Randomness
Overview

Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability
Predictability
Predictability is the degree to which a correct prediction or forecast of a system's state can be made either qualitatively or quantitatively.-Predictability and Causality:...

(or lack thereof) of events.

The Oxford English Dictionary
Oxford English Dictionary
The Oxford English Dictionary , published by the Oxford University Press, is the self-styled premier dictionary of the English language. Two fully bound print editions of the OED have been published under its current name, in 1928 and 1989. The first edition was published in twelve volumes , and...

defines 'random' as "Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard." This concept of randomness suggests a non-order or non-coherence in a sequence of symbol
Symbol
A symbol is something which represents an idea, a physical entity or a process but is distinct from it. The purpose of a symbol is to communicate meaning. For example, a red octagon may be a symbol for "STOP". On a map, a picture of a tent might represent a campsite. Numerals are symbols for...

s or steps
Procedure (term)
A procedure is a sequence of actions or operations which have to be executed in the same manner in order to always obtain the same result under the same circumstances ....

, such that there is no intelligible pattern or combination.

Applied usage in science, mathematics and statistics recognizes a lack of predictability
Predictability
Predictability is the degree to which a correct prediction or forecast of a system's state can be made either qualitatively or quantitatively.-Predictability and Causality:...

when referring to randomness, but admits regularities in the occurrences of events whose outcomes are not certain.
Quotations

For I do not believe that it is through the interference of Divine Providence ... that the spittle of a certain person moved, fell on a certain gnat in a certain place, and killed it.

Maimonides, Guide for the Perplexed|Guide for the Perplexed, 12th century, Friedländer translation

The generation of random numbers is too important to be left to chance.

Robert R. Coveyou, Oak Ridge National Laboratory, 1969

How dare we speak of the laws of chance? Is not chance the antithesis of all law?

Joseph Bertrand, Calcul des probabilités, 1889

Random numbers should not be generated with a method chosen at random.

Donald Knuth|Donald E. Knuth, The Art of Computer Programming|The Art of Computer Programming, Vol. II, 1969, section 3.1

The sun comes up just about as often as it goes down, in the long run, but this doesn't make its motion random.

Donald Knuth|Donald E. Knuth, The Art of Computer Programming|The Art of Computer Programming, Vol. II, 1969, section 3.3.2