What are the best examples of randomness out there?
The notion of randomness began to be explored from a scientific (quantitative) perspective from the latter half of the 19th century as a result of the development of the kinetic theory of gases (thanks largely to the work of Boltzmann and Maxwell).
The three major instances of randomness occur in the following contexts:
(a) At the molecular level in gases: Here the distribution of the velocities of molecules is random, i.e. various individual molecules move about along different directions and with different speeds at any given temperature. However (and this was the major contribution of Boltzmann and Maxwell) it is possible to calculate how many molecules are there in the sample whose velocities lie within a specified range. Randomness in a population of incredibly large numbers was tracked down to a quantitative measure for the first time!
(b) In the chaos context: Chaos theory has shown that very small perturbations in a complex physical system may lead to utterly unpredictable consequences in utterly random ways. Recall the famous butterfly effect.
(c) The hypercomplex level (the term is of my coinage): This is at the human (consciousness/interaction level). The manner in which one thought leads to another is utterly random. So are expected and unpredictable (random) encounters between people, leading to totally unforeseeable consequences. The simplest example may be found by considering how one met and came to marry one’s spouse.
How would you define randomness?
There are technical and quantitative definitions of randomness in statistics, mathematics, information theory, philosophy, thermodynamics, etc. More generally, as I see it, randomness refers to the presence/emergence of a sequence of elements/events which are (to all appearances) utterly unconnected, and in whose totality one is unable to detect any pattern or purpose whatever.”
Can you connect God with randomness?
Maybe in the following manner:
Randomness is the opposite of any order whatever which was the primordial state of the multiverse: somewhat like the heap of tiles in a game of Scrabble. God dwelt in that original Chaos until (for whatever reason) God decided to make some words and sentences out of the jumble, and so was born our Universe. The universe of order corresponds to the words that have been laid out on the board. There are still so many tiles under the cover: the randomness that is still present and potential, while we watch, analyze, and admire the spelt out words.