Complex Numbers (Book)

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Complex Numbers

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/

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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 2 hours 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

about 4 hours 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.

August 4, 2022 at 12:01am

#1036085

Off the Edge

Today's article is... well, see for yourself:

What we can learn from people who take the Flat Earth theory seriously
“Flat Earth enables people to cast out all previous information that they didn’t want to believe and rebuild the world from scratch.”

You know, I can almost appreciate that. Almost. There's a certain allure to things that tell you that everything you've learned is wrong, and here's the Truth.

Problem is, they're the ones that are almost always wrong. Sure, science is always revising itself, but when it comes to some really basic shit like the general shape of the planet, it's as close to certainty as it's possible to get that it's round.

Across the globe, millions of people believe the Earth — that whirling blue sphere, spinning through space — is, in fact, a flat plane.

Old joke: "The Flat Earth Society has members all around the globe."

Another old joke: "We know the Earth isn't flat because if it were, cats would have pushed everything off the edge by now."

It’s unclear how many people believe some version of Flat Earth theory.

And it doesn't matter. One would be too many. If it were eight billion, they'd still be wrong.

And polling gives us some sense of the scale of this belief system: As many as 1 percent of Americans (that’s more than 3 million people) and 7 percent of Brazilians (11 million people) say they believe the Earth is flat, for example.

Polling? "Polls just tell you what They want you to think."

The modern Flat Earth movement has its origins in a snake oil salesman and utopian named Samuel Rowbotham, said Kelly Weill, a journalist who covers fringe movements for the Daily Beast and spent years researching this movement and its adherents.

"Snake oil salesman" is all you should need to know.

Weill spoke to Grid’s misinformation reporter, Anya van Wagtendonk, about the movement’s appeal, its overlap with religious beliefs and the QAnon conspiracy theory, and how we’re all susceptible to conspiratorial thinking.

"Misinformation reporter" could have two distinct meanings. Just saying.

The rest of the article is the interview, which doubles as a stealth ad for Weill's book.

But I think there’s an emotional truth to Flat Earth. People come to it when they feel like the world is very broadly wrong.

Oh, but the world is very broadly wrong. For instance, there are flat-Earthers living in it.

Samuel Rowbotham, the theory’s inventor, used a lot of biblical tools in his writing, saying that the globe model conflicted with a round Earth. A lot of modern Flat Earthers will use the theory to get into other alternative Christian beliefs. A lot of them are creationists.

It is the case that a purely literal reading of the Bible (were such a thing actually possible) supports a flat Earth. It also sets the value of pi at exactly 3. I take this to indicate that the facts in the Bible are wrong. The same literal reading says that the sky is, in a real sense, a "firmament," keeping the waters above from crashing down (as supposedly happened in a certain flood). We know that this is not the case.

...a lot of Flat Earthers — depending on their belief in why there’s a Flat Earth cover-up — believe that, when the flat earth is finally revealed, that it will usher in a new era of peace or religious enlightenment, things that conveniently align with their vision of utopia.

Which is, incidentally, my version of dystopia. Not the peace part, but the religious endarkenment part; but remember: peace can be achieved by wiping out all of humanity. Peace is great, but it's important to know what one means by it.

I’ve had people tell me that there’s going to be a societal breakdown, but that we will rebuild a more enlightened, Christly version of society.

There is going to be a societal breakdown if we don't rein in these flat-earthers. And an enlightened society is the exact opposite of a Christly one. Don't believe me? Look at history. Individual belief is fine; I'm all for it. But when a bunch of True Believers get together, bad things happen to innocent people.

There’s a tendency to think of conspiracy theorists as tinfoil hatters, as crazy people. But the processes are really ones that we’re all susceptible to.

I would tend to agree with that. I catch myself in conspiracy thoughts sometimes. I'm usually able to logic my way out of them, but I'm still not convinced, for example, that PETA isn't run by synthetic fur and vegan food manufacturers.

Maybe we can bring that empathy to those conversations and use that as a basis for bringing people back to reality.

I don't want to bring them back to reality. I want to push them off the edge of the planet.

Wait...

5 Like • Comment • View 2 comments

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