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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Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

July 12, 2023 at 10:24am

#1052515

Generational Drama

As an Aquarius, I think astrology is nonsense.

Eight out of 10 millennials know demographics are horseshit
Millennials are no more similar to each other than they are to Gen X or Gen Z, so it’s time to leave this lazy approach to segmentation behind.

Yes, this article caters to my confirmation bias. I'm going to give it a look anyway. I've ranted about this sort of thing before, but it's been a while, and this is a new article.

The Pew Research Center is one of the most influential and important places for social science on the planet.

They do seem to garner respect, but I'm sure someone can come up with an example of why they can't be trusted.

But one thing it won’t be doing any more is using generational terms like ‘millennials’ or ‘Gen Z’ to describe different cohorts of society.

Which won't stop the rest of the world from doing so.

“The question isn’t whether young adults today are different from middle-aged or older adults today,” Parker notes. “The question is whether young adults today are different from young adults at some specific point in the past.”

I'm... well, I'm not sure that's entirely true. It's likely a quote out of context, but it seems to me that you want to know, for example, who buys Cheerios, parties with the Druids, or votes Libertarian, broken down by age. You'd also want to see how these things evolve over time, of course.

It's mostly the arbitrary cutoff dates between generations that I've objected to.

Another problem for Pew is that the United States has seen significant population change during recent decades. When studies do pick up statistically different attitudes and behaviours across generational cohorts, the likely explanation is as much down to its different racial and ethnic constitution rather than any fundamental age related issue.

The "likely" explanation? If only there were a place that could do polls and run them through statistical analysis to verify this claim.

This part, though, I can accept:

Finally, Pew is uncomfortable with the gigantic swathes of society that are suddenly lumped together under a single arbitrary identifier when names like millennials are used. “A typical generation spans 15 to 18 years,” Parker explains in her article. “As many critics of generational research point out, there is great diversity of thought, experience and behaviour within generations.”

It's one thing to claim, for example, that Millennials as a group tend to buy organic produce (I don't know if this is true or not, but bear with me). You slice up groups by age and see that, of all the arbitrary age cohorts, Millennials buy more organic produce than other generations. One problem comes in when you get people who don't understand statistics and assume that, upon meeting a Millennial, that individual therefore buys organic produce.

Another problem is that if you're a Millennial in that scenario and you see "Millennials buy organic produce!" then you may be tempted to do so yourself to fit in. This is like when you find out you're a Taurus, and what Tauri supposedly act like, and you suddenly start playing up the stubborn aspects of your personality.

Most of our industry constantly talks about Gen Z, Gen X and their current obsession – millennials – as if these segments are well supported by data and instantly ready for target marketing. But so much of this stuff lacks any legitimate foundation. There are three enormous issues with using demographics to segment markets.

The rest of the article deals with these "three enormous issues," and while it's targeted to marketers (now there's an example of recursion if there ever was one), the arguments are worth looking at.

When I was young, "laziness" wasn't attributed to youth, as it has been throughout pretty much every other period of human history, but to being part of "Generation X." Well, Gen-X is in their 40s to 50s now, and it's Gen-Z who's called "lazy" and "slackers," because, well, they're young and it's the entire purpose of older people to call younger people lazy, and lie about how much more hard-working and conscientious we were.

I can only reply with the rallying cry of my own supposed cohort, Gen-X:

"Meh. Whatever."

2 Like • Comment • View 3 comments

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