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Saturday, Nov. 16, 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:

Write_Mikey_Write!

a day ago
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

a day ago
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

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

May 21, 2022 at 12:02am

#1032660

Sermon on the Mound

Hey, this time it's not a war.

Well... kind of not a war.

On This Day
21-May-1988
Sermon on the Mound

When most people think of the 1980s, they think of the movies, music and hairstyles of the era. And generally, they mock these things, forgetting that, 40 years from now, our movies, music and hairstyles will be mocked.

To be fair, today's music sucks almost as bad as it did in the 80s. Oh, there are (and were) exceptions, but for the most part, the 80s were a musical wasteland for me, broken up only by the presence of three great Springsteen albums, Pat Benatar, the continued existence of Rush, and the debut of Melissa Etheridge.

But I digress. That's what most people think about when they encounter something about the 80s. Me? I mostly remember the Axis of Evil, which was centered around Reagan and Thatcher, the ascendance of whom proved to me that this world was too wicked for me to ever be responsible for bringing a child into.

Periodically, someone will bring up the idea that women should run the world, that they'd do a better job of it. I reply with "Margaret Thatcher." At which point they shout, "SHE DOESN'T COUNT."

Now, I generally try to avoid the Big Taboos in here: politics, religion, and sex; and today's anniversary contains all of these things. Well, okay, maybe not sex. Unless you're into that sort of thing, which, hey, you do you. As with religion and politics.

In the address, Thatcher offered a theological justification for her ideas on capitalism and the market economy.

You know what's interesting about theology? You can use it to justify anything. During the time when slavery was a thing here in the US, the pro-slavery people used religion to justify their ownership of people

, and abolitionists used religion to fight against it.

Who was right? Obviously the latter, but it wasn't a religious victory.

What people think happens is: they follow their religion and their ideals spring from that. Given, however, that the same religion (and I'm talking about pretty much any of them here) can provoke such vastly opposing ideals, it seems to me that, instead, people come to some conclusion and then reverse-engineer their religion to support it. So you get, for example, what we have here in the US: different Christian denominations preaching opposing things, like "poverty is a virtue" and "prosperity is a virtue."

That particular dichotomy echoes some of the stuff Thatcher said in her address.

As the link above doesn't contain the actual text of her speech, here it is.

The UK is, of course, a completely different country from (they would say "to") the US. We made sure of that back in the 18th century. They're explicitly a theocracy; we are not (though there's a strong effort to make us into one). And yet, I often note parallels. When they lean right, we lean right. When they lean left, we lean left. When we have high unemployment, they tend to have high unemployment, and the reverse. We may be two countries separated by an ocean and a common language, but for whatever reason, our fates are linked. I'm not implying any directional causation here, only correlation.

Which is one reason I find it interesting that some of the stuff Thatcher said in her speech on this day in 1988 is still echoing down the corridors of time.

We are told we must work and use our talents to create wealth. "If a man will not work he shall not eat" wrote St. Paul to the Thessalonians.

This particular quote stood out to me as, perhaps, a reason why the speech was mocked as the Sermon on the Mound. In the actual Sermon on the Mount, as recounted in the NT, Jesus is reported to have said: “Why take ye thought for clothing? Consider the lilies of the field, how they grow; they toil not, neither do they spin. And yet I say unto you that even Solomon in all his glory was not arrayed like one of these.”

As an outsider to both religion and UK politics, these statements strike me as incompatible. Oh, sure, you can do mental gymnastics to attempt to reconcile them -- see my above comment about theology -- but the Paul quote seems to be a straightforward call for toxic productivity, while the Jesus quote encourages slacking off.

Again, as an outsider, the tension between Jesus and Paul seems to me to be the fundamental cognitive dissonance of Christianity.

Personally, I'm on Jesus' side on this issue.

To assert absolute moral values is not to claim perfection for ourselves. No true Christian could do that.

I don't know if this is irony or not: there is a logical fallacy called the No True Scotsman Fallacy. It goes something like this:

Person A: "No Scotsman puts sugar on his porridge."
Person B: "But my uncle Angus is a Scotsman and he puts sugar on his porridge."
Person A: "But no true Scotsman puts sugar on his porridge."

So there was Thatcher, addressing a church in Scotland, explicitly invoking the No True Scotsman fallacy.

I'm gonna go ahead and call that irony.

When Abraham Lincoln spoke in his famous Gettysburg speech of 1863 of "government of the people, by the people, and for the people", he gave the world a neat definition of democracy which has since been widely and enthusiastically adopted. But what he enunciated as a form of government was not in itself especially Christian, for nowhere in the Bible is the word democracy mentioned.

1) I'm using this quote as justification for ragging on the Sermon on the Mound. If Thatcher can quote an American, then by Bast's breasts, an American can quote Thatcher.

2) Nowhere in the Bible is pedophilia (UK: paedophilia) mentioned, and yet we have laws against that. For example.

3) Of course Lincoln wasn't espousing Christianity. We, unlike the UK, are not a Christian country -- despite efforts from the modern-day Axis of Evil. Lincoln's relationship with religion was, from what I've seen, complicated.

A friend sent me a photo the other day. Without context, at first it was a little hard to figure out, but it finally clicked for me. The photo showed a statue of Thatcher, which for whatever reason was surrounded by a security fence. As I'm painfully aware of here in Charlottesville, statues are an endangered species these days; statues of terrible people, even moreso. I wasn't aware that their impending extinction carried over across the pond, but see above about how we tend to move in parallel. But you could still see the image of the Iron Bitch (probably bronze in this case) looming above the fence.

Outside the fence, some bloke was sitting at a table selling chicken eggs.

To paraphrase Chris Rock, I'm not saying that egging a statue of Thatcher, or selling the means to do so in front of the statue, is right... but I understand. Maggie, you wanted an unregulated, free market economy? Well, there it sits.

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