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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 9 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 11 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.

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.

February 19, 2022 at 7:10am

#1027019

Being Catty

And now for today's example of why one should read science reporting critically.

No, your cat isn’t a psychopath
A new study takes a biased look at cats

The article references some study that had been making the rounds late last year, prompting smug responses from dog people and indifference from cats.

But the headlines keep coming: “Is Your Cat a Psychopath? Probably, Researchers Say,” “Is Your Cat an Actual Psychopath? Take This Test and Find Out,” and so on.

As usual, the answer to a headline question is "No." But people fell for this crap, so I'm sharing the article that helps to explain exactly why it's crap.

But sometimes a study is actually misleading or potentially even harmful, especially when it perpetuates faulty ideas about cats.

There has been a thing circulating around the internet for a while to the effect of "your cat wants to murder you." Some people seem to think it's funny. Having known assholes who go out of their way to kill cats because they hate them, though, this sort of thing can only add to their desire to eradicate cats from existence. Also, your cat doesn't want to murder you. Unless you forget to feed it, of course.

Rather than explore typical cat behavior in search of things that might indicate a maladaptive response or problematic behaviors, the researchers start with a human-biased concept: looking for psychopathy in cats.

Which is not to say there aren't feral cats. They're much closer to being wild animals than dogs are, so yeah, if they're not socialized, they use their natural defenses. This is called "being a wild animal" and no one expects, say, bears not to do it.

The authors propose that there has been a lack of research on feline psychopathy because there’s no available questionnaire for exploring these traits in cats. (I might instead argue that there’s no point in studying something that doesn’t really exist). We already have an excellent, validated tool for assessing cat behaviors (including ones that might be considered problematic) in the Fe-BARQ, a 100-item survey that started with a full range of feline behaviors (not just “negative” traits).

Fe-BARQ? Look, if you're going to force an acronym for something related to cats, make it MEOW, not BARQ. Come on, a three-year old could tell you that.

Anyway, the article goes on to provide examples of clear bias in the methodology used in the study, and I'm not pasting the whole thing here.

Words matter. Labeling a cat as a psychopath instead of describing their behavior does not help cats, humans, or the cat-human relationship. It does not advance our scientific understanding of cat behavior or personality.

Cats are cats. People are people. Of course cats exhibit traits that would be undesirable in a fellow human. If my housemate came up to me twice a day and said "FEED ME! FEED ME NOW!" I'd find a new housemate. For that matter, if your friend licked your face, sniffed your ass, and made you pick up their shit, they wouldn't be your friend very long (well... depending...) but you put up with that crap from your dog because it's a dog and that's what dogs do.

So as much as the original reporting on this study tickled the confirmation bias of ailurophobes, it's bad science and bad reporting on bad science. Fake mews.

I tried. I really tried to go through this whole entry without making a cat pun. I failed.

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