Speculation and Apex Artillery: Order, Chaos and the Mathematical Pendulum · 3:55pm Jul 7th, 2015
The dichotomy of order and chaos is a common theme not only in storytelling in general, but also very much present in My Little Pony fanfiction in particular (Not surprising since there is a character denominated as spirit of chaos and disharmony).
Of course, we all know that the topic is a bit more complicated than the other common dichotomy, the one of good and evil.
Most people who put a bit of thought into the topic will come to the conclusion that both absolute chaos and absolute order are quite, er, undesirable. Often, they will advocate some sort of balance, however that may look like.
In the world of Equestria, chaos is automatically associated with Discord. The part of order is a more variable thing in this setting, and greatly depends on who you ask.
The part of balance as a "good" alternative to both chaos and order is often given to the Elements of Harmony and all associated forces.
It is this entire topic of order, chaos, harmony, balance and whatnot I will now add my two cents to.
As aid to get my points across I shall use the mathematical pendulum.
Now that I have scared off half of my potential audience by using the word "mathematical", I will get rid of half of the remainder by telling you I won't actually be doing any math in this post.
First of all, I will assume you all know the concept of a pendulum in a homogeneous gravitational field and how it behaves.
Now the mathematical pendulum has a few important characteristics:
1. It uses a two-dimensional rigid rod and a point mass instead of slinky string and a voluminous weight.
2. The rod is massless and there is no friction.
3. The rod can be rotated freely a full 360° around its hinge.
Of course, no such things exist in actual reality. However this bothers neither mathematicians nor physicists, so it shouldn't bother you, either.
Firstly, let us see what happens if the mass hangs straight downwards. Well, obviously nothing. The pendulum is in perfect, stable equilibrium and won't ever start moving on its own. Why is that important?
Well, it's our first example of balance, a stable balance.
Second, I think you'll agree with me that this is also a very orderly state, since the pendulum is completely static. For illustration, imagine a random microscopic disturbance of the pendulum that doesn't add energy. Obviously, still nothing happens, since you need energy to lift the mass out of equilibrium.
Now take the mass and lift it a bit, then let it go. The pendulum will start swinging back and forth. Since there's no friction, it won't ever stop and will continue to swing forever in exactly the same way.
If you, again, imagine a random microscopic disturbance that doesn't add energy, you'll find that such a disturbance won't be able to change the pendulum's path.
So this also is quite an orderly system, not in equilibrium, but oscillating around equilibrium.
On an aside note, this kind of swinging can be approximated very closely to something called a "harmonic oscillator".
Next thing, we lift the mass all the way up to the top, where we reach another point of equilibrium with the mass directly above the hinge. If we balance the mass perfectly, it will stay up there forever.
However, if you add a random microscopic disturbance that doesn't add energy now, the pendulum will swing all the way round until it reaches the highest point again and then stop, since we didn't add or remove energy.
This is because we are now at a point of unstable equilibrium - any deviation from that point of balance, and the pendulum will start moving.
At this point, motion in any possible direction can be achieved by a microscopic disturbance - even without a change in energy.
This is our second example of balance, and our first example of chaos.
A deterministic system is called chaotic if an infinitesimal change in the starting conditions (or anywhere along the way) results in a macroscopic change. This is also called the butterfly effect. (On a totally unrelated note think of Fluttershy and Discord for a moment).
If a system is complex enough, it will behave chaotically.
I bring forth this definition of chaos because it seems most in line with Discord's flavour of chaos. He makes things more complex. He makes things behave erratically and unpredictably. He allows unusual and counter-intuitive transitions of states.
I think the pendulum in its unstable equilibrium under influence of random microscopic disturbances that don't add energy is a very, very simple example of Discord's chaos.
First, the pendulum seems to hang upside down.
Second, it will start moving randomly, seemingly without cause.
Third, after going round once, it will stop. This is not how we expect a pendulum to behave.
Of course, Discord's chaos is not quite as simple as that, but that's because Discord creates chaos, he adds complexity and possibilities.
Now, since it is brought up quite often, let's talk about entropy for a bit.
If you look at history for a bit, you'll see that the word entropy was invented by physicists.
So I asked one Ludwig Eduard Boltzmann about entropy. He told me (not personally; he's dead, but had the gallantry of writing it on his tombstone) that entropy is a measure of the possible microstates of a system for a specific macrostate.
Ooh. What's that mean? Now, let's look back at the pendulum.
If we have stable equilibrium, the mass can only be at one specific point: at the bottom. That is one microstate (position of the mass) for our macrostate (stable equilibrium). That must mean our entropy is pretty low. (In fact, it's zero.)
If we look at the swinging pendulum, we can easily see that any position the pendulum can reach while swinging back and forth corresponds to a microstate. Therefore, our entropy is a bit higher now.
If the pendulum in unstable equilibrium, the mass can reach any possible position it could possibly reach without coming off the rod. Entropy is at a max.
So, in our example, the most orderly state has the lowest entropy, and the chaotic state has the highest possible entropy of our system.
However, both states are a state of balance.
Make of that what you want.
P.S.: This is mostly serious, but not entirely. It is also not quite up to my usual standard, I believe.
P.P.S.: Now, who can tell me whether a thriving bureaucracy is inherently orderly or chaotic?
Dude...What the fuck did I just read?
On another note, I'm quite intrigued by this whole neutral mathematical pendulum thingy. (Sorry, only understand a fraction of what you're saying.)
I'm sure if I was more intelligent I'd be able to get more out of this. But alas, I'm quite stupid and lack the noodle power required to process this information. Idk, I think I'll forward this is a person of my interest and see what he makes of this. (He's much smarter than me.)
A thriving bureaucracy is both eristic and aneristic in nature. Chaos is the only true constant in any system, and as such, it is the only inherent force of order. Everything else is inconsistent and has a margin of error.
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I almost completely agree. I wouldn't go as far as to say chaos is the only constant, though.
I must say, I just like using bureaucracy as an example for why the definition of chaos as "lack of order" is flawed.
Neither chaos nor order are actually privative.