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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Elycia Lee ☮

about 5 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

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Wordsmitty ✍️

about 18 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

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Annette in France

about 21 hours ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

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Elisa: Middle Aged Stik

about 23 hours ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

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Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

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Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

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Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

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Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

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Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

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Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

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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