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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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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