After the long, gruelling process that is inputting a Gold level password from my Clear Data (I don't have a GBA link cable with me), I'm now starting The Lost Age. I will miss Isaac and Co. for now.
I love ATLAS' design. I wish he and P-body had opposite eye color.
Also, the free DLC is called Peer Review. This speaks to me as a scientist.
Cave Johnson is the best. I could listen to him talk forever about ignoring human rights in the name of advancing science.
I hope everyone had some awesome holiday funtimes! Mine were packed with traveling, visiting friends, gift giving and receiving, and all the food. All of it.
I also saw The Force Awakens twice while I was home. It was pretty fantastic. The part where we find out that Chewbacca is Rey's father was quite the twist![/trololololol]
Now I am back at school. Though classes don't start until next week, I'm in my lab typing this and sorta doing work. (I've been at a loss to find a certain physical quantity for the past week and have been trying to cope with this by watching various videos. Right now I'm watching Cosmos: A Spacetime Odyssey. When Knowledge Conquered Fear = WIN!)
Otherwise, things are going the way they've always been going.
Should the Earth-Moon system be considered a binary planet? This sounds outlandish at first, since the Moon is a moon, obviously. It orbits the Earth as a natural satellite, just as the Galilean moons (Ganymede, Callisto, Io, and Europa) orbit Jupiter, Titan orbits Saturn, Triton orbits Neptune, and so on, right?
The definition of a moon is vague, and thus there are multiple ways of determining whether or not a planet-moon system is really a binary planet. One way of drawing the line between the two descriptions is by finding the barycenter (or center-of-mass) of the system. The center of mass of a collection of N masses is given by
where M is the total mass of the system, and mi and ri are the mass and position of the ith object, respectively. If the center of mass of a two-body system lies outside the larger object in that system, call it a binary planet. This makes sense, right? This means that the smaller body doesn't orbit the larger body, but instead they both orbit some point in space. For instance, the barycenter of the Pluto-Charon system lies outside Pluto (0.83 Pluto radii above Pluto's surface), the larger of the two bodies, while the Earth-Moon barycenter lies within the Earth (just under 3/4 of an Earth radius from the planet's center). By this definition, the Pluto-Charon system is a binary (dwarf) planet system, while the Earth-Moon system is is a planet-moon system. (Although, we are slowly losing our moon due to tidal acceleration. In a few billion years, the Moon will have drifted far enough away that the barycenter of the Earth-Moon system will leave the interior of our planet.) However, when you plug in values for the Sun-Jupiter system, you find that the center of mass lies outside the Sun! Indeed, Jupiter is the only natural satellite of the Sun for which this is true. (Does this mean Jupiter should have a different classification from the rest of the planets? Not really; the Sun is around 1000 times more massive than Jupiter, so the reason for this is that Jupiter is very distant from the Sun.)
Maybe a different definition is needed to distinguish planet-moons from binary planets, then, since the Sun-Jupiter system is not a binary star (Jupiter is slightly too small to generate nuclear fusion). Another proposition is to look at the so-called tug-of-war value of a body. The tug-of-war value of a moon determines which Solar System object has a stronger gravitational hold, the Sun or the moon's "primary" (the Earth is the Moon's primary). Using Newton's law of gravitation
we can take a ratio of the Sun's pull on a satellite to the primary's pull. The result is the tug-of-war value, proposed by Isaac Asimov.
Here the subscripts s and p refer to the Sun and the primary, respectively; m is the mass of the body referred to by the subscript; and d is the distance between the moon and the body referred to by the subscript. If the tug-of-war value is larger than 1, then the primary has a larger hold on the moon than the Sun, whereas if it's less than 1, the Sun's gravity dominates. For the Earth-Moon system, it turns out this number is 0.46, which means that the Sun pulls on the Moon with more than twice the force of Earth's pull. This is an oddity among moons, but is not unique. It does mean, though, that the Moon, when viewed from the Sun, never undergoes retrograde motion; it moves across the solar sky without changing direction. Another way to put this is that the Moon is always falling toward the Sun (like the planets), and never in its orbit does it fall away from the Sun (unlike most moons). If you look at the orbits of the Earth and Moon from the point of view of the Sun, they dance around each other in careful step, which is unlike most other moons in the Solar System. For Asimov, this was reason enough to consider the Earth and Moon as a binary planet system.
This tug-of-war value does not, however, classify Pluto and Charon as a binary dwarf planet system (they're too far from the Sun for their tug-of-war value to be less than 1). Perhaps the definition of a binary planet is a difficult one to pin down.
Should the Moon be promoted to planet, just as Pluto was renamed as a dwarf planet? I don't know, but it gives us something to think about as we look up at the starry night, watching the dance of all the chunks of rock and gas hurtling through space in our sky, to music written by nature and heard through science.
