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 17 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 18 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.

March 6, 2020 at 12:03am

#977269

Psychology Today

Psychology has come a long way since Freud and Jung. But it's still not what I'd call an exact science. This article takes a global point of view on the subject.

https://theconversation.com/how-knowledge-about-different-cultures-is-shaking-th...

How knowledge about different cultures is shaking the foundations of psychology

Granted I'm no expert on psychology (my experience being limited to a biological psychology class in college and a few sessions of getting my head shrunk), but I'd say the "foundations" were on fairly shaky ground to begin with.

The academic discipline of psychology was developed largely in North America and Europe. Some would argue it’s been remarkably successful in understanding what drives human behaviour and mental processes, which have long been thought to be universal. But in recent decades some researchers have started questioning this approach, arguing that many psychological phenomena are shaped by the culture we live in.

You'd think they'd have taken that into account...

Psychologists have long disproportionately relied on undergraduate students to carry out their studies, simply because they are readily available to researchers at universities.

Science 101: choose your samples to be as free of selection bias as possible. Fail.

More dramatically still, more than 90% of participants in psychological studies come from countries that are Western, Educated, Industrialised, Rich, and Democratic (W.E.I.R.D).

I wonder what a psychologist would make of how much I snickered at this.

Consider which two of these objects go together: a panda, a monkey and a banana. Respondents from Western countries routinely select the monkey and the panda, because both objects are animals.

My first thought was "monkey, banana." Because monkeys eat bananas. Like, kids know this. But apparently that makes me an outlier. Well, I've always known I was WEIRD.

This is a holistic thinking style, in which object and context are perceived to be interrelated.

I really wish they'd either stop using the word "holistic," or at least define it more precisely. To me, it's encrusted with connotations of new-age shenanigans. A quick Google lookup provided the definition: "characterized by comprehension of the parts of something as intimately interconnected and explicable only by reference to the whole."

Individuals in the western world are indeed more likely to view themselves as free, autonomous and unique individuals, possessing a set of fixed characteristics. But in many other parts of the world, people describe themselves primarily as a part of different social relationships and strongly connected with others.

Seems like a great big thing to miss, psychology.

Another domain that was originally dominated by studies on W.E.I.R.D. samples is mental health. However, culture can affect our understanding of mental health in different ways. Because of the existence of cultural differences in behaviour, the framework – based on detecting deviant or non-normative behaviours – isn’t complete. What may be seen as normal in one culture (modesty) could be seen as deviating from the norm in another (social phobia).

Again, I think anthropologists have known about this sort of thing for a long time. Don't they ever speak with shrinks? I guess they're all too well-adjusted.

In addition, a number of culture-specific syndromes have been identified. Koro sufferers (mostly in Asia), are men which have the mistaken belief that their genitalia are retracting and will disappear. Hikikomori (mostly Japan) is a condition that describes reclusive individuals who withdraw from social life.

Can I call myself hikikomori, or would that be cultural appropriation? Would it help if I also ate sushi (ordered for delivery) with chopsticks? Or does that actually make it worse?

The question is to what extent it will inform psychology as a discipline going forward – some see it as an extra dimension of it while others view it as an integral and central part of theory making.

And let me guess: these differences in perception are correlated to culture? No? Not going to tell me? Fine.

3 Like • Comment • View 2 comments

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