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 2 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 4 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.

August 22, 2022 at 12:01am

#1036797

Weight a Minute...

I don't have a lot to say about today's article; I just think it's a good, fairly simple, example of how science gets scienced.

Which Weighs More, a Pound of Stone or a Pound of Styrofoam?
It’s not a trick question: your brain answers differently, depending on whether the materials are part of the same object or not

Ah, but it is kind of a trick question, isn't it? There's objective weight, which can be measured by a scale, and subjective weight, which is what your muscles anticipate and feel. Consider two packages of the same weight, one large, one small (maybe the large one contains nothing but packing pillows). The small one will be easier to pick up and carry if only because of the bulk involved.

That's not what this article is about, though.

For more than a century, scientists thought they knew the answer to a curious question: why does 10 pounds of a low-density substance such as Styrofoam feel heavier than 10 pounds of stone? It isn’t heavier, of course, but repeated experiments have shown that it feels that way.

Science tip #1: Just because you think you know the answer, doesn't mean you do. Always test.

Now psychologists say their initial explanation may have been incomplete, and the new explanation could have far-reaching consequences, including for the way Netflix designs the algorithms that recommend movies to its customers.

Science tip #2: Your experiment doesn't have to have practical, everyday applications. But if you can come up with one, it'll be easier to communicate it to the teeming hordes.

The article goes on to describe the experiment and their results, which, as the headline hints, are that people are ass at guessing weights. Or something.

Knowing how the brain estimates weight isn’t just an interesting experiment—it can actually help scientists develop smarter technologies that we use every day. Now that we know more about how context changes the brain’s decisions, programmers might be able to update technologies such as Netflix to imitate the brain more accurately and provide more fine-tuned recommendations for users.

Article is from 2019. Netflix is still trying to recommend shows and movies to me that there's no way in hell I'd watch.

Anyway, like I said, not much else to say, and you'll have to go to the article to see what the actual experiment was, because it wouldn't be easy to take any of it out of context. And I'm all about easy. Give me the smaller package.

4 Like • Comment • View 1 comment

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