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E-grāmata: Reckonings: Numerals, Cognition, and History

4.00/5 (18 ratings by Goodreads)
  • Formāts: 264 pages
  • Sērija : The MIT Press
  • Izdošanas datums: 15-Dec-2020
  • Izdevniecība: MIT Press
  • Valoda: eng
  • ISBN-13: 9780262360883
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  • Formāts: 264 pages
  • Sērija : The MIT Press
  • Izdošanas datums: 15-Dec-2020
  • Izdevniecība: MIT Press
  • Valoda: eng
  • ISBN-13: 9780262360883
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"An anthropological exploration of evolving number systems and how they are used, and eventually displace, by newer number systems"--

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 Most of these are barely known today; where they are known, they are often derided as cognitively cumbersome and outdated.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.

Chrisomalis shows that numeration is a social practice. He argues that written numerals are conceptual tools that are transformed to fit the perceived needs of their users, and that the sorts of cognitive processes that affect decision-making around numerical activity are complex and involve social factors. Drawing on the triple meaning of reckon&;to think, to calculate, and to judge&;as a framing device, Chrisomalis argues that the history of numeral systems is best considered as a cognitive history of language, writing, mathematics, and technology.

Chrisomalis offers seven interlinked essays that are both macro-historical and cross-cultural, with a particular focus, throughout, on Roman numerals. Countering the common narrative that Roman numerals are archaic and clumsy, Chrisomalis presents examples of Roman numeral use in classical, medieval, and early modern contexts. Readers will think more deeply about written numbers as a cognitive technology that each of us uses every single day, and will question the assumption that whatever happened historically was destined to have happened, leading inevitably to the present.

Acknowledgments vii
Introduction: Three reckonings xi
Note: On "Western numerals" xv
1 I The limits of numerical cognition
1(26)
Constraints against universals and particulars
3(3)
Constraining infinity
6(3)
Constraining spoken and written numbers
9(8)
The 99% problem
17(3)
Constraint, history, and cognition
20(7)
2 II Conspicuous computation
27(28)
Dynamic philology
28(5)
Conspicuous computation
33(13)
Roman numerals redux
46(5)
Conclusion
51(4)
3 III The decline and fall of the Roman numerals, I: Of screws and hammers
55(36)
Evaluating the merits of numerical notations
57(8)
Screws, hammers, and Roman numerals
65(11)
Awareness and metanotational commentary
76(10)
From awareness to causation
86(5)
4 IV The decline and fall of the Roman numerals, II: Safety in numbers
91(32)
Three kinds of frequency dependence
92(8)
Networks and frequency in communication systems
100(3)
Roman and Western numerals: A case study in frequency dependence
103(13)
Conclusion
116(7)
5 V Number crunching
123(22)
Sequoyah's numerals
126(7)
A quinary quandary
133(6)
Outnumbering the Cherokee numerals
139(6)
6 VI How to choose a number
145(38)
Agency without variation
152(6)
Blended modalities
158(4)
Hybrid modalities
162(6)
Parallel modalities
168(6)
Code choice
174(5)
Conclusion
179(4)
7 VII To infinity and beyond?
183(26)
Is your number system weird?
183(3)
Is the past like the present?
186(4)
Why is there no medieval anthropology?
190(4)
What is the future of numeral systems?
194(9)
What are the limits on human variation?
203(6)
Notes 209(4)
Bibliography 213(24)
Index 237