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!

about 14 hours 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

about 15 hours 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.

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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.

April 11, 2022 at 12:02am

#1030515

Asking Persimmon

I'd never heard of this before reading the article, so here it is:

For Enslaved Cooks, Persimmon Beer Combined Ingenuity and Joy
A conversation with Michael Twitty about the powerful history behind a centuries-old beverage.

When I was a kid, we had a persimmon tree. Apparently, the trick to persimmons is you have to wait for first frost (usually around October 15 in my area) to pick them, because they only ripen with extreme bitter cold (I consider anything below 45F "extreme bitter cold"). Never did appreciate the taste of them, but all kids have weirdnesses about food.

Michael Twitty, the James Beard Award–winning culinary historian, estimates he has brewed his grandmother’s persimmon beer about a dozen times. Made by fermenting Diospyros virginiana, the diminutive North American persimmon, with sugar, honey, and yeast, persimmon beer is more akin to fruit wine or liqueur than anything brewed with barley, malt, and hops.

In general, beer is fermented grain, while wine is fermented fruit. However, exceptions abound. Cider, usually from apples or pears, is its own category. Japanese sake is most often known as "rice wine" in English, probably because its alcohol content is higher than most beer and it's generally not bubbly. For example. So if someone wants to call this "persimmon beer," well, they don't need my permission.

For generations of Black families across the American South in the 18th and 19th centuries, persimmon beer played an integral role in daily life. In his quest to uncover more about the foodways of his ancestors, Twitty learned that American persimmon trees are a genetic echo of fruit trees in West Africa, and that both the plant and the beverage provide a thread across the history and geography of the African diaspora.

Now, that is interesting. Of course, humans also all have genetic roots in Africa, just some more recent than others.

Persimmon beer was really important for the people working in the fields. That was a typical thing to be brought to them in a gourd or a bottle or a crock. Remember, they didn’t have Gatorade.

I can't imagine Gatorade would have been better. Or permitted.

Some of these foraged foods that are the grandeur of younger white folks that are into this now, quite frankly, this is not white people food. One of the best quotes I’ve ever seen in reference to pawpaws was “The food fit for Negros and Indians.”

We had pawpaw trees too, growing wild.

The article delves into some cultural issues that I think are relevant. It does not, however, provide an actual method for preparing persimmon beer -- but the mere fact of its existence should be enough, and probably it's in the book the guy is trying to promote.

4 Like • Comment • View 2 comments

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