Busy Beaver
One example of a class of noncomputational functions and an unsolvable problem in mathematics. Being a "Turing Machine unsolvable problem," the busy beaver function cannot be computed by a Turing Machine. To compute busy beaver of n, one creates all the n-state Turing Machines that do not write an infinite number of 1s on their tape. The largest number of 1s written by the Turing Machine in this set that writes the largest number of 1s is busy beaver of n.
Articles on KurzweilAI.net that refer to Busy Beaver
The Age of Intelligent Machines, Chapter Three: Mathematical Roots By Ray KurzweilThe Age of Spiritual Machines: Glossary By Ray Kurzweil
Turing's Prophecy By Ray Kurzweil
The Age of Intelligent Machines: Footnotes By Ray Kurzweil
The Age of Intelligent Machines, Chapter One: The Roots of Artificial Intelligence By Ray Kurzweil
Book Review: A New Kind of Science By Scott Aaronson
Gelernter, Kurzweil debate machine consciousness By Rodney Brooks, Ray Kurzweil, and David Gelernter
Related Links
Busy Beaver ProblemBusy Beavers
Busy Beaver (and other resources)