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Complex Numbers
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.
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The equinox will occur later today (or early tomorrow if you live in certain time zones), so it's appropriate that this cosmological link resulted from my random die roll today. Warning: It's from Salon, a source I don't normally use and that might be problematic.
Personally, I think it's the most meaningful, profound insight in all of science. As far as I know, most cultures have an origin story: we were shaped from trees; we appeared out of literal nothing; we were formed from clay; whatever. I use passive voice there because, usually, gods were involved, powerful entities that predated humanity. Some origin stories also attempt to explain where those creator gods came from, but you quickly run into the turtle problem: if Earth is a flat disc resting on the back of a giant turtle, what's holding up the turtle? Another turtle? Well, what's holding up that one? It's turtles all the way down.
Now, you could say, "But science runs into the same problem. If all that exists was created in a Big Bang, how and where did the Big Bang... well... bang?"
This is a fair question, however it's stated. And science doesn't have a definitive answer. The difference between that and creation myths is that science doesn't pretend to have a definitive answer.
In any case, one reason I find it meaningful is that it doesn't just focus on one human tribe, or even on humanity in general, but the entire universe; that is to say, everything. How humans came to be from non-humans is the focus of evolutionary biology, not cosmology. And how different tribes formed is in the purview of, among other disciplines, anthropology. I'll grant that the creation stories our ancestors came up with have a certain poetry to them (and say an awful lot about the cultures involved), but to me, they all read like "Just-So" stories. Or, well, vice-versa. But my point stands.
With that, I won't be quoting too much from the article. That was really the thing I most wanted to say.
As the poets at NASA put it, “from the carbon in our DNA to the calcium in our bones, nearly all of the elements in our bodies were forged in the fiery hearts and death throes of stars.”
Poetry again. It depends what you mean by "nearly all."  By mass, it's mostly oxygen (the "ox" in "Hydrox" from yesterday's entry). By number of atoms, we're mostly hydrogen (the "hydr" in "Hydrox" from yesterday's entry). You might also recognize these elements as the atoms of water, and I'm sure you've heard that we're well over 50% water, so that all tracks, though both hydrogen and oxygen are part of other molecules in our bodies, notably carbon-based ones.
Point being that hydrogen is mostly primordial, not forged in stars. Though an argument could be made that, at the very least, protons are mostly primordial, no matter how many of them are in a given nucleus.
And they’ve been around far longer than we have. Light elements started forming an estimated 14 billion years ago, actually, in the first few minutes after the Big Bang, though others didn’t come around till a few hundred thousand years later when the universe cooled down enough for electrons to stay in orbit around atomic nuclei.
That... doesn't quite mesh with my understanding, though I admit my understanding may be off. An element is defined by the number of protons in its nucleus, irrespective of the number of electrons associated with it. A proton is a hydrogen atom (technically, it's a hydrogen ion, but whatever). So once you have free-roaming protons, you have hydrogen. Therefore, it doesn't matter if a proton (or a bound pair or triad of protons, together with the appropriate number of neutrons) has electrons or not; it's still hydrogen, helium, or lithium, respectively.
In fairness, the article calls out these elements in the next paragraph; I just have quibbles with how the information is phrased.
But you don’t just kill a star and get an entire cupboard of elements suitable for whipping up whatever material good — whether Uranus or, with apologies, your anus — you’re after.
Apology absolutely not accepted. Seventh-planet puns are never funny. Well, almost never.
Apart from that, well, the article delves into the science of it all, and I won't rehash it further. Suffice it to say, for my purposes, that we know, insofar as we can ever truly know anything, that we are indeed stardust. So is your dog. And poison ivy. And plastic and concrete. The good, the bad, and the ugly. |
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