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Monday, Nov. 18, 2024

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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 15 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

August 30, 2023 at 9:20am

#1054851

The Problem of Stupid

I've done entries about this topic a few times, so I had to double-check to ensure I hadn't linked this particular article before, or that it's not some variation on a previous article. And also to try not to duplicate a title. It looks like something different, though I can always make stupid mistakes.

Bonhoeffer’s “theory of stupidity”: We have more to fear from stupid people than evil ones
Evil is easy to identify and fight against; not so with stupidity.

I'm not so sure evil is so easy to identify and fight against, but I guess that compared to stupidity, it's a cakewalk.

The most relevant previous blog entry is here, from two years ago, if you're interested in comparing views on the subject: "Fight The Power"

Today's article isn't all that long, so this entry won't be, either.

There’s an internet adage that goes, “Debating an idiot is like trying to play chess with a pigeon — it knocks the pieces over, craps on the board, and flies back to its flock to claim victory.” It’s funny and astute. It’s also deeply, depressingly worrying.

I would like to once again draw a distinction between stupidity and ignorance. Ignorance is our natural, base state; it's only through learning stuff that we become not-ignorant. The key there is to be open to learning stuff, even if it sometimes contradicts stuff we've already learned. Ignorance is, therefore, forgivable, and fixable... if it doesn't turn into willful ignorance.

For theologian and philosopher Dietrich Bonhoeffer, the stupid person is often more dangerous than the evil one.

The core of theology and philosophy is to build logical edifices. Unfortunately, often those edifices have no foundation. Someone can be smart and still wrong, due to false premises.

In comic books and action movies, we know who the villain is. They wear dark clothes, kill on a whim, and cackle madly at their diabolical scheme.

The whole point to comic books and action movies is to have a clear villain, someone that the very clear hero can successfully thwart. It simplifies, and is therefore satisfying. More recently, both sides have been written to be on shaky moral ground, which can be satisfying, too.

Once something is a known evil, the good of the world can rally to defend and fight against it.

Except that it's blindingly obvious that this doesn't happen on a regular basis. You know Russia's still trying to invade Ukraine? Sure, we're helping Ukraine (the clear Good Guys), but not enough to win a definitive victory against the Bad Guys.

And propaganda has convinced some people that the Good Guys are the Bad Guys, and vice-versa.

Stupidity, though, is a different problem altogether. We cannot so easily fight stupidity for two reasons. First, we are collectively much more tolerant of it. Unlike evil, stupidity is not a vice most of us take seriously. We do not lambast others for ignorance. We do not scream down people for not knowing things.

I don't really buy this, either, and once again, let's not conflate ignorance with stupidity. There are words I struggle to pronounce, because I've only ever seen them in writing. Other people struggle to spell words they've only ever heard. Which of us is more ignorant? Neither, really. But I tend to be more judgmental of people who can't spell than of people who can't pronounce, because I can relate better. I'm aware of this flaw and can therefore work to mitigate it; certainly, I have others I'm not aware of.

Bonhoeffer’s argument, then, is that stupidity should be viewed as worse than evil. Stupidity has far greater potential to damage our lives.

I mean, I kinda see the point, and agree, to some extent. But none of this addresses the definition problem, whereby, for example, the extreme right thinks that the extreme left is stupid, ignorant, and evil, while the extreme left believes these things of the extreme right.

But stupidity is much harder to weed out. That’s why it’s a dangerous weapon: Because evil people find it hard to take power, they need stupid people to do their work.

This is why the trope of the criminal mastermind with brainless minions is perpetual. Think Lex Luthor and Otis in the 1977 Superman movie.

So, in short, I'm not completely convinced. This may be source-bias on my part (theologians in particular are always suspect for me), but, in keeping with the theme, I try to keep an open mind. I think that earlier entry's article presented a more cogent argument.

5 Like • Comment • View 2 comments

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