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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.
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As an Aquarius, I think astrology is nonsense.
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." |
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