As defined by the Free Online Dictionary:
1. Having no specific pattern, purpose, or objective2. Mathematics & Statistics Of or relating to a type of circumstance or event that is described by a probability distribution.3. Of or relating to an event in which all outcomes are equally likely, as in the testing of a blood sample for the presence of a substance.
1. A condition or place of great disorder or confusion.2. A disorderly mass; a jumble.3. The disordered state of unformed matter and infinite space supposed in some cosmogonic views to have existed before the ordered universe.4. Mathematics A dynamical system that has a sensitive dependence on its initial conditions.
Today, I'm looking at randomness vs. chaos in the scientific and mathematical sense. Is there a difference between something being chaotic, and something being random? Yes.
Randomness, as summarized in the mathematical lingo, is closest to definition #2 above. It has to deal with the probability distribution*. The point is that truly random things are out of our hands; systems including randomness cannot be predicted because they cannot be controlled.
*To get an idea of what probability distribution is, it's the odds of something happening. Your chances of rolling any given number are theoretically 1 out of 6 on a 6-sided die. However, rolling two dice means you can roll any number 2-12. It's more likely that you'll roll a seven than a twelve because there are more ways to roll a 7 (5+2, 4+3, 1+6) than ways to roll a 12 (6+6). So if you roll one die, your probability distribution says that every possible outcome has an equal chance of occurring (i.e., you're equally likely to roll any number 1-6); if you roll two dice, you're more likely to roll certain numbers than others, according to your probability distribution.
Chaos, on the other hand, is all about not having randomness. The idea is that every teeny-tiny differences in beginning circumstances make huge differences later on, and that the equation is affected by many, many things. It's considered unpredictable because the equation is so complicated that people cannot hope to measure everything that goes into it.
Weather is considered to be chaotic. There are so many variables that it's impossible to predict exactly what will happen. Yet this doesn't change the fact that weather follows patterns and is certainly affected by circumstances.
It's not random (you know in August at the equator you won't have snow), but the difference between a hurricane hitting the coast or missing it may be something tiny (like the heat rising off a concrete parking lot making an updraft that slightly shifts the course of a breeze that warms a current of air that rises up and leaves room for colder air below it...). Systems including chaos cannot be predicted because they are too complicated to measure every bit that goes into them.
What does this mean as writers, in terms of which to use?
It means that random should be used when nothing influences how something turns out. Obviously what you put in will determine what comes out (you won't roll a 14 on a 6-sided die), but which of the possible outcomes occurs is not definitively controlled. Examples of random things: rolling a die, drawing names from a hat, winning the lottery, possibly meeting a soul mate (depending on world), which genes you'll get from each parent
It means that chaotic should be used when the results are too complex to be predicted. Examples of chaotic events: horse racing, weather systems, the results of a medicine on a new patient, the effects of a childhood trauma on an adult
Taking into account standard usage, you can get away with using random in most scenarios. It's almost impossible to create a truly random system (I could make arguments about rolling dice being chaotic, and I'm sure someone is already debating the randomness of genetics), but as far as most people are concerned, "close enough" means "I can't predict how this will turn out, so it counts."
However, if you're dealing with a mathematical or scientific issue, your character is more likely to use chaotic if they're a scientist. They probably won't notice (or won't mention) if someone else uses random instead, unless it's a particularly clear-cut case and they're feeling picky.
What does this mean as writers, in terms of plot?
Personally, I want major points of randomness to be foreshadowed beforehand, so they don't seem to be coming out of left field. Minor points can make good plot twists, or be part of the world - but beware of misusing them. "And then she rolled a 7 and won the hero's freedom" will probably leave the reader feeling cheated.
Chaotic elements are when things escalate out of a character's control. Now those are fun. Even better if the character sees it getting out of hand and tries to do something to stop it. Then it becomes a chase of trying to change the outcome by adding in favorable variables to the problem, and those don't always turn out as they should.
I recommend using random elements only to create problems, and never to solve them. As I heard Cherry Adair once put it, your reader will never believe it if random chance helps your character, but will always believe it if chance makes things harder.
Do you have any random elements in your stories? If so, what are they? If not, is there anything that appears random, but isn't?