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Interpreting Interpreter: Combinatorial Plates

This post is a summary of the article “A Combinatorial Approach to Modeling All Possible Golden Plates” by Josh Coates in Volume 66 of Interpreter: A Journal of Latter-day Saint Faith and Scholarship. All of the Interpreting Interpreter articles may be seen at https://interpreterfoundation.org/category/summaries/. An introduction to the Interpreting Interpreter series is available at https:/interpreterfoundation.org/interpreting-interpreter-on-abstracting-thought/.

A video introduction to this Interpreter article is now available on all of our social media channels, including on YouTube at https://youtube.com/shorts/cGCXaR_Jf3I.

 

The Takeaway

Coates provides an analysis of the physical characteristics of the gold plates as well as the script they contained, scouring the historical record to identify the plausible ranges those characteristics could’ve taken. This helps him draw conclusions about the gold content, weight, dimensions, and number of plates, as well as the physical and linguistic density of Reformed Egyptian script.

 

The Summary

In this article, Josh Coates, Executive Director of the B.H. Roberts Foundation, tackles the problem of determining the characteristics of the gold plates. He employs a two-part combinatorial process that evaluates the historical record (don’t sleep on Appendix H, which includes an invaluable list of all historical accounts related to the properties of the plates), assigns reasonable ranges and steps for various properties, calculates all possible combinations of those properties, and then applies filters to eliminate impossible or unsupported configurations. He does this for both the physical properties of the plates themselves as well as the writing present on the plates.

In terms of physical properties, Coates evaluates seven characteristics: plate length, plate width, plate thickness, the void between plates, the weight of the plates, the gold content of the alloy, and the proportion of the plates that were sealed. Starting with over 4 billion combinations, he applies several filters that eliminate 99.9% of those combinations (leaving 37,657), including:

  • Privileging the first-hand accounts of Joseph Smith regarding the size of the plates (at 6” wide, 8” long, and near 6” in height, with Coates assuming about a half-inch margin of error).
  • Using an experiment with 165 fabricated copper discs to obtain a reasonable upper-bound for voids between plates.

In terms of the writing, Coates evaluates three additional properties: character size, translation density, and the number of characters assigned to the lost 116 pages. Using ancient examples of Near East metal engravings and the translation density of various languages, he calculates nearly 2 billion combinations of writing properties, which he then filters based on alignment with the valid physical properties outlined above, as well as two additional filters:

  • Higher translation densities (with Hebrew as the lower bound) based on Moroni’s description of Reformed Egyptian.
  • A reduction of the characters assigned to the 116 pages, based on readings from the Book of Mormon and D&C, which suggest it was a shorter summary of the material on the small plates.

The final result leaves 868,830 valid combinations, which allows him to draw some refined conclusions about the plates’ general properties:

  • Gold content less than 20% (with trace silver and the rest copper)
  • Weight of at least 54 lbs
  • Between 187 and 259 plates
  • Dimensions slightly smaller than Joseph’s description (but within 10%)
  • Character size of less then 5mm2
  • Character density similar to that of Demotic Egyptian.

Coates also helpfully includes a number of appendices that outline his process in detail, including:

  • Algorithms. Coates stepwise process for calculating and discarding combinations based on the resulting height of the plates and the available space for writing.

  • Translation Density Sources. The sources for his calculations of translation density, including translations of Genesis, as well as ancient sources for Demotic and Hieratic.
  • Gold and Copper Alloy. Information on various ancient gold alloys, including tumbaga, which could have the properties required by Coates’ analysis, and which would appear gold after depletion gilding.

  • Plate Void Experiment. Additional details on his copper plate experiment.
  • Nineteenth-Century Tinplate. Historical references to various thicknesses of tinplate to which the plates were compared.
  • Lost 116 Pages. A discussion of the 116 pages and how they’re characterized in the Book of Mormon and D&C.
  • Examples of Valid Combinations. Tables outlining examples at the extremes of valid combinations, as well as those configurations average and standard deviation.
  • Historical Plate Descriptions. An exhaustive and invaluable list of all the historical records that reference the physical properties of the plates.

 

The Reflection

The combinatorial method is a useful one to apply here, and though it produces some flashily large (and largely arbitrary) numbers, what’s most interesting is how many of those possibilities Coates was able to exclude. He was able to eliminate 99.99999999999% of otherwise reasonable options for the characteristics of the book (combining his 4 billion options for physical characteristics and 2 billion for the writing yield 8.3 x 1018 combinations, reduced to 868,830), and, honestly, it’s a bit of a miracle that it wasn’t 100%. Coates’ search could’ve easily turned up no valid combination of characteristics, rendering the plates and any reports of them as an implausible fable. Instead, we have a set of boundaries that help firm up a credible vision of the plates as a grounded, concrete artifact–one that just happens to hold voices from the dust proclaiming God’s continuing love for his children.

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