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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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Congratulations on winning an honorable mention for Best Blog at the 2018 Quill Awards for [Link To Item #1196512] . *^*Smile*^* This award was sponsored by the blogging consortium including [Link To Item #30dbc] , [Link To Item #blogcity] , [Link To Item #bcof] and [Link To Item #1953629] . For more details, see [Link To Item #quills] .](https://images.Writing.Com/imgs/writing.com/writers/badges/type-Blogging-2180.gif) ![Merit Badge in Highly Recommended
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| More science. Fossil Discoveries Challenge Ideas About Earth’s Start  A series of fossil finds suggests that life on Earth started earlier than anyone thought, calling into question a widely held theory of the solar system’s beginnings. There are some compelling hypotheses about how life got its start. There are also not so compelling ones, like "it came from somewhere else in space." That one just kicks the can down the road and doesn't explain how life first arose out of non-life; it just postulates that it didn't begin on this planet. Regardless, the question of "when" might shed some light on "how." In the arid, sun-soaked northwest corner of Australia, along the Tropic of Capricorn, the oldest face of Earth is exposed to the sky. Drive through the northern outback for a while, south of Port Hedland on the coast, and you will come upon hills softened by time. They are part of a region called the Pilbara Craton, which formed about 3.5 billion years ago, when Earth was in its youth. That's if you can avoid the drop bears and everything else that's trying to kill you in Australia. Really, it's a wonder anyone can live there at all. Maybe the reputation is exaggerated and promoted by the locals to keep tourons away. In the past year, separate teams of researchers have dug up, pulverized and laser-blasted pieces of rock that may contain life dating to 3.7, 3.95 and maybe even 4.28 billion years ago. Those are all a Really Damn Long Time Ago. For reference, the Sun is probably about 5 billion years old, a little more than 1/3 the age of the Universe itself. Also for reference, human civilization is maybe 10,000 years old - not even as big as the error bars in whatever they used to date those (possible) fossils. Taken together, the latest evidence from the ancient Earth and from the moon is painting a picture of a very different Hadean Earth: a stoutly solid, temperate, meteorite-clear and watery world, an Eden from the very beginning. When you consider that all early life, up until (they think) about half a billion years ago, was aquatic, the water could have provided some protection from asteroidal catastrophes. The article includes a timeline for early Earth/Moon formation, with graphics that for some reason amuse me. Anyway, the rest of the story lays out the evidence and discusses some of the debate surrounding it. No need to reproduce most of it here. “Are there other explanations than life? Yeah, there are,” Bell said. “But this is what I would consider the most secure evidence for some sort of fossil or biogenic structure.” Thing is, just as it's important to be really, really sure when we find evidence of extraterrestrial life (by which I mean microbes, not Vulcans), it's also important to be skeptical of this sort of finding. Likely there will need to be additional evidence. Far from fussy and delicate, life may have taken hold in the worst conditions imaginable. I don't know about "worst." Venus is way worse. (Before anyone starts quoting the bit about finding signs of life in Venus' atmosphere, that finding was conclusively discredited.) But worse than we imagined, sure. We already know that simple life can withstand conditions that more complex life-forms cannot, so it's at least believable. There's also a video worth watching in the article, if you're interested in this sort of thing. With bonus explosion graphics. (You just have to suspend disbelief with all the sound effects about things going boom and thunk and whoosh in the near-vacuum of space.) The other reason this sort of thing is interesting is the implication for finding (simple) life elsewhere -- something the article doesn't get into until the very end: If there was no mass sterilization at 3.9 billion years ago, or if a few massive asteroid strikes confined the destruction to a single hemisphere, then Earth’s oldest ancestors may have been here from the haziest days of the planet’s own birth. And that, in turn, makes the notion of life elsewhere in the cosmos seem less implausible. Life might be able to withstand horrendous conditions much more readily than we thought. It might not need much time at all to take hold. And again, as a caution, I wouldn't make the leap to the kind of sophisticated life it would take to, say, make radio stations or flying saucers. Nothing in evolution requires that result. But it makes ideas like finding microbes or their equivalent on, say, Mars, Europa, or Titan that much more likely. Which would be cool. |
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