Randomness - What is it?

Randomness should not be confused with practical unpredictability, which is a related idea in ordinary usage. Some mathematical systems, for example, could be seen as random; however they are actually unpredictable. This is due to sensitive dependence on initial conditions (see chaos theory). Many random phenomena may exhibit organized features at some levels. For example, while the average rate of increase in the human population is quite predictable, in the short term, the actual timing of individual births and deaths cannot be predicted. This small-scale randomness is found in almost all real-world systems. Ohm's law and the kinetic theory of gases are statistically reliable descriptions of the 'sum' (i.e. the net result or integration) of vast numbers of individual micro events, each of which are random, and none of which are individually predictable. (Theoretically the micro-events of gases, for example, could be predicted if the exact position, velocity, atomic composition, angular momentum, and so on of each particle were known.) All we directly perceive is circuit noise and some bulk gas behaviors.It is important to note that chaotic systems are only unpredictable in practice due to their extreme dependence on initial conditions. Whether or not they are unpredictable in terms of computability theory is a subject of current research. At least in some disciplines computability theory the notion of randomness turns out to be identified with computational unpredictability.Unpredictability is required in some applications, such as the many uses of random numbers in cryptography. In other applications (e.g. modeling or simulation) statistical randomness is essential, but predictability is also required (for instance, when repeatedly running simulations or acceptance tests, it can be useful to be able to rerun the model with the exact same random input several times).Sensibly dealing with randomness is a hard problem in modern science, mathematics, psychology and philosophy. Merely defining it adequately, for the purposes of one discipline has proven quite difficult. Distinguishing between apparent randomness and actual randomness has been no easier. In addition, assuring unpredictability, especially against a well-motivated party (in cryptographic parlance, the "adversary"), has been harder still.Some philosophers have argued that there is no randomness in the universe, only unpredictability. Others find the distinction meaningless (see determinism for more information).