Definition (please) of 'Random' and "Chaos'?

Question

Random is equal chance.
Chaos may appear random.

These statements are not crisp and to the point.

Answer 1

Chaos, in the sense of chaos theory, has a very specific definition. A system is called "chaotic" if small differences in initial configuration of the system can lead to large differences in configuration with time.

Answer 2

Disregarding quantum mechanics for the moment, randomness is purely theoretical. We may call the roll of a die random, but the side that comes up is really determined by the way the die is thrown. If you had complete control over the way you threw a die, the surface on which you threw it, and your immediate environment, you could control the outcome.

If each side of the die had a certain, specific chance of coming up (not necessarily equal chance) and you had no way to control it, then the result would be random. This is not the case, but all of the factors that go into a die roll are so complicated that we cannot predict the results. Thus the results appear to us to be random, though the die roll is simply an example of chaos.

One of the things that quantum mechanics tells us is that there are certain things in the universe that are truly random. These are generally limited to very small things, and not normally observable. Examples would be the radioactive emissions of individual atoms, and the locations of subatomic particles like electrons.

Answer 3

Random means: (1) Having no specific pattern, purpose, or objective: random movements. (2) 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.

Example: A coin toss. There is an equal probability that you will get heads as there is that you will get tails. So if you toss a coin 10 times, you should get 5 heads and 5 tails. But RANDOM outcome explains why you sometimes get 10 heads and no tails.

Chaos means: (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) A dynamical system that has a sensitive dependence on its initial conditions.