Few mathematical constructs seem as conceptually simple as that of randomness. According to the traditional definition, a number is random if it is chosen purely as the result of a probabilistic mechanism such as the roll of a fair die. In their groundbreaking work regarding complexity and the limitations of formal systems, mathematicians Gregory Chaitin and A.N. Kolmogorov force us to consider this last claim more closely.

Consider two possible outcomes of throwing a fair die three times: first, 1, 6, and 2; second 3, 3, and 3. Now let us construct two three-member sets based on the results. Though the first set—{1,6,2}—intuitively seems more random than the second—{3,3,3}, they are each as likely to occur, and thus according to the accepted definition, must be considered equally random. This unwelcome result prompts Chaitin and Kolmogorov to suggest the need for a new standard of randomness, one that relies on the internal coherence of the set as opposed to its origin.

Which of the following best describes the organization of the passage as whole?

A) A concept is introduced; a traditional definition is put forward; a thought experiment is described; a new definition is proposed; the traditional definition is amended as a result.
B) A concept is introduced; a traditional definition is supported by authorities; a thought experiment is described; the implications of the experiment are discussed.
C) A concept is introduced; a traditional definition is considered and rejected; a thought experiment is described; a new definition is proposed.
D) A concept is introduced; a traditional definition is called into question; a thought experiment is described; the implications of the experiment are discussed.
E) A concept is introduced; authorities are called in to reevaluate a definition; a thought experiment is described; the implications of the experiment are considered and rejected.





Which of the following is an inference made in the passage above?

❑ The results of the same probabilistic mechanism will each be as likely as the other to occur.
❑ According to the traditional definition of randomness, two numbers should be considered equally random if they result from the same probabilistic mechanism.
❑ Different probabilistic mechanisms are likely to result in similar outcomes.