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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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Welcome to Trust No One Day. It's kind of appropriate that this article (from Mental Floss) came up at random today, because, while it's probably not intended as a prank, I don't really trust it.
For various definitions of "facts."
The solar system: It’s big, it’s heliocentric, and it’s got space junk to spare.
"Big" is relative. From our human perspective? Sure. Compared to the rest of space? Not even a pixel.
Here are 24 out-of-this-world facts about the corner of space that’s home to Earth, enough asteroids to keep Ben Affleck and Bruce Willis working for decades, and a football-shaped dwarf planet called Haumea, adapted from an episode of The List Show on YouTube.
Ah, YouTube, that bastion of fact-checking. Sure, I watch science videos there, but that doesn't mean I accept them all unconditionally.
I won't highlight all 24.
1. Our solar system is a group of celestial bodies in the Milky Way galaxy.
Thanks. That's so helpful.
I've mentioned before why "the Milky Way galaxy" is redundant: "Upward Spiral" 
One can think of "the solar system" as being everything affected by the gravitational pull of the Sun. Gravity drops off with distance, but never goes to zero, though at some point, the combined gravity of, well, everything else balances or outweighs the Sun's pull.
2. The sun is huge.
If you combined the mass of everything in the solar system, the sun would account for more than 99 percent of that mass.
Okay, fair enough, though it's much closer to 100% than 99 percent. And again, "huge" is relative. As stars go, the sun's somewhere in the middle.
4. A block of lead on Venus would melt like a block of ice on earth.
True enough, but misleading. There are plenty of places on Earth where a block of ice wouldn't melt, though I tend to avoid such places. Also, lead doesn't melt like water. Ice is less dense than water, which is why it floats to the top of your glass and forms skating surfaces. But okay, maybe that's too pedantic. The point is, Venus is bloody HOT (from our perspective, not the Sun's), and you wouldn't want to go there. Hotter than Mercury. The planet, not the metal that's liquid at normal temperatures here on Earth.
5. Rocks from space have been found all over planet Earth.
Okay, but also pretty trivial, and that's leaving aside that every rock on Earth is "from space;" it's just a matter of how long ago it arrived. I have a meteorite fragment; they're not that uncommon. They are, however, cool.
6. Jupiter is massive.
Well, duh. Compared to Earth, anyway. Compared to the sun, it's significantly less than 1% of the sun's mass.
If the sun is 99.86% of the solar system's mass, though, Jupiter is most of the rest.
Earth is a rounding error.
10. Space junk is a big problem.
No, they're not talking about space aliens' genitals.
13. One object in our solar system orbits the Sun backwards.
In 2008, astronomers discovered an object that orbits the sun at about a 104-degree tilt. Technically, this means that the 30-mile-wide object is orbiting backwards. The team that found it gave it the name Drac, based on the myth that Dracula could walk up walls.
Having a retrograde orbit, or one that's nearly at right angles to the plane of planets (the ecliptic), or, in this case, both, isn't that farfetched. If I had to guess, I'd guess "captured extrasolar object," but that's just a guess. No, what I like about this one is the name.
Sadly, the prank here is that "Drac" is just a nickname, not its official designation. Much easier to say than "(528219) 2008 KV42" though.
14. Drac was found in the Kuiper Belt.
The Kuiper Belt is an area of our solar system past Neptune containing a lot of icy objects; it's also where Pluto is located.
Also misleading. Pluto spends a significant fraction of its time closer to the sun than Neptune. Still, it is considered a Kuiper Belt object, but that's a categorization thing, like its non-status as a planet.
Plus, given Drac's orbital inclination from the ecliptic, maybe it should be the Kuiper Shell instead.
15. Neptune has a moon that’s a lot like Pluto.
Triton is probably one of those icy Kuiper Belt objects that at some point got trapped by Neptune’s gravity and has been orbiting it ever since. Triton has a couple other distinctive features: It orbits Neptune in the opposite direction than the planet is rotating, and it has geysers that erupt.
Hence my "captured object" guess for Drac.
18. One dwarf planet in our solar system has also been a planet and an asteroid.
Pluto’s fellow dwarf planet Ceres takes up about 25 percent of the mass of the main asteroid belt, which is located between Mars and Jupiter. In the 19th century, Ceres was considered a planet. Then it was demoted to asteroid. Finally, in 2006, it was upgraded to dwarf planet.
And yet, people aren't still salty about that one. Well, maybe astrologers are; I don't know.
19. There are millions of asteroids in the main asteroid belt between Mars and Jupiter.
They can range from less than 33 feet (10 meters) to 329 miles (530 kilometers) long.
See, it's because of statements like this (which is, to the best of my knowledge, accurate enough) that movies commit what I consider to be one of the most egregious errors: depicting the asteroid belt as some densely-packed rocky hazard that Our Hero has to demonstrate superhuman piloting skills to navigate. First of all, space is three-dimensional (at least); just go around. Second, if you were standing like Le Petit Prince on one of the asteroids and looking at the sky, you'd be hard-pressed to notice even one space rock.
The only show that did it right was The Expanse. But I give props to Guardians of the Galaxy Volume 2 for inventing the quantum asteroid field, which was funny enough to overcome my pedantry.
20. Two of Saturn's moon have water.
Yawn. Freakin' Mercury probably has water (ice) at the poles. So does the Moon. Not to mention the probable ocean covering Europa (one of Jupiter's moons). Water isn't rare. Water is probably second only to rock on my list of "things we find on moons." Liquid water with life swimming in it? Wake me up when we find that on a planet other than ours.
22. The tallest volcano we know of is on Mars.
Olympus Mons is estimated to be 16 miles tall, meaning it’s basically three Mount Everests.
That's cheating, on two levels. One, it's been extinct for an unimaginably long time, so calling it a "volcano" is nothing more than acknowledging its areological origin. Two, Mars has about 2/5 of our gravity, so of course mountains can be higher. The slope of its sides is comparatively gentle, though, and I question what datum they're measuring from. Everest is generally measured in height above sea level, but from its base on the Himalayan Plateau, it's much less tall. Measured from base, there's a volcano (an active one) in Hawai'i that's taller than Everest (the "base" there is underwater). Measured from the center of the planet, there's a peak in Ecuador that can be considered higher than either (Earth bulges at the equator), but I guarantee you Olympus Mons isn't higher by that standard, as Mars is smaller than Earth. Not to mention there's no sea level on Mars, even if there is water there. Somewhere. Probably frozen.
24. Many of these facts would still be unknown if not for space exploration.
Finally, something I can't quibble about.
No fooling. |
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