This book is a cross-cultural reference volume of all attested numerical notation systems, encompassing more than 100 such systems used over the past 5,500 years. Using a typology that defies unilinear evolutionary models, Stephen Chrisomalis identifies five basic types of numerical notation systems, tracks relationships between systems, and creates a general model of change that incorporates social, historical, and cognitive factors.

Insights from the history of numerical notation suggest that how humans write numbers is an active choice involving cognitive and social factors. Over the past 5,000 years, more than 100 methods of numerical notation--distinct ways of writing numbers--have been developed and used by specific communities. Most of these are barely known today; where they are known, they are often derided as cognitively cumbersome and outdated. In Reckonings, Stephen Chrisomalis considers how humans past and present use numerals, reinterpreting historical and archaeological representations of numerical notation and exploring the implications of why we write numbers with figures rather than words.

This is the first book to examine comprehensively the major systems of musical notation proposed during the past three centuries. Illustrating the many attempts to improve upon or replace the traditional system, this important work chronologically lists, describes, and critically analyzes the majority of the proposed reforms that have appeared over the years. No other book now available covers the subject in such depth or detail. It is not only a repository of suggested improvements in notation, but also a historical survey of the efforts made to simplify the standard practices.

The content of this book differs from the other volumes of the I Ching Project, because it is a mathematical analysis of the T'ai Hsuan Ching , another Chinese Classic, which is considered to be the lost companion of the I Ching. This research document is based on nine magic squares incorporated on an ancient Tibetan Mandala and the 81 linear line symbols of the T'ai Hsuan Ching, each of which have been given a numerical notation based on the transposition of linear line symbols. The transposition of the three linear line symbols of the I Ching is known and may be represented by the numbers 6, 7, 8 and 9. However, the transposition of the four linear line symbols of the T'ai Hsuan Ching is NOT known. The author's research and mathematical analysis shows that the transposition of these four linear line symbols may be represented by the numbers 1, 2, 3, 4 and 5, which conclusively proves that the T'ai Hsuan Ching may predate The I Ching as a divination oracle.

This two-volume set LNCS 12645-12646 constitutes the refereed proceedings of the 16th International Conference on Diversity, Divergence, Dialogue, iConference 2021, held in Beijing, China, in March 2021. The 32 full papers and the 59 short papers presented in this two-volume set were carefully reviewed and selected from 225 submissions. They cover topics such as: AI and machine learning; data science; human-computer interaction; social media; digital humanities; education and information literacy; information behavior; information governance and ethics; archives and records; research methods; and institutional management.

Based on the results of a third survey, the engineering and programming characteristics of 222 different electronic digital computing systems are given. The data are presented from the point of view of application, numerical and arithmetic characteristics, input, output and storage systems, construction and checking features, power, space, weight, and site preparation and personnel requirements, production records, cost and rental rates, sale and lease policy, reliability, operating experience, and time availability, engineering modifications and improvements and other related topics. An analysis of the survey data, fifteen comparative tables, a discussion of trends, a revised bibliography, and a complete glossary of computer engineering and programming terminology are included.

This book contains a series of commentaries, research notes and illustrations selected from the author's amazing research work. It shows how the notational values (for trigram transposition) which change the ancient symbolic language of the I Ching into a simple numerical language were oringinally derived from the combined symbolic mathematics of the ancient Ho-T'u - The Dragon Horse diagram and the Lo Shu - The Tortoise diagram. This document provides additional conclusive evidence that the originator(s) of the I Ching employed a mathematical system (developed during the Ch'in and Han dynasties) which encompassed a formalistic natural philosophy that sought to embrace the entire world in a system of number symbolism. In addition, the research work contained herein sets out to prove, by using mathematical operand gates methodology, that the destiny/fate of an individual being is dependent upon their own genetic DNA.