On the Glitch Phenomenon

TL;DR

This paper introduces the Glitch Principle, explaining how devices making discrete decisions based on continuous inputs can experience arbitrarily long decision times, grounded in a mathematical framework of continuity.

Contribution

It formalizes the Glitch Principle using a mathematical setting involving continuity of function mappings, providing a rigorous foundation for understanding glitches in decision devices.

Findings

Glitch phenomenon arises from continuity properties of decision devices.

Mathematical framework links device behavior to continuous mappings.

The principle explains delays in decision-making processes.

Abstract

The Principle of the Glitch states that for any device which makes a discrete decision based upon a continuous range of possible inputs, there are inputs for which it will take arbitrarily long to reach a decision. The appropriate mathematical setting for studying this principle is described. This involves defining the concept of continuity for mappings on sets of functions. It can then be shown that the glitch principle follows from the continuous behavior of the device.