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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Brandiwyn🎶

a day ago
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').

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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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

September 2, 2023 at 9:48am

#1055015

Faded Genes

Here's another volley in the age-old debate of nature vs. nurture.

Ancestry tests are “genetic astrology.” We must re-learn everything we know about DNA and cells
From the laying out of the body plan to the organization and functioning of our nervous system, cells rule gene expression and make us who and what we are.

People want things simple. Even scientists generally want to go with the most parsimonious theory possible. Biology, however, ain't simple. We're products of genetics and environment, both; the only question is in what proportions?

Yes, this article (from Big Think) is a book promotion; I've already stated multiple times how I feel about those.

We humans feel a great need to belong, to know our origins, and because we’ve been fixated on genes over the past hundred years, we’ve been using the language of genetics to write our stories.

I guess I'm not human then. I have almost no idea who my biological parents were, or what my genetic ancestry is. One family was drama enough; I don't need genetic testing (which I don't trust, anyway) or some epic quest to find my birth parents.

There’s immense allure to imagining connections to such remote peoples, places, and times. But as the organization Sense About Science says of such claims, “They are little more than genetic astrology.”

And that's even assuming that the DNA tests always produce accurate results, which I'm not convinced of. I'm also just paranoid enough to think the testing labs might have been started by law enforcement; the ancestry results don't have to be accurate if all you're really doing is building a database.

Geneticist Adam Rutherford has also rightly pointed out that if you go back far enough — and “far enough” isn’t all that long ago in human history — we’re all related to each other.

Go back even farther, and you're related to your dog. Farther even than that, and you're related to that kale you ate last night.

The article is amazingly light on detail and heavy on biology jargon, but it's short.

Our genes aren’t our identity, no matter what the DNA testing companies say in their advertising campaigns.

No, I agree; they're not. They are, however, part of it.

Indeed, these companies use the DNA from people’s tests to research how diseases caused by a single genetic mutation might be treated.

So much for my pessimistic paranoid fantasy. Or maybe They just want us to believe They're researching genetic diseases.

In the end, though, on a personal level, I have to look askance at anything that emphasizes our differences rather than our similarities.

4 Like • Comment • View 4 comments

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