An essay in european ethnomathematics: The social and cultural bases of the vara de Burgos and its relation to the basque septuagesimal system

Abstract

In 1780 the renowned French historian of metrology Alexis Paucton (1780:166, 191-195) argued that the physical length of the "feet" of the vara de Burgos (which are identical to those of the Basque bar standards of Gipuzkoa and Bizkaia) should be adopted as the universal linear standard, rather than the length of the new decimal meter bar standard which at that time had been proposed by a group of French astronomers, including Méchain and Delambre. Although Paucton was unaware of the Basque Septuagesimal System (BSS), his intuition was correct since, as the present study demonstrates, the geometric feet coded into the vara de Burgos produce a remarkably accurate geodetic model (Frank 1997b).Furthermore, given the evidence, the septuagesimal system of coordinates along with its unique celestial and terrestrial cartographic traditions and other related cognitive artifacts, e.g., an ingenious device called the Thread and Pearl Analog Calculator (TPAC) as well as the geometry embedded in the construction of the Basque stone octagons (Frank & Patrick 1993), suggests that the different modes of numerical and geometric thought intrinsic to the BSS should be considered indigenous to Western Europe while the cognitive origins of the system and its ecocentric cosmovision can be traced back to the Iron Age or even before (Frank 1996a; Zaldua 1996). Kurzreferat: Ein Essay über europäische Ethnomathematik:Soziale und kulturelle Grundlagen des vara de Burgos -Maßes und seine Beziehung zum baskischen Septuagesimalsystem. 1780 sprach sich der berühmte Metrologie-Historiker Alexis Paucton dafür aus, die physikalische Länge "feet" des vara de BurgosMaßes als universelles Längenmaß zu nehmen anstelle des neuen dezimalen Längenmaßes, das zu dieser Zeit von einer Gruppe französicher Astronomen, unter ihnen Méchain und Delambre, vorgeschlagen wurde. Obwohl Paucton das baskische Septuagesimalsystem (BSS) nicht kannte, war seine Intuition richtig, denn -wie diese Arbeit zeigt -geometrische Fuß kodiert nach vara de Burgos ergeben ein bemerkenswert genaues geodätisches Modell.Des weiteren wird durch das septuagesimale Koordinatensystem zusammen mit den einzigartigen Traditionen der Himmelsund Erdkartographie und anderen kognitiven Artefakten (wie z.B. ein raffiniertes, Thread and Pearl Analog Calculator genanntes Werkzeug) wie auch durch die Geometrie, die in der Konstruktion der baskischen steinernen Achtecke steckt, nahegelegt, den Ursprung der verschiedenen, dem BSS innewohnenden Arten des numerischen und geometrischen Denkens Westeuropa zuzurechnen, während die kognitiven Ursprünge des Systems und seiner ökozentrischen Kosmovision bis zur Eisenzeit und davor zurückverfolgt werden können.

A Newly Discovered Ethnocultural Substrate along the Atlantic Façade—Evidence for the Unique Counting System and Mathematical Strategies Shared by the Basque Country (Euskal Herria), Spain, France, Ireland and Scotland

“…In 1568, the latter was declared the official bar standard of Spain and all of the Spanish Empire (Bowman 1961, p. 17). That bar standard is identical in length to the one used in Castile and the two Basque provinces of Gipuzkoa and Bizkaia (Frank 1999b).…”

“…This staff was based on the vara de Burgos discussed earlier, a unit that once functioned as the bar standard throughout all of Spain and the Spanish Empire. Meanwhile, lower-ranking officials were charged with carrying a shorter insignia, a half-staff, one half the length of the vara real (Frank 1999b). In the case of Euskal Herria, similar functions were fulfilled by the fieles regidores (faithful rulers).…”

“…Once reconceptualized as a royal scepter, it was no longer viewed exclusively as a measuring device, but rather as a kind of extension of the authority of the Crown (Figure 16). This occurred even though its name vara real 'royal bar' continued to be the same one used to refer to the bar standard of Spain and the Spanish Empire until the adoption of the decimal metric system (Frank 1999b(Frank , 2022.…”