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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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| Here we go with the alien theories again. No, I don't mean of the "abducted by" sort; that's a whole other issue. I mean the semi-scientific "where are they" variety. https://www.popsci.com/where-are-aliens-new-model If the galaxy is billions of years old and it took humans just a few decades to visit the moon and launch space stations, why hasn’t single alien spaceship landed on the White House lawn? And already they're asking the wrong question. I'm not saying there's not some interesting ideas in that article - else I wouldn't have bothered to read it, let alone link it here. And I definitely think the search for extraterrestrial life is of the utmost importance, as much for what it doesn't tell us as for what it does. So I'm not saying that we shouldn't be doing these things. I can also accept that the people who study these things for a living know more about this sort of thing than I do. But. I'll call our attention to this bit from the article: Second, no single habitat can endure forever, as humanity is rapidly realizing. Spreading to other stars can extend a civilization’s overall lifespan, but from the moment a new settlement is born its days are numbered. It may last for hundreds of thousands or even millions of years, but at some point, a catastrophe almost certainly will take it out. People who think we may be alone in the galaxy - and here, I'm going to limit the discussion to this galaxy alone, as others are further away than any of us can properly comprehend - have been accused of hubris. What, the argument goes, makes us so special? Here's the rub, though - I contend that the idea that other life-forms will necessarily evolve a species that is technologically capable is also full of hubris. So here are some points to consider. I'll try to be brief, because this is a blog post and not a book. Best estimates put the age of the universe at about 14 billion years. Age of the Sun, 4.6 billion years. Age of Earth, a bit less than that. Beginning of life, about 4 billion years ago. Modern humans, dunno, call it one million years - give or take. Exact time doesn't matter. What we call civilization, maybe 10-12 thousand years. Length of time we've been technologically capable of leaving the atmosphere: 60 years. There might be other types of chemical reactions that can produce life, but as far as we know, there are none more efficient than those involving water and carbon molecules. Water is unique for several reasons that I won't go into right now, but there's very good reason to believe that the easiest - and, therefore, fastest - way to cook life is to start with good old H2O. And while silicon might replace carbon in life processes, the sheer number of possible combinations of carbon with other elements makes that element by far the most likely (again, therefore, fastest) choice for developing life. Life as we know it also requires higher-weight elements such as nitrogen, iron and calcium. Again, there may be replacement options, but the point is that their atomic numbers are higher. Why does this matter? Because the only way to get them in sufficient quantities is to fuse them from lighter elements. Briefly, the universe started out as mostly hydrogen; this hydrogen condensed into stars; these stars fused it into (mostly) helium. Our solar system, including the sun, planets, and us, condensed out of cosmic dust that had been scattered by massive stellar explosions that created elements higher on the periodic table. Until you have a few supernovae, you simply don't have enough heavier elements to produce life as we know it - not to mention enough to fuel technological advancement, about which I'll have more to say later. Point is, this process takes time. So - with this knowledge, just how fast can life begin? Well, given that there was only about half a billion years between the formation of Earth (which was then molten slag) and the first known life, probably pretty quickly in cosmic terms, once a suitable planet is formed. But the formation of a suitable planet - one with the heavier elements available - was extraordinarily unlikely in the early universe, and only became possible after a few supernovae seeded the galaxy with oxygen, nitrogen, etc. But wait, there's more. Remember I pointed out that life on Earth probably got its start about 4 billion years ago. (People have argued that it might have been seeded from other planets, but to me, that just kicks the can down the road and, if true, would only support my upcoming point.) Consequently, it was a long time before a species capable of technology appeared. If the first humans evolved one million years ago, that's comfortably within the error bars of the 4 bya estimate for the beginning of life. So, for four billion years, life on Earth chugged right along, evolving to fit its environment, adapting to new environments, consuming itself, without the benefit or detriment of humans complicating the works. And here's the thing a lot of people miss about evolution: thanks to years of bad science fiction (and even some good science fiction), combined with some good old-fashioned narcissism, we tend to think of some life-forms as "more evolved" than others. But every single species on this planet has been evolving for the same amount of time, and the evolution of each of them was a matter of survival and, ultimately, adaptation. A snake is not "less evolved" because it has no limbs; it gets along just fine. A chicken is not "less evolved" because it has all the cognition of a plant; it, too, survives. And a human is not "more evolved" because we can blog; we, too, adapted to environmental conditions - it just so happens that those qualities that we call "intelligence" turn out to be fairly useful in hunting, and avoiding becoming, prey. Now, look, I'm not one of those misanthropes who insist that the world would be better off without us. But it would go on, and other species would keep on feeding, fighting, and fucking. Point is, there is absolutely no known law or principle of evolution that requires the development of those qualities that lead to space travel. As long as a species can thrive in a given habitat, there's simply no need, from an evolutionary perspective, to devote energy to bigger brains or opposable thumbs. And if it can't survive, as millions or billions of species have not, then it's far more likely to simply die out. And I can make the usual misanthropic arguments about how we're probably going to wipe each other out before we seriously get going into space, but that's irrelevant - we can't project that on other, hypothetical, technological species from other worlds. And, going back to the paragraph I quoted above, a planetary catastrophe (meteor strike, whatever) could have stopped the evolutionary line that led to humanity in the first place. In other words, it's possible that we got lucky. This isn't as unlikely as it seems, since we're here; after all, the chance of winning a lottery might be 1 in a trillion, but once you've won it, the chance of having won it is 1 in 1. There are other arguments to make - for instance, that without the event that led to the formation of the Moon, then most of those heavier elements I mentioned earlier could have simply sunk to the interior of the early, molten Earth, like rocks sinking in a pond - but I think I've gone far enough to make my main point, which is that, even given the 200 billion or so stars in our galaxy, it's entirely possible that we're on the only planet with spacecraft. I mean, life is probably prevalent. We don't know yet. But I think we can safely rule out a Doctor Who or Star Trek galaxy. It's bleak to think about, I suppose, but I guess we might just have to make our own destiny. |
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Talk about retaining water... 
