Shannon Revisited: Considering a More Tractable Expression to Measure and Manage Intractability, Uncertainty, Risk, Ignorance, and Entropy

TL;DR

This paper proposes a new, adaptable measure called MARK to better quantify and manage uncertainty, intractability, and progress in complex knowledge-driven activities by refining traditional entropy concepts.

Contribution

It introduces a novel formula for Missing Acquirable Relevant Knowledge (MARK) that improves upon Shannon's entropy by focusing on relevant knowledge within an 'interval of interest.'

Findings

MARK effectively tracks progress towards specific challenges.

The approach corrects distortions in traditional entropy measures.

It enhances optimization in research, risk management, and opportunity exploitation.

Abstract

Building on Shannon's lead, let's consider a more malleable expression for tracking uncertainty, and states of "knowledge available" vs. "knowledge missing," to better practice innovation, improve risk management, and successfully measure progress of intractable undertakings. Shannon's formula, and its common replacements (Renyi, Tsallis) compute to increased knowledge whenever two competing choices, however marginal, exchange probability measures. Such and other distortions are corrected by anchoring knowledge to a reference challenge. Entropy then expresses progress towards meeting that challenge. We introduce an 'interval of interest' outside which all probability changes should be ignored. The resultant formula for Missing Acquirable Relevant Knowledge (MARK) serves as a means to optimize intractable activities involving knowledge acquisition, such as research, development, risk management, and opportunity exploitation.