Not for the faint of art. |
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. |
You know why you should never trust atoms? Because they make up everything. Why atoms are the Universe’s greatest miracle With a massive, charged nucleus orbited by tiny electrons, atoms are such simple objects. Miraculously, they make up everything we know. I could quibble about some of the words here, like "miracle," "simple," and "everything," but fine, they're not writing for scientists but to get ordinary people to know something about science. I can't be mad about that. Similarly, I don't have much to say about the article itself. It's not technical, and it's got lots of cool illustrations, some of them animated. Highly recommended for anyone with curiosity. One of the most remarkable facts about our existence was first postulated over 2000 years ago: that at some level, every part of our material reality could be reduced to a series of tiny components that still retained their important, individual characteristics that allowed them to assemble to make up all we see, know, encounter, and experience. I mean, technically, light (which obviously enables us to see) isn't made of atoms. But it's generated from them, so okay. Incidentally, I'm pretty sure that Democritus (the Greek who came up with the above idea) would be almost entirely forgotten had he not turned out to have been onto something. Lots of stuff the Greeks came up with didn't pan out (pun intended). And the Greek atomist theory wasn't exactly correct, either. It was more philosophy than science. Everything that’s made up of normal matter within our Universe — whether solid, liquid, or gas — is made of atoms. I could also quibble that this statement is a tautology, but why bother? If all of human knowledge were someday wiped out in some grand apocalypse, but there were still intelligent survivors who remained, simply passing on the knowledge of atoms to them would go an incredibly long way toward helping them not only make sense the world around them, but to begin down the path of reconstructing the laws of physics and the full suite of the behavior of matter. That's assuming they'd have the time to do so, between running from predators, finding prey, and hiding from aliens and/or zombies. This is, however, just their framing device to communicate the idea of building atomic theory from the ground up. Best to not take these things too literally. Like I said, I don't have much else to add. Mostly I just wanted to hold it up as an example of how one might communicate complex ideas to a wider audience. |