popper-logic-scientific-discovery

APPENDIX *vi
On Objective Disorder
or Randomness
It is essential for an objective theory of probability and its application
to such concepts as entropy (or molecular disorder) to give an
objective characterization of disorder or randomness, as a type of order.
In this appendix, I intend to indicate briefly some of the general
problems this characterization may help to solve, and the way in which
they may be approached.
(1) The distribution of velocities of the molecules of a gas in equilibrium
is supposed to be (very nearly) random. Similarly, the distribution
of nebulae in the universe appears to be random, with a constant
over-all density of occurrence. The occurrence of rain on Sundays is
random: in the long run, each day of the week gets equal amounts of
rain, and the fact that there was rain on Wednesday (or any other day)
may not help us to predict whether or not there will be rain on Sunday.
(2) We have certain statistical tests of randomness.
(3) We can describe randomness as ‘absence of regularity’; but this
is not, as we shall see, a helpful description. For there are no tests for
presence or absence of regularity in general, only tests for presence or
absence of some given or proposed specific regularity. Thus our tests
of randomness are never tests which exclude the presence of all regularity:
we may test whether or not there is a significant correlation