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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QPdoll

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With all that walking, I hope you stayed hydrated.

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WakeUpAndLive️~Happiness

a day ago
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a day ago
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Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

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Aiva Raine

a day ago
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

Sum1's In Kalispell Montana

Sep 20, 2024 at 9:08am
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

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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.

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