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 3 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 16 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 19 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 21 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

April 19, 2020 at 12:07am

#981452

Top Bunk

One today from someone at my alma mater

https://aeon.co/essays/is-debunking-more-about-the-truth-teller-than-the-truth

Debunking debunked
Secular modernity requires the weeding out of all the baloney. Yet it’s not clear that we are any less credulous than before

What's not clear is that the goal was ever to make us "any less credulous than before."

Just as you can deworm a puppy, you can debunk a religious practice, a pyramid scheme, a quack cure. Get rid of the nonsense, and the polity – just like the puppy – will fare better. Con men will be deprived of their innocent marks, and the world will take one more step in the direction of modernity.

Read articles like this one, and the world will take one more step in the direction of postmodernity.

What we should imagine instead of an impartial skeptic is a person who gets a charge out of being the rational member of the exchange – someone who is drawn, for reasons that might or might not be clear to him or her, and that are probably difficult to articulate, to the drama of unmasking.

"And I would have gotten away with it, too, if it weren't for these meddling kids!"

There's really a lot more here, so much that my choice is to either quote it excessively or leave it at that. I'm choosing the latter because I'm lazy. But to summarize my takeaway from it, as I understand it, the author turns debunking into a social exchange, and skewers the idea of "modernity" (as defined by her) throughout. One could even say she debunks it.

My rebuttal? While it's not always easy -- or even possible -- to ascertain the truth of a situation, I think it's important to try. I agree that sometimes people go too far, perhaps by ascribing ill intentions to those they're trying to debunk. Maybe that's not clear; let me give you an example.

I had a friend who's a chiropractor. She spent many, many years at a school learning how to chiropract. It's her job and she makes a decent living at it, last time I checked. Meanwhile, many people consider chiropractic to be nonsense, a thing to be debunked. Someone like that might accuse my friend of lying, turning it on her instead of the practice itself. But she's not lying; she actually believes in what she's doing. Whether it's promoting falsehood or not, in her mind, it's truth. So no, she's not intentionally deceiving anyone, and I'm pretty sure that it would hurt her a great deal to be accused of being a con woman.

As for me, from what I can tell, there's some benefit to chiropractic, but many chiropractors' knee-jerk rejection of "allopathic medicine" is dangerous and a rejection of evidence-based treatments. Obviously, this didn't mean that we couldn't be friends, but it's not like her way would have helped me when I had a heart attack.

Sure did help with my back pain, though. (And yes, I'm aware that's anecdotal and not actual scientific evidence that it works, but that's not the reason I'm relating this.)

Point is, this article has issues, and if you want to debunk it yourself, go for it. Me, I'm going to have another beer.

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