Pre-Columbian Measures

Post contributed by

Scripture Central

Abstract

Mosiah’s monetary system has parallels with proposed weights and measures from Mesoamerica and Andean cultures.

Mosiah’s Monetary System

The Nephite monetary system established by King Mosiah is outlined in Alma 11. It is made up of 7 units of silver and 5 of gold, which are described as having the following values:

Value	¹/₈	¹/₄	¹/₂	1	1 ¹/₂	2	4	7
Silver	Leah	Shiblum	Shiblon	Senum		Amnor	Ezrom	Onti
Gold				Senine	Antion	Seon	Shum	Limnah

These values—comprised of whole numbers, fractions, and a mixed fraction—are given in relation to measures of barley or other kinds of grain (Alma 11:7). Unfortunately, the text never clarifies exactly how these units of metal and grain were being measured (whether by weight, volume, etc.). Despite this uncertainty, the primary commodities and their respective values are still present in the text, allowing analysis of their mathematical relationships. With this information in hand, meaningful correlations can be made between the Nephite monetary system and proposed examples from ancient America.

Pre-Columbian Weights and Measures

It has been known for some time that various Andean cultures of South America used systems of weights and measures during pre-Columbian times.¹ To date, no weighing devices or systematized weights have yet been positively identified in Mesoamerica,² where many scholars believe the primary events of the Book of Mormon took place. There is, however, at least one known account of indigenous use of weights and measures in Mesoamerica. According to Della Sprager,

Virtually overlooked is the report of another primary chronicler, Gonzalo Fernandez de Oviedo y Valdes, a Spanish gold-smelting supervisor named Official Chronicler of the Indies. In his accounts is a brief discussion of a sizeable marketplace in the Mayan town of Cachi, Yucatan. In the corner of that market was a building similar to a town hall which housed “their inspectors of weights and measures” and judges who administered immediate justice to wrongdoers.³

Adding to the plausibility of this report, Sprager has identified several possible sets of weights or groups of weighed artifacts from Mesoamerica that date to pre-Columbian times.⁴ These include metal disks, beads, worked stones, and other groupings of assorted items. Their plausible identification as weights (or precisely weighed artifacts) is primarily due to patterns found in their varying measures of mass, as well as their similarities to systems of exchange in South America and the Old World.⁵

A depiction of stone artifacts (3 of 9) from Oaxaca, Mexico that may have served as weights in pre-Columbian times. Image via Sprager, “An investigation of ancient weights,” 110.

Sprager has theorized that weights and measures may have been introduced into Mesoamerica in pre-Columbian times through trade with Andean cultures,⁶ and that they were “needed to weigh precious substances such as metals.”⁷ Not only would it seem strange for Mesoamerican cultures not to have ever used weights and measures,⁸ but there may be valid explanations for why such items and systems could have slipped through the archaeological and historical record undetected.⁹

Doubling

Doubling is the primary mathematical principle involved in the Nephite monetary system, where 9 of the 12 units are described as either being twice as much or half as much as another unit.¹⁰ As explained by Sprager, most ancient sets of weights and measures (including those proposed in Mesoamerica) also implement “some form of doubling, either in mass duplication (pairs) or in masses which double one another.”¹¹ For instance, a set of six disk-shaped slate stones from Huaniqueo, Mexico contain the following weight measurements, some of which adhere to the doubling principle:¹²

Huaniqueo Stones
Item #	Weight in Grams	Doubling
#1	0.35 gm.
#2	0.70 gm.	2 x #1
#3	1.50 gm.	2 x #2
#4	3.80 gm.
#5	4.00 gm.
#6	8.00 gm.	2 x #5

Huaniqueo Stones. Image via Image via Sprager, “An investigation of ancient weights,” 96.