Chaos is complexity that arises from simplicity. Put in a clearer way, it's when a deterministic process leads to complex results that seem unpredictable. The difference between chaos and randomness is that chaos is determined by a set of rules/equations, while randomness is not deterministic. Everyday applications of chaos include weather, the stock market, and cryptography. Chaos is why everyone (including identical twins who having the same DNA) have different fingerprints. And it's beautiful.
How does simplicity lead to complexity? Let's take, for instance, the physical situation of a pendulum. The equation that describes the motion of a pendulum is
where θ is the angle the pendulum makes with the imaginary line perpendicular to the ground, l is the length of the pendulum, and g is the acceleration due to gravity. This leads to an oscillatory motion; for small angles, the solution of this equation can be approximated as
where A is the amplitude of the swing (in radians). Very predictable. But what happens when we make a double pendulum, where we attach a pendulum to the bottom of the first pendulum?
Can you predict whether the bottom pendulum will flip over the top? (Credit: Wikimedia Commons)
It's very hard to predict when the outer pendulum flips over the inner pendulum mass, however the process is entirely determined by a set of equations governed by the laws of physics. And, depending on the initial angles of the two pendula, the motion will look completely different. This is how complexity derives from simplicity.
Another example of beautiful chaos is fractals. Fractals are structures that exhibit self-similarity, are determined by a simple set of rules, and have infinite complexity. An example of a fractal is the Sierpinski triangle.
Triforce-ception! (Image: Wikipedia)
The rule is simple: start with a triangle, then divide that triangle into four equal triangles. Remove the middle one. Repeat with the new solid triangles you produced. The true fractal is the limit when the number of iterations reaches infinity. Self-similarity happens as you zoom into any corner of the triangle; each corner is a smaller version of the whole (since the iterations continue infinitely). Fractals crop up everywhere, from the shapes of coastlines to plants to frost crystal formation. Basically, they're everywhere, and they're often very cool and beautiful.
Chaos is also used in practical applications, such as encryption. Since chaos is hard to predict unless you know the exact initial conditions of the chaotic process, a chaotic encryption scheme can be told to everyone. One example of a chaotic map to disguise data is the cat map. Each iteration is a simple matrix transformation of the pixels of an image. It's completely deterministic, but it jumbles the image to make it look like garbage. In practice, this map is periodic, so as long as you apply the map repeatedly, you will eventually get the original image back. Another application of chaos is psuedorandom number generators (PRNGs), where a hard-to-predict initial value is manipulated chaotically to generate a "random" number. If you can manipulate the initial input values, you can predict the outcome of the PRNG. In the case of the Pokémon games, the PRNGs have been examined so thoroughly that, using a couple programs, you can capture or breed shininess/perfect stats.
Dat shiny Rayquaza in a Luxury ball, tho.
So that's the beauty of chaos. Next time you look at a bare tree toward the end of autumn or lightning in a thunderstorm, just remember that the seemingly unpredictable branches and forks are created by simple rules of nature, and bask in its complex beauty.
I've been away a while attending friends' weddings, visiting various peeps, rereading Harry Potter (still as magical as always), and working on research. If all goes well, this Friday will see me submitting a paper to the Journal of Chemical Physics. All in all, it's been a good few months. But now is the season of autumnal haunts, and I have grown very happy with the drop in temperature and the swap of palette.
Over my fall break, I visited KK in the land of cheese, Wisconsin, and he introduced me to the joys of Punch Out!! for Wii and Super Mario Maker. I now own both, and have been having loads of fun playing others' levels and designing levels of my own (mostly goofing off). When I've finalized a level I'll post it for you all to play if you like. In particular I've been working on a Ghost House.
It's been super fun. Also, RubberRoss' levels are utterly evil.
EDIT: Untimely Haunt v2: CD1D-0000-00C8-8D19
Oak Log Bans
Stone Champion Nuva
+2 for Premier Membership
+1 from Pohuaki for reporting various things in Artwork
Real Name: Forever Shrouded in Mystery
Likes: Science, Math, LEGO, Bionicle, Comics, Yellow, Voice Acting, Pixel Art, Video Games
Notable Facts: One of the few Comic Veterans still around
Has been a LEGO fan since ~1996
Bionicle fan from the beginning
Hieroglyphs And The Like
That moment when you realizeSwagtronYOLO - Feb 17 2017 04:41 PM
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Equation of the Day #19: Golden PentagramsTaka Nuvia - Feb 13 2017 04:11 PM
Equation of the Day #19: Golden PentagramsSwagtronYOLO - Feb 10 2017 03:08 PM
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