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.

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March 11, 2020 at 12:03am

#977747

If You Don't Mindful

I've railed against this "mindfulness" crap in here before. Sometimes I know why I don't like something. Other times, it's a vague feeling and it takes another writer to put into words what my issues are. This is a case of the latter.

https://www.theguardian.com/lifeandstyle/2019/jun/14/the-mindfulness-conspiracy-...

The mindfulness conspiracy
It is sold as a force that can help us cope with the ravages of capitalism, but with its inward focus, mindful meditation may be the enemy of activism.

Prophesying that its hybrid of science and meditative discipline “has the potential to ignite a universal or global renaissance”, the inventor of Mindfulness-Based Stress Reduction (MBSR), Jon Kabat-Zinn, has bigger ambitions than conquering stress.

"Hybrid of science and meditative discipline?" Where's the "science?" Is it studies that show that meditation has beneficial effects? Yeah, we've known that for a long time. I'm not doubting that there's some benefit.

So, what exactly is this magic panacea?

Magic = not science. Pretty much by definition.

The accompanying feature described a signature scene from the standardised course teaching MBSR: eating a raisin very slowly.

This shit again. Be the raisin, Danny.

But anything that offers success in our unjust society without trying to change it is not revolutionary – it just helps people cope.

And here we get to why I have a knee-jerk reaction to "mindfulness."

Instead of encouraging radical action, mindfulness says the causes of suffering are disproportionately inside us, not in the political and economic frameworks that shape how we live.

The "suffering" bit betrays mindfulness's Buddhist roots.

Although derived from Buddhism, it’s been stripped of the teachings on ethics that accompanied it, as well as the liberating aim of dissolving attachment to a false sense of self while enacting compassion for all other beings.

Just as science without ethics is dangerous, religion without ethics is bleak and self-serving. I don't know enough about Buddhist ethical teachings to comment on the differences, myself, so I can't really speak to the truth of this quote.

Instead of setting practitioners free, it helps them adjust to the very conditions that caused their problems. A truly revolutionary movement would seek to overturn this dysfunctional system, but mindfulness only serves to reinforce its destructive logic. The neoliberal order has imposed itself by stealth in the past few decades, widening inequality in pursuit of corporate wealth. People are expected to adapt to what this model demands of them. Stress has been pathologised and privatised, and the burden of managing it outsourced to individuals. Hence the pedlars of mindfulness step in to save the day.

The way I see it, one of the aims of religion since there has been religion has been to preserve the social order by teaching people to accept their place in it, even if that place is unjust. "You are a slave because that's just the way things are. Pray to this god to help you understand why this has to be so, and to make peace with it." Periodically, of course, a new religion crops up that is revolutionary -- and here, by "religion," I'm including systems such as Marxism. The problem with all of these revolutions, of course, is that once they've gone on long enough, they become the establishment, and the establishment proceeds to enforce its own social order.

Christianity, for instance, was revolutionary when it began. Then it took over the Western world and started to enforce conformity, urging, for example, peasants to accept their place at the bottom of the social food chain.

The fundamental message of the mindfulness movement is that the underlying cause of dissatisfaction and distress is in our heads.

Once again, we have the same old refrain as with weight issues or financial distress: it's really your fault, and you're the one who needs to change your mindset.

Rather than discussing how attention is monetised and manipulated by corporations such as Google, Facebook, Twitter and Apple, they locate the crisis in our minds. It is not the nature of the capitalist system that is inherently problematic; rather, it is the failure of individuals to be mindful and resilient in a precarious and uncertain economy. Then they sell us solutions that make us contented, mindful capitalists.

Capitalism is another "religion" as I use the term above.

There's a lot more to the article I'm quoting here; it's fairly long, and I think makes some good points. Whether you agree or not, it's worth the read. Whether it's worth buying the book it's promoting, well, I'm going to remain agnostic about that; I know I'm not buying it any more than I'm buying a course in mindfulness.

Bottom line as far as I'm concerned: sometimes it's best to reject the status quo and be a revolutionary. But be mindful that in doing so, all you're really doing is establishing a new social order.

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