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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-turkey-jobble-jobble-hard-J

about 14 hours ago
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

Turkey DrumStik

a day ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

July 7, 2023 at 10:24am

#1052279

Thought for Food

Here's a liberating take on food.

There Is No Such Thing as “Junk” Food
Food hierarchies are, in truth, sorting mechanisms. It does not make you a worse person to eat “junk” food, and it certainly doesn’t make you a better person to eat whole grains.

Except that food has been linked to morality and virtue-signaling for a long time.

When I was in elementary school, I filled out a well-intentioned worksheet that asked me to sort foods into boxes.

What you were really learning was that humans like to stick everything into neat little boxes.

The worksheet didn’t consider how to feed your child when you’re a single parent working swing shift and a Happy Meal or a frozen pizza is the cheapest and most reliable way to feed your kids, or if the nearest fresh broccoli was an hour’s drive away.

And this is the often-overlooked dirty little secret of food snobbery: eating foods considered healthy is expensive and time-consuming. Being able to do so is a product of privilege.

My understanding that certain foods were so “bad” they were junk was complicated by the peculiar diet culture of the ’90s, which convinced me that cheese and avocados were high-fat and to be avoided, bananas had too much sugar and should also be avoided, but Starburst Jellybeans (lot of sugar, sure, but fat-free!) or Snackwell Devil’s Food Cookie Cakes (cake...but diet?) were somehow okay.

I've ragged on nutrition science in here before; no need to repeat it.

I entered my 20s with deeply illogical ideas about food and nutrition, which became even more contradictory when injected with the sustainability gospel of Michael Pollan, anti-GMO politics, the locavore movement, and the rise of “fast casual” cuisine.

But the problem isn't just nutrition science; it's that, as evidenced by the anti-GMO bit, people will believe whatever suits them.

Some people, regardless of age, need more salt in their diet, not less; some people need more fat, or caffeine, or dairy, or none at all. And others just need more things in their lives that are delicious—that remind them of the true bounty and delights of being human.

And really, as a hedonist, that last part resonates strongly with me. Food isn't penance. Food isn't medicine. Food isn't virtue. Food is about not being hungry, and, ideally, enjoying life.

People weren't nearly as neurotic about food before we got all these choices. But now that we have them, sure, it's good to be healthy, but not at the expense of eating cardboard.

The article goes on to link food snobbery with racism and classism, and it makes some good points, but it's tangential to my purpose in linking this.

This is, to me, the important bit, right at the end:

Contrary to what those worksheets might tell us, food does not have moral character, and consuming it does not influence or infect our own character. Food is delightful, and food is fuel, and food is culture. It becomes shadowed with shame—often, the sort that can distort our eating habits for years to come—not when we eat it, but when we restrict it, and attempt to spread that shame to others who do not.

I noticed this in particular with the low-carb or gluten-free fads. There has not been a food that I'm aware of in the entire history of agriculture that has been more culturally significant than bread. It is symbolic to many religions, but even just culturally, it's something that brings people together. I can't help but feel that the attempts to demonize it are just another way to separate us from each other, and give us yet another thing to feel shame about—shame that can only be ameliorated if you Buy My Product.

6 Like • Comment • View 5 comments

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