The book contains lots of interesting information on the history and mathematics of the abacus (and arithmetic in general). The perspective is a bit dated (as is to be expected of a 1971 edition): the basic premises are 1. that the need for computation will grow with the increasing complexity of society (correct) and 2. that electronic computers and even "desk calculators" and slide-rules will always be too expensive to be used for the majority computation tasks (incorrect). Therefore the author investigates if the abacus could in any way be a viable alternative tool for routine computation. Although this question has lost some of its urgency, the book contains a lot of interesting information.The first part gives a broad overview of many aspects of the abacus and some related subjects (the history of number systems, base-10 versus alternative bases, a short history of European abaci and counting boards, basic operations on the abacus). Chapter three ("arithmetic") is sort of a catalogue of shortcuts to basic arithmetic operations, many of them based on pencil-and-paper methods, some on the abacus and a few on other arithmetic tools such as Napier's rods.The second part of the book discusses different designs of the abacus, such as the types generally used in Russia (10 beads per rod), China (5+2 beads per rod) and Japan (4+1 beads per rod), but also some new inventions, for instance with some beads having a negative value. These designs are analysed and compared in terms of efficiency, the main criterion being the average number of bead movements required for addition.One thing I find missing from this book is some historic and cultural background on the abacus in Russia, China and Japan. Apart from that, I think it is covers many intersting subjects; my favourite part is the section that describes the operation of ancient and medieval counting boards and the advantages and disadvantages in comparison to the abacus.
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