Similarly, a grouping of four proposed Classic-era stone weights (shaped into 3/4 spheres) from the site of Lambityeco in Oaxaca, Mexico “approximately double one another” in mass and “may be considered multiples of the smallest, with a 3% margin of error or less.”¹³

Lambityeco Stones
Item #	Weight in Grams	Doubling
#1	14.7 gm.
#2	30.9 gm.	2 x #1
#3	60.8 gm.	2 x #2
#4	116.0 gm.	2 x #3

Sprager noted that if the mass of the smallest stone (14.7 gm) is “considered the standard for this group, the denominations of the other 3/4-spheres … are those of a classic binary progression: 1,2,4, and 8.”¹⁴ This is similar to the units of the greater numbers of reckoning used by the Nephites, which progressed as 1, 2, 4, 7.

Additive Principle

Another feature of known weights and measures is the additive principle. Essentially, this involves the way that different groupings of units add up or combine together into an important figure in the system. For instance, regarding the disk-shaped Huaniqueo stones, Sprager explains,¹⁵

At first glance the masses of the three tiny discs (#1–3 = 2.55 gm.) appear obtuse in their relationship to the heavier masses of #4, 5, and 6. When considered as individual units, they are. Their combined mass relates clearly, however, to the combined masses of #4–5 (7.8 gm.) and #4–6 (15.8 gm.):

#1–3 = 1/3 (#4–5)

#1-3 = 1/6 (#4–6).

Mosiah’s system of weights and measures also utilizes the additive principle. For instance, the limnah of gold and the onti of silver were both said to be worth the combined total of the smaller units described in each respective system (Alma 11:10, 13). In other words, an onti of silver seems to have been a collective unit which equaled 1 ezrom + 1 amnor + 1 senum. Likewise, the limnah would have been worth 1 shum + 1 seon + 1 senine.

Value	1	2	4	7
Silver	Senum	Amnor	Ezrom	Onti
Gold	Senine	Seon	Shum	Limnah

Also of interest in the Nephite system is the gold antion. Mormon described this unit as being “equal to three shiblons” (Alma 11:19). Thus, the antion, which is a combination of smaller measures, ends up being 1½ times the value of the standard units of gold and silver (the senine and senum). This outcome is similar to the cumulative weight of a set of cobble stones discovered in the Tiristaran community in Michoacan, Mexico. According to Sprager’s analysis, the total weight of the 11 stones in this set was 1½ the standard unit in the set.¹⁶

Fractions

Mosiah’s system of exchange also utilized fractional units, each of which is described as being “half” the value of another unit (Alma 11:15–17). While most pre-Columbian cultures did not utilize written fractions, there is a notable exception. According to John W. Welch,

It comes from the Quiché Maya in highland Guatemala and appears in the Popol Vuh. … Interestingly, the basic way to represent a fraction in Quiché was to add the suffix il to a numeral. In this way, a person would express one-third by adding the suffix il to the number three.¹⁷

Although it is uncertain if the Quiché language has any relationship to languages spoken or written in the Book of Mormon, this at least provides a hint that some other indigenous Mesoamerican societies could potentially utilize fractional units of measurement.

A Contemporary Example

No direct relationship can be suggested, but the Nephite monetary system is actually quite reminiscent of a system used in Guatemalan markets today, which is comprised of six weights with the following measures in ounces: ½ , ½ , 1, 2, 4, 8.¹⁸ The following chart compares these measures with the Nephite system:

System	Unit	Measures
Nephites	senine	¹/₈	¹/₄	¹/₂	1	1 ¹/₂	2	4	7
Guatemala	ounce			¹/₂(x 2)	1		2	4		8

As can be seen, both systems use fractions and whole numbers, both are primarily based on the mathematical principle of doubling, and both have a final weight (or measurement) that is a total of the lesser weights (or measurements) in the system combined.¹⁹ In addition, 4 of the 5 relative weight values in the Guatemalan system (½, 1, 2, 4) are present in the Nephite system.²⁰ While this comparison is with a modern (rather than pre-Columbian) system of weights and measures, it nevertheless demonstrates that the example found in Alma 11 is passable as an authentic system of exchange.

Nested bronze weights. Image via etsy.com.

