Chapter 12: The Principle of Computational Equivalence

Section 3: The Content of the Principle

History [of universal objects]

There are various precedents in philosophy and mysticism for the idea of encoding all possible knowledge of some kind in a single object. An example in computation theory is the concept emphasized by Gregory Chaitin of a number whose nth digit specifies whether a computation with initial condition n in a particular system will ever halt. This particular number is far from being computable (see page 1128), as a result of the undecidability of the halting problem (see page 754). But a finite version in which one looks at results after a limited number of steps is similar to my concept of a universal object. (See also page 1067.)

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]