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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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| Today, I'm going to talk about aliens again. If these topics seem random, that's because they are, in part. https://aeon.co/ideas/proof-of-life-how-would-we-recognise-an-alien-if-we-saw-on... Proof of life: how would we recognise an alien if we saw one? I feel compelled to point out, again, that we shouldn't conflate "alien" and "intelligent alien." To recap: I use "intelligent" to refer to a species capable of building spacecraft; by this definition, humans are intelligent. I do this to forestall jokes from smartasses like me. I make the "alien" distinction because, in the popular mind, thanks to shows like Star Trek (which, again, I love), we have this image of a hugely diverse galaxy, with different intelligent aliens on myriad planets (the fact that most of these fictional aliens resemble humans in makeup/prosthetics is a combination of limited budgets and a desire for relatability to the audience). One reason, I think, that this confusion is so widespread is that there are two ways in which we could encounter extraterrestrial life: it finds us, or we find them. In the former case, it's either in the form of fossils, spores, or whatever hitchhiking on an interstellar asteroid (such as the one astronomers detected a couple of years ago, dubbed ʻOumuamua) - or, more interestingly, actual spaceship-building intelligent ETs, which, despite years of UFO sightings and their dissemination into popular culture, have never been shown to actually exist. In the latter case, it could be we find some simple life on another planet or moon in our solar system, or see indisputable evidence through some sort of telescope (another option, physically going to another solar system to find it, is so unlikely in the near future that I'm discounting it for now). I should note here that I'm not discounting the idea that at least some of the people who claim to have encountered aliens are being truthful - in a sense. While some are clearly hoaxes, and others might be, I don't deny that some people have seen something. But just because we don't know what something is doesn't mean it's aliens; that's a hell of a leap. We know less about our own minds than we do about the composition of the rest of the universe and its natural laws; and our minds have been known to create their own realities. Anyway, back to the actual article. What would convince you that aliens existed? The question came up recently at a conference on astrobiology, held at Stanford University in California. Several ideas were tossed around – unusual gases in a planet’s atmosphere, strange heat gradients on its surface. But none felt persuasive. Finally, one scientist offered the solution: a photograph. There was some laughter and a murmur of approval from the audience of researchers: yes, a photo of an alien would be convincing evidence, the holy grail of proof that we’re not alone. I'm not sure that would convince me. After all, photographs can be faked, and the technology needed to fake them is widespread and always getting cheaper. One thing that sets life apart from nonlife is its apparent design. Living things, from the simplest bacteria to the great redwoods, have vast numbers of intricate parts working together to make the organism function. Think of your hands, heart, spleen, mitochondria, cilia, neurons, toenails – all collaborating in synchrony to help you navigate, eat, think and survive. An argument can be (and repeatedly has been) made that life can be seen as an entirety, a continuum, and by some definitions of life, the entire troposphere of our planet is alive. It has "vast numbers of intricate parts," all communicating with each other in some sense; it's robust, in that it tries to keep itself alive; and it's even trying to reproduce, by producing a species that wants to visit other planets. The article goes on to explain evolution by natural selection, a decent enough summary of the process. Are there exceptions? We can’t get complex life, even something as simple as a bacterium, without natural selection. Due to the vagaries of language, this part may be a bit confusing. Biologists differentiate between two major groups of organisms: prokaryotes and eukaryotes. Prokaryotes, like bacteria, are considered simple organisms; they don't have nuclei, and while they might thrive in a colony, they're not what we think of as multicellular organisms. Eukaryotes, by definition, have nuclear cells, though they might be unicellular (amoebae, e.g.) or multicellular (us, e.g.). I mention this because I've seen several biologists make the argument that while simple (prokaryotic) life might arise fairly often, the particular combination of factors that produce eukaryotes is probably rare and, even if it does happen, doesn't necessarily lead to spaceship-builders. In other words, if we happen to find life elsewhere (say under the surface of Mars or in the world-ocean of Jupiter's moon Europa), it's very likely it will be simple. But we won't know until we find some, which brings us back to the point of the article. Previous work in astrobiology has extrapolated from what’s happened on Earth, potentially limiting our vision to certain special features, such as DNA or carbon-based life, that won’t hold on other planets. Natural selection, on the other hand, is universal. It doesn’t depend on DNA (remember, Charles Darwin knew nothing of genes) or carbon chemistry or the presence of water. It’s incredibly simple – it just requires a few ingredients – and it’s the only way to generate life. So I also want to point out, here, that while carbon-based life is what we're used to, being us, there has been speculation about other possible chemical scaffolding upon which to build some sort of DNA analogue. None of this speculation is particularly convincing to me; carbon's nearest congener (something in the same column on the Periodic Table), silicon, just doesn't have the same capacity to form the long-chain molecules that carbon does. Which is not to say that it's impossible; I just find it extremely unlikely. It's a big universe, though, and while I won't say that "anything" is possible, we just don't know. Also, natural selection doesn't "generate" life. It propagates life. We don't know how life started on Earth (though I read an extraordinarily convincing hypothesis recently), but once it did, natural selection took over and here we are, 4 billion years later. That, by the way, is more than a quarter of the age of the entire universe. As another aside, some people like to hand-wave it by saying that life might have started on another planet and migrated here. There's no compelling evidence for this and some evidence against it; and besides, all that does is kick the can down the road. Even if life began on, say, Mars, and got here through asteroid impacts or whatever, how did it start on Mars? The photo, if and when it comes, will be something entirely exotic to the naked eye. Yes, and you'll still get a lot of people denying that it's actually life. The more exotic it is, the less likely we are to recognize it. One thing remains true, though: be it LGMs in flying saucers or bacteria in Europa's ocean, finding extraterrestrial life will be a big milestone in humanity's history of exploration and discovery. |
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