A superclass[1] is a group of numbers determined by the way that humans can perceive them. Although he does not take credit for their invention, Robert Munafo coined the term in analogy with his own classes. The superclasses are defined as:

  • Superclass 1: A number that can be visualized, for example, 12.
  • Superclass 2: The number cannot be visualized but it can be understood, for example, quadrillion.
  • Superclass 3: The number cannot be understood, but the procedure for computing can be visualized, for example, tritri.
  • Superclass 4: The procedure cannot be visualized, but it can be understood, for example, Moser.
  • Superclass 5: The procedure for generating the number is so abstract that it cannot be understood, for example, gongulus.

Robert Munafo also defines:

  • Superclass 0: The number can be experienced by certain animals, for example, 3.
  • Superclass 6: The number is so big that nobody can understand its definition well enough to know anything useful about it, for example, BB(100) in the busy beaver function.

None of these terms define clear-cut ranges of numbers, since the capacity to visualize or understand a number or procedure can vary from person to person.

Sources Edit

  1. Superclasses