Aztec arithmetic revisited: Land-area algorithms and acolhua congruence arithmetic

Science

Volumn 320, Issue 5872, 2008, Pages 72-77

  Williams, Barbara J ^a   Jorge Y Jorge, María Del Carmen ^b  

^a University of Wisconsin Whitewater at Rock County   (United States)

^b IIMAS UNAM   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

AGRICULTURAL LAND; ALGORITHM; MATHEMATICS;

ALGORITHM; ARITHMETIC; ARTICLE; CALCULATION; DECOMPOSITION; EASTERN HEMISPHERE; HISTORICAL PERIOD; LAND USE; PRIORITY JOURNAL; REFERENCE DATABASE;

AGRICULTURE; ALGORITHMS; HISTORY, 16TH CENTURY; HUMANS; INDIANS, NORTH AMERICAN; MATHEMATICS;

ACOLHUA;

EID: 41749100838     PISSN: 00368075     EISSN: 10959203     Source Type: Journal    
DOI: 10.1126/science.1153976     Document Type: Article

References (23)

1. Located in the Fondo reservado Ms. 1497bis, Biblioteca Nacional de México, Universidad Nacional Autónoma de México (UNAM), Mexico City.
2. Located in the Bibliothèque Nationale de France, Ms. Mexicain 37-39, Paris.
3. H. R. Harvey, B. J. Williams, Science 210, 499 (1980).
4. B. J. Williams, M. C. Jorge y Jorge, Symmetry Cult. Sci. 12, 185 (2001).
5. T. N. Headland, K. L. Pike, M. Harris, Eds., Emics and Etics: the Insider/Outsider Debate (Sage, Beverly Hills, CA, 1990).
6. P. Carrasco, The Tenochca Empire of Ancient Mexico: The Triple Alliance of Tenochtitlan, Tetzcoco, and Tlacopan (Univ. of Oklahoma Press, Norman, OK, 1999).
7. D. Robertson, Mexican Manuscript Painting of the Early Colonial Period: The Metropolitan Schools (Yale Univ. Press, New Haven, CT, 1959).
8. B. J. Williams, H. R. Harvey, The Códice de Santa María Asunción: Households and Lands in Sixteenth Century Tepetlaoztoc (Univ. of Utah Press, Salt Lake City, UT, 1997).
9. Papeles de la embajada americana, Museo Nacional de Antropología, Archivo Histórico, Instituto Nacional de Antropología e Historia, Mexico City.
10. F. de Alva Ixtlilxochitl, Obras históricas de Don Fernando de Alva Ixtlilxochitl, publicadas y anotadas por Alfredo Chavero (Editorial Nacional, Mexico City, 1952).
11. With some exceptions, Tenochca and Acolhua property plans share similar numerical symbols, but with differing values. The cemmatl, "one hand," is the Tenochca standard linear measure and equals two Spanish varas (0.83 m x 2 ∼ 1.67 m). Thus, it is shorter than the Acolhua three-vara "land rod." Unlike the "land rod," the Tenochca cemmatl is typically glyphed by a hand symbol.
12. H. J. Nissen, P. Damerow, R. K. Englund, Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East, trans. P. Larsen (Univ. of Chicago Press, Chicago, IL, 1993).
13. E. Robson, Mesopotamian Mathematics, 2100-1600 BC: Technical Constants in Bureaucracy and Education (Clarendon, Oxford, UK, 1999).
14. Examples of triangular-shaped field area calculations are found in (4).
15. Unless otherwise noted, Spanish translations and metric equivalents of native measures not based on Tepetlaoztoc data are drawn from (21-23).
16. Two integer numbers are congruent "modulus n," where n is an integer, if their remainders are the same when divided by n. For example, 8 and 50 are congruent "modulus 2", 21 and 56 are congruent "modulus 5." 17. Located in the Library of Congress Map Division, Washington, DC; http://memory.loc.gov.
17. H. F. Cline, in Actas y memorias. Thirty-seventh International Congress of Americanists (ICA, Buenos Aires, 1968), vol. 3, pp.119-38.
18. H. R. Harvey, in Land and Politics in the Valley of Mexico: A Two-Thousand-Year Perspective, H. R. Harvey, Ed. (Univ. of New Mexico Press, Albuquerque, NM, 1991), pp. 163-185.
19. In ethnohistorical sources, considerable confusion surrounds the definitions and lengths of lower arm measures (codos in Spanish, cubits in English, in Nahuatl specifically the cenmolicpitl, cenmatzotzopaztli, cemomitl), all of which vary only by a few centimeters.
20. M. Matías Alonso, Medidas indígenas de longitud (Centro de Investigaciones y Estudios Superiores en Antropología Social, Mexico City, 1984).
21. V. M. Castillo, Estud. Cult. Nahuatl 10, 195 (1972).
22. L. Reyes García, E. Celestino Solís, A. Valencia Ríos, C. Medina Lima, G. Guerrero Díaz, Documentos nahuas de la Ciudad de México del siglo XVI (Centro de Investigaciones y Estudios Superiores en Antropología Social, Archivo General de la Nación, Mexico City, 1996).
23. We gratefully acknowledge the Departamento de Matemáticas y Mecánica at Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas-UNAM for research and technical support. The expertise of A. C. Pérez Arteaga was indispensable for research, design, and various iterations of the database, and graphics preparation. We thank A. R. Rodríguez for data entry.