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 |    Not for the faint of art. |
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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. ![Merit Badge in Quill Award
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| Full moon tonight. Also a lunar eclipse, but one that's too late to stay up for and definitely too early to wake up for. So instead, we get to read about the Incredible Shrinking Brain. Given the state of the world right now, I would think "thirty years ago" rather than "three thousand years ago." Did the 12th century B.C.E.—a time when humans were forging great empires and developing new forms of written text—coincide with an evolutionary reduction in brain size? Well, it's not in the headline; it's the lede. The answer is still "no." Think again, says a UNLV-led team of researchers who refute a hypothesis that's growing increasingly popular among the science community. One thing I should note: brain size isn't strongly correlated with intelligence. If it were, elephants would be ruling the planet. While I'm convinced they're intelligent, it's not like they've invented the internet, sliced bread, or beer. Last year, a group of scientists made headlines when they concluded that the human brain shrank during the transition to modern urban societies about 3,000 years ago because, they said, our ancestors' ability to store information externally in social groups decreased our need to maintain large brains. That's... not really how evolution works, anyway. Their hypothesis, which explored decades-old ideas on the evolutionary reduction of modern human brain size, was based on a comparison to evolutionary patterns seen in ant colonies. "What is this, a study for ants?" That by itself would raise a bunch of red flags for me. "We re-examined the dataset from DeSilva et al. and found that human brain size has not changed in 30,000 years, and probably not in 300,000 years," Villmoare said. "In fact, based on this dataset, we can identify no reduction in brain size in modern humans over any time-period since the origins of our species." The date for the appearance of what's called "anatomically modern" humans, from what I've read, is about 100,000 years ago. The UNLV team says the rise of agriculture and complex societies occurred at different times around the globe—meaning there should be variation in timing of skull changes seen in different populations. However, DeSilva's dataset sampled only 23 crania from the timeframe critical to the brain shrinkage hypothesis and lumped together specimens from locations including England, China, Mali, and Algeria. The only information we have on human brains from that long ago is cranial capacity, which puts an upper limit on brain size. But, again, the relationship between brain size and intelligence isn't absolute. I'm linking this article because, while I didn't see reports on the original study (the one that claimed brain size reduction 3,000 years ago), apparently, lots of people did. And when a study like that comes out, it's natural for people to want to share it, especially if it fits in with their worldview. In this case, it would be the (demonstrably false) worldview that we're stupid and never should have invented agriculture or civilization. Or possibly that we shouldn't be relying on what I like to call "auxiliary memory" (my smartphone) or we'll become even stupider. (Incidentally, there's a picture making the rounds purporting to show a misshapen human with a cell-phone-holding claw and a crooked neck and calling it "the future evolution of humankind;" that's also utter bullshit.) It's like when a nutrition scientist says "dark chocolate is good for you," and people crow about it while stuffing their faces with Godiva, and then never hear that the study was suspect because it was funded by Willy Wonka. So I'm here setting the record straight to the best of my ability. Now you can be That Person at the party who, upon hearing someone confidently proclaim that our ancestors' brains shrank 3,000 years ago, can go, "Well, ackshually..." |
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