Mind Matters Natural and Artificial Intelligence News and Analysis

TagPositive integers

metallic numbers.jpg
abstract metallic number background

The Paradox of the Smallest Uninteresting Number

Robert J. Marks sometimes uses the paradox of the smallest “uninteresting” number to illustrate proof by contradiction — that is, by creating paradoxes

In this week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin on how he proved that the number that determines whether computer programs are elegant (in the sense of maximally efficient) is “unknowable.” As Dr. Chaitin explained in the segment published yesterday, any solution would be contradictory. Thus, his proof is a proof by contradiction. By way of illustrating the concept of proof by contradiction, Dr. Marks then offered his proof by contradiction that “all positive integers — numbers like 6 or 129, or 10 100 — are interesting.” This portion begins at 19:45 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: If [some Read More ›