Education and Didactics

2001 Submissions

[1] viXra:2001.0023 [pdf] submitted on 2020-01-02 09:59:43

Interpretation of Shannon Entropies with Various Bases by Means of Multinary Searching Games

Authors: Hsuan-Hao Chao, Chang Hsu, Long Hsu, Sien Chi
Comments: 8 Pages.

Ben-Naim used twenty question games to illustrate Shannon entropy with base 2 as a measure of the amount of information in terms of the minimum average number of binary questions. We found that Shannon entropy with base 2 equal to the minimum average number of binary questions is only valid under a special condition. The special condition is referred to as the equiprobability condition, which requires that the outcomes of every question have equal probability, thus restricting the probability distribution. This requirement is proven for a ternary game and a proposed multinary game as well. The proposed multinary game finds a coin hidden in one of several boxes by using a multiple pan balance. We have shown that the minimum average number of weighing measurements by using the multiple pan balance can be directly obtained by using Shannon entropy with base b under the equiprobability condition. Therefore, Shannon entropy with base b can be interpreted as the minimum average number of weighing measurements by using the multiple pan balance when the multiple outcomes have equal probability every time.
Category: Education and Didactics