Conclusion

As noted in the introduction, the proposed identification of weights and precisely weighted items provided by Sprager is not conclusive. Thus, any relationships between Mosiah’s monetary system and those proposed in Mesoamerica must remain tentative. In addition, Mosiah’s system never states that measurements were given in weight, so on that front as well there is uncertainty.²¹ However, even if the Nephite units of measurement weren’t given in weight, and even if the proposed Mesoamerican weights and measures are invalid, the methods and principles involved in Sprager’s analysis would still be relevant.

What emerges from this exploration is that the system described in the Book of Mormon would fit well alongside Sprager’s other proposed examples of Mesoamerican weights and measures, which themselves compare favorably with known systems of weights and measures from the Andes and the Old World.²² In particular, the way that Mosiah’s system utilizes both doubling and additive measures is typical of ancient monetary systems.

John W. Welch, “Weighing and Measuring in the Worlds of the Book of Mormon,” Journal of Book of Mormon Studies 8, no. 2 (1999): 36–45, 86..

John W. Welch, “The Laws of Eshnunna and Nephite Economics,” in Pressing Forward with the Book of Mormon: The FARMS Updates of the 1990s, ed. John W. Welch and Melvin J. Thorne (Provo, UT: FARMS, 1999), 147–149.

John L. Sorenson, “A Mesoamerican System of Weights and Measures? Did the ancient peoples of Mesoamerica use a system of weights and scales in measuring goods and their values?” Journal of Book of Mormon Studies 8, no. 2 (1997): 47, 86–87.

