Editing Inca Empire (section)

=== Measures, calendrics and mathematics ===
{{Main|Mathematics of the Incas}}
[[File:Inca. Quipu.jpg|thumb|Quipu, 15th century. [[Brooklyn Museum]]]]

Physical measures used by the Inca were based on human body parts. Units included fingers, the distance from thumb to forefinger, palms, [[cubit]]s and wingspans. The most basic distance unit was ''thatkiy'' or ''thatki'' or one pace. The next largest unit was reported by Cobo to be the ''topo'' or ''tupu'', measuring 6,000 ''thatkiy''s, or about {{convert|7.7|km|1|abbr=on}}; careful study has shown that a range of {{convert|4.0|to|6.3|km|1|abbr=on}} is likely. Next was the ''wamani'', composed of 30 ''topo''s (roughly {{convert|232|km||disp=or|abbr=on}}). To measure area, 25 by 50 wingspans were used, reckoned in ''topo''s (roughly {{convert|3280|km2||disp=or|abbr=on}}). It seems likely that distance was often interpreted as one day's walk; the distance between ''tambo'' way-stations varies widely in terms of distance, but far less in terms of time to walk that distance.{{sfn|D'Altroy|2014|pp=246–247}}{{sfn|McEwan|2008|pp=179–180}}

Inca [[calendar]]s were strongly tied to [[astronomy]]. Inca astronomers understood [[equinox]]es, [[solstice]]s and [[zenith]] passages, along with the [[Transit of Venus|Venus cycle]]. They could not, however, predict [[eclipse]]s. The Inca calendar was essentially [[lunisolar]], as two calendars were maintained in parallel, one [[solar calendar|solar]] and one [[lunar calendar|lunar]]. As 12 lunar months fall 11 days short of a full 365-day solar year, those in charge of the calendar had to adjust every winter solstice. Each lunar month was marked with festivals and rituals.{{sfn|D'Altroy|2014|pp=150–154}} Apparently, the days of the week were not named and days were not grouped into weeks. Similarly, months were not grouped into seasons. Time during a day was not measured in hours or minutes, but in terms of how far the sun had travelled or in how long it had taken to perform a task.{{sfn|McEwan|2008|pp=185–187}}

The sophistication of Inca administration, calendrics and engineering required facility with numbers. Numerical information was stored in the knots of ''[[quipu]]'' strings, allowing for compact storage of large numbers.<ref name="NYT-20160102">{{cite news |last=Neuman |first=William |title=Untangling an Accounting Tool and an Ancient Incan Mystery |url=https://www.nytimes.com/2016/01/03/world/americas/untangling-an-accounting-tool-and-an-ancient-incan-mystery.html |archive-url=https://ghostarchive.org/archive/20220103/https://www.nytimes.com/2016/01/03/world/americas/untangling-an-accounting-tool-and-an-ancient-incan-mystery.html |archive-date=3 January 2022 |url-access=subscription |url-status=live |date=2 January 2016 |publisher=[[The New York Times]] |access-date=2 January 2016}}{{cbignore}}</ref>{{sfn|McEwan|2008|pp=183–185}} These numbers were stored in [[base-10]] digits, the same base used by the Quechua language<ref>{{cite web |url=http://www.arch.cam.ac.uk/~pah1003/loe/Eng/SupplInfo/2008Heggarty.htm |title=Supplementary Information for: Heggarty 2008 |website=arch.cam.ac.uk |access-date=24 September 2012 |url-status=dead |archive-url=https://web.archive.org/web/20130312203340/http://www.arch.cam.ac.uk/~pah1003/loe/Eng/SupplInfo/2008Heggarty.htm |archive-date=12 March 2013}}</ref> and in administrative and military units.{{sfn|D'Altroy|2014|pp=233–234}} These numbers, stored in ''quipu'', could be calculated on ''[[yupana]]s'', grids with squares of positionally varying mathematical values, perhaps functioning as an [[abacus]].<ref>{{cite web |url=http://www-history.mcs.st-and.ac.uk/HistTopics/Inca_mathematics.html |title=Inca mathematics |website=history.mcs.st-and.ac.uk |access-date=24 September 2012}}</ref> Calculation was facilitated by moving piles of tokens, seeds or pebbles between compartments of the ''yupana''. It is likely that Inca mathematics at least allowed division of integers into integers or fractions and multiplication of integers and fractions.{{sfn|McEwan|2008|p=185}}

According to mid-17th-century Jesuit chronicler Bernabé Cobo,<ref>Cobo, B., (1983 [1653]), Obras del P. Bernabé Cobo, Vol. 1, Edited and preliminary study By Francisco Mateos, Biblioteca de Autores Españoles, vol. 91, Madrid, Ediciones Atlas.</ref> the Inca designated officials to perform accounting-related tasks. These officials were called quipo camayos. Study of khipu sample VA 42527 (Museum für Völkerkunde, Berlin)<ref>{{cite journal |last=Sáez-Rodríguez |first=A. |date=2012 |title=An Ethnomathematics Exercise for Analyzing a Khipu Sample from Pachacamac (Perú) |journal=Revista Latinoamericana de Etnomatemática |volume=5 |issue=1 |pages=62–88 |url=http://www.revista.etnomatematica.org/index.php/RLE/article/view/37}}</ref> revealed that the numbers arranged in calendrically significant patterns were used for agricultural purposes in the "farm account books" kept by the khipukamayuq (accountant or warehouse keeper) to facilitate the closing of accounting books.<ref>{{cite journal |last=Sáez-Rodríguez |first=A. |date=2013 |title=Knot numbers used as labels for identifying subject matter of a khipu |journal=Revista Latinoamericana de Etnomatemática |volume=6 |issue=1 |pages=4–19 |url=http://www.revista.etnomatematica.org/index.php/RLE/article/view/52}}</ref>