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Saturday, Feb. 1, 2025

11:47am 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 19 hours ago
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 ✍️

about 23 hours ago
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

Elisa, Stik of Clubs

a day ago
In response to "Unscheduled"

"Only by making us feel guilty can they sell us stuff to assuage that guilt."

This might change thanks to the underconsimption(core) trend/movement that's currently circulating on social media. This trend may start with getting people to use what they've already purchased, but along the way it can help people rethink a wide variety of spending habits.

3 Like

Ichabod Crane

a day ago
In response to "An Eye For a Lie"

Thats just smaller windows.

2 Like

tj wanderlust-words-in-motion

a day ago
In response to "An Eye For a Lie"

I've heard it said that the eyes are the window to the soul, except for those people with those beady little eyes...

3 Like

Ichabod Crane

Jan 30, 2025 at 10:12am
In response to "An Eye For a Lie"

Close my eyes and I'm not saying anything!

4 Like

Quilli ☕

Jan 30, 2025 at 10:10am
In response to "An Eye For a Lie"

I've heard that drug use also influences pupil size. However, I have no direct knowledge of this, ahem.

4 Like

🌖 HuntersMoon

Jan 30, 2025 at 9:49am
In response to "An Eye For a Lie"

Next you'll be telling me there's a correlation between eyes and teeth...

2 Like

tj wanderlust-words-in-motion

Jan 29, 2025 at 4:29pm
In response to "Looking to the Yeast"

Sure, they start out eating specific types of plastic waste but soon evolve to eat every kind of plastic, waste or in use. Eventually evolving to eat any synthetic product, then evolving to eat organic substances with a very high attraction to meat, any meat. This sounds like a great sci-fi book.

On the other hand, better beer and nudity—maybe they're on to something...

2 Like

🌖 HuntersMoon

Jan 29, 2025 at 10:39am
In response to "Looking to the Yeast"

Just sayin...

2 Like

February 1, 2025 at 9:00am

#1083106

This Is the Whey

Sometimes I'll hear about science that seems nearly useless, like, I don't know, the effectiveness of positive reinforcement whilst teaching pigs how to sing. But every so often, a study comes out that truly pushes the limits of human knowledge and has a profound effect on our everyday lives. Like this one, from a two-year-old article in Smithsonian:

What Makes Cheddar Cheese Taste So Good?
After a year-long cheddar-making experiment, scientists have unraveled the microbial underpinnings of the cheese’s buttery flavor

And here I was, thinking that the buttery flavor of cheese is because it's made from the same stuff as butter. Another point against "common sense."

Eating cheese, for many, is one of life’s great pleasures.

Yep, it's right up there with eating good bread. And there are few greater pleasures than doing both at the same time. Gods, I miss France.

And while cheese-makers and scientists have long understood that bacteria transforms milk into the creamy, flavor-packed product, they haven’t fully understood the roles different microorganisms play in developing the unique flavors of cheeses.

Now, researchers are one step closer to unraveling some of this delicious mystery for cheddar.

While the US just doesn't have the cheese culture that France does, or even the UK, cheddar (a cheese of British origin) is quite popular here and, from what I understand, pretty much everywhere.

Cheese is a fermented food—just like beer, kombucha, kimchi and yogurt, to name a few.

While I appreciate beer being categorized under "food" there, I don't think "just like" is the proper description.

To produce it, cheese-makers add bacteria to milk. The bacteria chow down on the sugars present in the milk, transforming them into lactic acid—which helps give cheese (and other foods, like sourdough bread) its tangy taste.

For one thing, yeast is an entirely different microorganism to bacteria. They're not even in the same kingdom; yeast is a eukaryote.

To better understand what’s happening at the microbial level, researchers set up a cheddar-making experiment.

This. This is what science is for.

The article goes into how the experiment worked, then:

Though past research has explored the roles of individual microorganisms, the paper “brings together the bacterial communication that are at play in the complex metabolic landscape that leads to the overall cheese flavor profiles,” says Bart Weimer...

On a more serious note, this sort of thing really is different from a lot of science, which tends to work by isolating variables. This research combines variables, and acknowledges that cheese, like life, isn't all about the effect of one factor, but rather about the interplay between different factors.

And look, I made it all the way through the article without making a cheesy pun. Well, except for the entry title.

2 Like • Comment

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