Alma 11:1–20

¹ See Della Hurlbut Sprager, “An investigation of ancient weights and weighing in the complex societies of Mesoamerica and the Andes” (PhD. Dissertation, The University of Texas at Austin, 1994), 20–21, 33–35.
² See Sprager, “An investigation of ancient weights and weighing,” 17–18; John L. Sorenson, “A Mesoamerican System of Weights and Measures? Did the ancient peoples of Mesoamerica use a system of weights and scales in measuring goods and their values?” Journal of Book of Mormon Studies 8, no. 2 (1999): 47, 86–87; John L. Sorenson, Mormon’s Codex: An Ancient American Book (Salt Lake City and Provo, UT: Deseret Book and Neal A. Maxwell Institute for Religious Scholarship, 2013), 443–443.
³ Sprager, “An investigation of ancient weights and weighing,” 8.
⁴ Although not seen as weights or precisely weighted artifacts, a variety of items were used as a medium of exchange in ancient Mesoamerican societies. See, for example David A. Freidel, Marilyn A. Masson, and Michelle Rich, “Imagining a Complex Maya Political Economy: CountingTokens and Currencies in Image, Text and the Archaeological Record,” Cambridge Archaeological Journal 27, no. 1 (2017): 29–54; Steven E. Jones, Samuel T. Jones, and David E. Jones, “Archaeometry Applied to Olmec Iron-ore Beads” in BYU Studies Quarterly 37, no. 4 (1997): 138.
⁵ See Sprager, “An investigation of ancient weights and weighing,” 93–189. See also, Evidence Central, “Book of Mormon Evidence: Ancient Near Eastern Weights and Measures,” August 31, 2020, online at evidencecentral.org; Evidence Central, “Book of Mormon Evidence: Monetary Systems of Mosiah and Eshnunna,” August 31, 2021, online at evidencecentral.org.
⁶ See Sprager, “An investigation of ancient weights and weighing,” 194: “The probable introduction of metallurgy from South America did not necessarily introduce weighing to Mesoamerica, but it did provide a logical vehicle for its possible transmission.” See also pp. 18–19.
⁷ Sprager, “An investigation of ancient weights and weighing,” 21.
⁸ See Sprager, “An investigation of ancient weights and weighing,” 23: “It may be that Mesoamerica was an exceptional civilization in which some metal objects circulated as money, and in which standardized gold ingots were stored but not weighed. The possibility, however, seems highly unlikely.”
⁹ Sprager, “An investigation of ancient weights and weighing,” draws attention to several issues and possibilities: government control over weights and measures may have limited the number of archaeological specimens that could have survived (pp. 9–10, 22); depicting weights and measures may not have been culturally significant in Mesoamerican artwork during pre-Columbian times, in contrast to cultures like Egypt where weights were crucial religious symbols (pp. 15–16); the widespread notion that weights and measures were almost certainly absent in ancient Mesoamerica may be inhibiting investigation or recognition of them by the scholarly community (pp. 17–18, 189–192); there are examples of weights and weight systems (from both the New World and the Old) that are absent in some data sets (physical remains, history, artwork, etc.) even when other types of data suggest they existed (pp. 9–10, 16, 20). Concerning this last point, see also Raz Kletter, Economic Keystones: The Weight System of the Kingdom of Judah, Journal for the Study of the Old Testament Supplement Series 276 (United Kingdom: Sheffield Academic Press, 1998), 106: “The Maneh is mentioned rarely in the Old Testament, but the Kikar is very common. On the other hand, not even one inscribed Maneh or Kikar weight was found in Judah.”
¹⁰ Only the limnah, onti, and antion don’t adhere to this mathematical principle.
¹¹ Sprager, “An investigation of ancient weights and weighing,” 180.
¹² Sprager, “An investigation of ancient weights and weighing,” 96. Note that stone #4 has been slightly damaged, and therefore its original weight be more or less than reported (perhaps being close to the weight of stone #5).
¹³ Sprager, “An investigation of ancient weights and weighing,” 112. While there is a greater total number of relevant stones from this site, the four presented in this evidence summary were all found together in association with the same specific location (Mound 190), and were thus presented as somewhat of a sub-group by Sprager. The following chart assigns their numbers as #1–4 rather than their original designations.
¹⁴ Sprager, “An investigation of ancient weights and weighing,” 112.
¹⁵ Sprager, “An investigation of ancient weights and weighing,” 97.
¹⁶ Sprager, “An investigation of ancient weights and weighing,” 119.
¹⁷ See John W. Welch, “Weighing and Measuring in the Worlds of the Book of Mormon,” Journal of Book of Mormon Studies 8, no. 2 (1999): 41. In p. 86n.14, Welch expresses appreciation to John Sorenson for this information and cites Munro S. Edmonson, The Book of Counsel: The Popol Vuh of the Quiche Maya of Guatemala (New Orleans: Tulane University, 1971), 6; Walter Hough, “Balances of the Peruvians and Mexicans,” Science 21 (1893): 30 [which Welch notes is also cited in John L. Sorenson and Martin H. Raish, Pre-Columbian Contact with the Americas across the Oceans: An Annotated Bibliography (Provo, Utah: FARMS, 1996), 478].
¹⁸ See Sprager, “An investigation of ancient weights and weighing,” 68.
¹⁹ This, of course, only works when fractional units are excluded in the Nephite system (limiting the values to 1 + 2 + 4 = 7) and yet included in the Guatemalan system (expanding the values to ¹/₂ + ¹/₂ + 1 + 2 + 4 = 8). It should be remembered, however, that the Nephite text itself presents the whole-numbered units (1, 2, 4, 7) as a subset in its system, which means that the resemblance on this point isn’t arbitrarily assumed.
²⁰ Considering that Lehi’s family migrated to the New World from Jerusalem around 600 BC, it is noteworthy that limestone weights from the kingdom of Judah have a somewhat similar (bolded) set of values:¹/₂, ²/₃, ⁵/₆, 1, 2, 4, 8, 12, 16, 24, 40. See Raz Kletter, Economic Keystones: The Weight System of the Kingdom of Judah, JSOT 276 (England: Sheffield Academic Press, 1998), 56.
²¹ See John L. Sorenson, “A Mesoamerican System of Weights and Measures? Did the ancient peoples of Mesoamerica use a system of weights and scales in measuring goods and their values?” Journal of Book of Mormon Studies 8, no. 2 (1997): 47, which discusses the Aztec’s propensity to sell everything by volume, rather than weight.
²² See Sprager, “An investigation of ancient weights and weighing,” 25–57, 121–134.

Culture

Weights and Measures

Pre-Columbian Measures

Book of Mormon

Evidence #235 | September 7, 2021

Pre-Columbian Measures