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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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October 9, 2019 at 12:15am
October 9, 2019 at 12:15am
#967503
https://whyevolutionistrue.wordpress.com/2019/05/17/railing-about-rails-again-no...

It is a truth universally acknowledged that the two most prestigious science journals in the world are Science, published in the U.S., and Nature, published in England.

Anyone who trolls Jane Austen fans is okay in my book.

But Science slipped up this time when reporting on the independent evolution of flightlessness on the island of Aldabra twice: in an ancient white-throated rail that colonized the island and went extinct when sea levels rose, and then in more modern times (i.e., several hundred thousand years ago) when birds from the same flying lineage colonized Aldabra again and once again evolved flightlessness.

This post is fairly old in internet terms; it's been languishing in my blog fodder cache for a few months. But it's important to my crusade to call out crappy science reporting. As this has long ago passed beyond the veil of our collective memory, I'll summarize the situation (the post I linked above goes more in-depth about it): Lots of places reported that "the same species" had evolved twice in the same place, with a new population replacing the old. This is a misrepresentation of what actually happened.

Further, the species concept used by nearly all evolutionary biologists deems two individuals members of the same species if, where they meet in nature, they can mate and produce fertile offspring. It’s a concept based on reproductive compatibility and incompatibility.

I expect people to get things wrong about evolution. Not all of us are, like the author I'm linking here, evolutionary biologists. But that's why it's important for science journals to get things right. When they don't, the misinformation sticks in readers' minds as True Fact, which is difficult if not impossible to rectify (see also: misattribution of "blue moon" as the second full moon in a Gregorian calendar month).

And when it comes to evolution, there's already enough misinformation and outright lies out there.

The journal in question ended up printing a correction, but we've all seen what happens with corrections - they get lost in the shuffle and forgotten. See also: Andrew Wakefield and the falsified "link" between vaccinations and autism.

So I'm just throwing this out there in case the whole "speciation" thing stuck in someone's memory.

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