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!

a day 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

a day 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 9, 2019 at 12:06am

#963948

Mind over Matter

https://aeon.co/essays/mindfulness-is-loaded-with-troubling-metaphysical-assumpt...

The problem of mindfulness
Mindfulness promotes itself as value-neutral but it is loaded with (troubling) assumptions about the self and the cosmos

Hey, look, an article that critiques this mindless "mindfulness" bullshit.

Three years ago, when I was studying for a Masters in Philosophy...

Normally, that's my cue to Stop Reading There, but hey - can't pass up a chance for Confirmation Bias.

We gathered in strangers’ houses to meditate at odd hours, and avidly discussed our meditative experiences. It was a strange time.

Okay, I'll say it: meditation annoys me. Not other peoples' meditation - if it works for you, great - but my own attempts at it. There is no difference, to me, between meditation and going to sleep.

A popular activity (though I’ve never tried it myself) even involves eating a raisin mindfully, where you carefully observe the sensory experience from start to finish, including changes in texture and the different tastes and smells.

Yeah, whatever.

Something about the mindfulness practice I’d cultivated, and the way it encouraged me to engage with my emotions, made me feel increasingly estranged from myself and my life.

You mean... it's just more snake oil? Tell me more.

Instead of engaging in deliberation about oneself, what the arts of mindfulness have in common is a certain mode of attending to present events – often described as a ‘nonjudgmental awareness of the present moment’.

There is no such thing as the present moment. There is only the immediate past. By the time you become aware of something, even within your own body, that something is in the past.

In his book Wherever You Go (1994), Jon Kabat-Zinn, a founding father of the contemporary mindfulness movement, claims that mindfulness ‘will not conflict with any beliefs … – religious or for that matter scientific – nor is it trying to sell you anything, especially not a belief system or ideology’.

"I'm not trying to sell you anything. Buy this book!"

As well as relieving stress, Kabat-Zinn and his followers claim that mindfulness practices can help with alleviating physical pain, treat mental illness, boost productivity and creativity, and help us understand our ‘true’ selves.

And make your dick bigger, and help your hair grow back, and...

Buddhist scholars have accused the contemporary mindfulness movement of everything from misrepresenting Buddhism to cultural appropriation.

Don't fucking get me started on "cultural appropriation." But if someone from a certain culture accuses you of appropriating something from their culture, maybe listen? We're not talking about sushi or kimonos here; we're talking about something that messes with your mind.

Kabat-Zinn has muddied the waters further by claiming that mindfulness demonstrates the truth of key Buddhist doctrines.

There have been books purporting that certain aspects of quantum mechanics also demonstrate the truth of key Buddhist doctrines. Those books are, without exception, bovine excrement. So I'm not going to believe that there is a "truth" in the scientific sense to any religious teaching. Not without hard evidence, at least.

Critics such as the author David Forbes and the management professor Ronald Purser argue that, as mindfulness has moved from therapy to the mainstream, commodification and marketing have produced watered-down, corrupted versions – available via apps such as Headspace and Calm, and taught as courses in schools, universities and offices.

Meanwhile, Drunk Yoga is still a thing. (Yes, I know that's from a different culture and religion. My point stands.)

Contrary to Kabat-Zinn’s loftier claims to universalism, mindfulness is in fact ‘metaphysically loaded’: it relies on its practitioners signing up to positions they might not readily accept.

Yeah, like proclamations from philosophers of old.

One technique in Buddhism, for example, involves examining thoughts, feelings and physical sensations, and noting that they are impermanent, both individually and collectively.

I take the exact opposite stance to Buddhist thought in this: I note that everything in the Universe is impermanent, and thus, the only "reality" is one of impermanence. Anything you think is eternal? That's the illusion. This worldview is controversial, I know, but without it, you start thinking that reality is fantasy and fantasy is reality, and that way lies madness.

The problem is the current tendency to present mindfulness as a wholesale remedy, a panacea for all manner of modern ills.

Like I said: snake oil.

The questions of consciousness, of self, are tricky ones. It's possible that none of us can comprehend our own consciousness because we're living it. And the desire for easy answers is a very human one; we want to answer these questions definitively and finally - without complication.

We can't get what we want, and that's annoying. I do know one thing, though: if the matter of consciousness is ever resolved, it will be by science, not religion. Religion and spirituality provide guesswork, no matter how intricate their frames or how firm their foundations seem. Science doesn't provide final answers, either, but we can get asymptotically close.

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