Numerical Notation: A Comparative History by Stephen Chrisomalis

By Stephen Chrisomalis

This e-book is a cross-cultural reference quantity of all attested numerical notation platforms (graphic, non-phonetic structures for representing numbers), encompassing greater than a hundred such platforms used during the last 5,500 years. utilizing a typology that defies revolutionary, unilinear evolutionary types of swap, Stephen Chrisomalis identifies 5 simple varieties of numerical notation structures, utilizing a cultural phylogenetic framework to teach relationships among structures and to create a normal thought of swap in numerical platforms. Numerical notation platforms are basically representational structures, no longer computational applied sciences. Cognitive elements that aid clarify how numerical platforms switch relate to normal rules, akin to conciseness or avoidance of ambiguity, which observe additionally to writing platforms. The transformation and alternative of numerical notation platforms pertains to particular social, fiscal, and technological alterations, reminiscent of the improvement of the printing press or the growth of the worldwide world-system.

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Geographic proximity of the regions where two systems were used. All other factors being equal, a system is more likely to have been modeled on one that is used by neighboring groups than on one used more distantly. This is a particularly dangerous criterion to invoke, especially where there is less cultural contact between neighboring regions than with more distant regions. Many times, two very different and unrelated systems are used in proximity to one another, and other times, closely related systems are used at considerable distances from one another.

This extremely naïve view of processes of cultural contact denies entirely the role of imperialism, peer-polity networks, and power structures. For instance, many numerical notation systems developed in societies just as they began to enter into longdistance trading relationships with larger, more politically complex state societies that already possessed numerical notation. Numerical notation, in this instance, is not simply something that happens to be transmitted due to cultural contact; it is a medium through which contact takes place and a feature that becomes important just as societies are becoming integrated into larger intersocietal networks.

Identifying these systems and distinguishing them from other, superficially similar ones helps explain the diffusion of numerical notation throughout the ancient Mediterranean region. 1 The hieratic and demotic systems are too complex to be included on this chart; consult their individual entries for their numeral-signs. 1. Hieroglyphic numerical notation systems System 1 10 100 1000 10,000 100,000 1,000,000 Egyptian hieroglyphic q ù= Å Å Å q r • É• É É É s 0 æ æ t ÿ Æ Æ u‹ ( ) Cretan hieroglyphic Minoan Linear A Mycenean Linear B Cypriote syllabic Hittite hieroglyphic v w ô The hieroglyphic phylogeny of numerical notation systems is ancestral to the Levantine (Chapter 3), Italic (Chapter 4), and Alphabetic (Chapter 5) phylogenies, but its systems differ sharply from those of its descendants.

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