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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Write_Mikey_Write!

about 17 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 19 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.

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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').

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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.

March 22, 2020 at 12:06am

#978794

Universal Consciousness

Today in "Just Because You Can Think It Doesn't Mean It's True..."

(Buckle up, folks, this one's a bit complicated.)

https://whyevolutionistrue.wordpress.com/2020/01/17/panpsychism-an-interview-and...

Panpsychism: an interview and a critique

"Panpsychism" is, as I understand it, the philosophical position that consciousness exists because everything is conscious.

Is that the whiff of bovine excrement my nose detects?

Harris gives the same two justifications for panpsychism as does Philip Goff in the interview below: there is no way to understand how subjective perception (“qualia”) can arise from purely materialistic phenomena in the brain (this is the “hard problem of consciousness”, and, second, because science cannot tell us what the real intrinsic nature of matter is. Supposedly philosophy can, and that intrinsic nature includes consciousness. How philosophy alone can supply this conclusion baffles me.

Now, I don't think it's a bad thing to come up with ideas like this. All great discoveries start out with an idea. But most ideas don't lead to great discoveries. But where's the supporting evidence? Hint: lack of evidence isn't supporting evidence. Worse, it can't be disproved.

It's like the pernicious idea that we're living in a simulation, like in The Matrix. I maintain that a well-designed simulation wouldn't give us the leeway to conceive of this possibility; therefore, if we are living in a simulation, it's not a well-designed one. If it's not a well-designed one, we should see cracks in it ("glitches in the matrix"). We don't, at least not compelling ones. Therefore, we're not living in a simulation. But that's not disproof; that's just my personal argument against it.

Besides, even if we were, we can't get out of it, so what bloody difference does it make?

From a quoted section of text:

But when I use the word consciousness, I simply mean experience: pleasure, pain, visual or auditory experience, et cetera.

If you simply mean experience, then say experience.

Assertion:

The qualitative experience of consciousness cannot be understood by a program of scientific materialism.

Any actual proof of that, or are you just declaring it to be so?

No need to quote much else, I think. The link is worth a read if you like to think about thinking.

I used to hang out with people who would say things like, "The Universe loves you and wants to keep you alive." This is demonstrably untrue; as far as we know, we can stay alive in a shell, proportionally thinner than an eggshell, surrounding the Earth. Even some parts of this shell, like Antarctica for instance, aren't very hospitable and will kill you in hours. Everywhere else? Everywhere in the entire universe? Dead in less than a minute.

But the people saying this really believed it, because they wanted it to be true.

(I should acknowledge here that there very well might be other shells that can support our life processes. As I've noted before, it's a big universe. Still, the number of such places surely rounds off to zero when compared to the vast emptiness of space and the burning hearts of stars.)

But hey, the panpsychists very well might get the last laugh; they might turn out to be right after all. After all, the Universe has been known to throw us a few curveballs every now and then. But until we see some evidence, it remains just as much wishful thinking as the idea that the Universe is actively working to keep us alive.

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