff to assuage that guilt."

I agree, everyone has their own "productive time" and sleeping patterns change, growing up I was an early riser no matter what time I went to bed; it worked great. Then, for whatever reason, I started sleeping later and was more productive in the evenings and into the night. Now, it's somewhere in between.

1 Like

Wordsmitty ✍️

Jan 31, 2025 at 12:37pm
In response to "Unscheduled"

My mom would recite in the morning: "Here is dawning another new day, whilst thou let it slip useless away?" Thinking back, even if I got up and went to school, sometimes it still was a useless day.

3 Like

February 4, 2025 at 1:09pm

#1083307

That Healthy Glow

How about some applied science from Gastro Obscura?

How to Make Fluorescent Food
A UV light and specific ingredients can make a dish or drink change color.

Because the greatest thing about science is all the cool shit we can do with it.

When I was in college, I went to a party that I’ll never forget.

Then it wasn't that great a party.

But the real spectacle was inside. There was not a piece of furniture to be seen. The walls of all the empty rooms were covered in newspapers, and all the overhead lights had been replaced with black-light bulbs, filling the air with a purple haze.

I sometimes idly speculate whether you can still get those bulbs, and if they make LED versions. But I don't care enough to look it up.

Of course, there was beer on offer, but everyone was drinking gin and tonics. Because of the black light, the drinks all glowed an eerie blue, due to the quinine in the tonic water.

I've seen that effect. They used real quinine, though, not the severely watered-down stuff from Schweppes or Canada Dry. I don't know if it would still work with those; I think so, but not to the same intensity. In any case, a gin and tonic is one of Nature's most perfect cocktails.

So when my coworker showed me a post about making a fluorescent cake, I knew I had to try baking one myself.

Someone got baked, anyway.

Extracted from the bark of the Peruvian cinchona tree, quinine was once the only known treatment for malaria.

Legend has it the G&T was invented by Brits in India. They used quinine for its antimalarial properties, and to make it more palatable, they added London dry gin.

Leave it to Brits to add gin to something to make it taste better.

George Gabriel Stokes, the Irish physicist, coined the term fluorescence in 1852 after scientists observed that a quinine sulfate solution glowed when exposed to what is now known as UV light.

Thus leading to possible confusion in chemistry class: it doesn't have much to do with the element fluorine, whose etymology has to do with "flow." Fluorescence was named for one fluorescent material, which happened to have fluorine in it. But fluorine isn't the only element that can be involved with fluorescence. Quinine doesn't contain fluorine.

I told you it could be confusing.

Outside the minibar and medicine cabinet, there’s another extremely common substance that gives off a shocking glow under ultraviolet light: chlorophyll.

I don't have houseplants. Every time I've tried, they realized they were living with me and lacked locomotion, so committed suicide. But if I did, I'd totally put them under black light every once in a while.

So I went to the health-food store and bought a tiny bottle of liquid chlorophyll—which some people consume for its supposed health benefits, ranging from weight loss to improving the skin.

I don't doubt that vegetables have health benefits. Liquid chlorophyll sounds more like a duck: quack, quack, quack.

The author goes on to describe the psychedelic-cake-making process, which didn't end up involving liquid chlorophyll solution. You know, in case you might want to try it. Personally, I at least see no harm in trying, but I don't know everything.

Or you could simply pour yourself a glass of tonic water. The gin is optional.

No, it is not.

3 Like • Comment

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