“Dowsing rods and transmutative alchemy, mining tools and popular magic have all been analysed by modern historians. Mathematics, on the other hand, is surprisingly missing from historical accounts of mines, caves, and the underground world.”
-from Underground Mathematics (2022) by Dr Thomas Morel
In early March, a team from the ScanPyramids project confirmed the existence of a hidden corridor in the Great Pyramid of Giza. Particularly exciting about the news was how the scientists made the discovery. According to National Geographic, they used “a technology called muon radiography—which uses cosmic ray particles to probe objects and construct 3-D models of their insides”.
Techniques like this–which would have mystified ancient treasure-hunters–have revolutionised the mining and archaeological sectors, enabling engineers and researchers to safely and precisely identify, measure, and extract natural resources and artefacts that otherwise would have remained invisible.
Similarly innovative advancements, mutatis mutandis, were also made in the early modern Holy Roman Empire during the rise of the mining surveyor. Unlike the scholastici vagantes, who relied on spellcraft and mischievous spirits to guide them to long-buried riches, these mining surveyors and masters devised unique mathematical systems to map the subterranean world. They even developed their own mining language: Bergmannsprache.
The work of these practical mathematicians was critically important for the expansion and security of various European states–many of whose economies depended on ores like silver, gold, and cobalt.
To learn more about the world and practices of the mining surveyors, The Thinker’s Garden spoke with Dr Thomas Morel, the author of Underground Mathematics: Craft Culture and Knowledge Production in Early Modern Europe. Published in December 2022, Morel’s book has been described as providing “unprecedented insights into mining surveyors’ activities and the art-science of underground geometry”.
The Custodian: What are mining maps and how were they used in the early modern era?
Dr Thomas Morel: First of all, one should remember that early modern metallic mines, although they could be long and deep, were ultimately networks of narrow, sinuous tunnels. Miners followed the minable veins looking for silver ore (but also cobalt, gold, antimony…), which was then extracted to be refined in smelting huts. What they avoided was digging into the surrounding “deaf” stone, because it was extremely hard, and therefore slow and costly.
So this is a situation where people travelled through many underground routes, but could hardly tell exactly where they were (“for one cannot see through stone” was a common saying at the time to express that something was impossible).
The first uses of maps, in that context, was to settle concession disputes. Limits were set at the surface, using big carved stones, and had to be respected underground–in fact the very name of local surveyors was Markscheider, which translates into something as “stone/mark setters”. To do this, mining officials would measure with cords and compasses, coming up with the idea of recording the measurements on paper. Thus mining maps were born.
The uses of maps then evolved; when dark powder was introduced, it became cheaper and quicker to dig in straight lines in the “deaf” stone. Authorities quickly seized the opportunity to connect the countless sinuous galleries into unified underground districts. These operations involved a good deal of geometry–and more precise maps.
A final stage, reached around the middle of the eighteenth century, was even closer to our modern engineering: surveyors began to plan draining galleries and other major works directly on paper. While such modern maps seem unremarkable, it amazes me to see the confidence people slowly built up in measurements and geometry!
C: Could you tell us more about the political and economic side of underground mathematics?
TM: When I began working on the mathematics of mining, I expected to deal with a lot of dry technical stuff. It turned out quickly that the main factors that defined and constrained extractive operations were not technical, but belonged to the politics and economy of the “mining states”. In the Holy Roman Empire, silver fuelled the rise of the Hapsburg and Saxony states, and their leaders carefully designed the legal framework of mining.
The concession system–mentioned above–was meant to spur investments by securing property. Maps and marking stones were concrete objectification tools to avoid intractable conflicts. Unlike the King of France for instance, German rulers did not seize underground properties; they designed a legal framework and then taxed private investors from Nuremberg or Venice.
In that context, underground mathematics really was the keystone of the whole system. It was meant to ensure trust and objectivity; measurements were often public, and could be publicly challenged too. Surveys were couched on papers in books and maps; this data served as a memory of the mines and was often used during trials.
In the book, I carefully analysed what I call a “culture of accuracy”, which was amazingly much broader and more concrete than the academic mathematics of the time. Beyond politics and economy, underground mathematics even became an important topic in the religious literature of the time, as a genre of mining sermons developed.
C: What was the relationship between scholarly writers on mining and the surveyors/mining masters themselves?
TM: The relationship between artisans and scholars was ambiguous, and I wanted the book to show its many facets. Historians such as Pamela Long have shown that the “skilled” and the “learned” did not ignore each other, but could sometimes learn from one another. Analysing Georgius Agricola’s famous mining treatise, the De re metallica (1556), I was able to show that although the author thoroughly knew the mining disciplines, its Latin book was written for a learned audience and does not conveys the real mathematics of mining in detail.
Still, scholars from Leibniz to Paracelsus were attracted by mining regions and frequently visited mines–to the point where mining masters had to introduce “guest books”, to make sure that no visitors got lost and forgotten in the mines.
Some university professors wrote theoretical treatises on underground mathematics, the so-called geometria subterranea, and in some cases harshly criticised the practitioners. Still, others were more open and had a genuine curiosity for the vernacular knowledge of craftsmen. The last chapter deals with Jean-André Deluc, reader to the English Queen Charlotte and fellow of the Royal Society. Deluc visits deep silver mines to experiment with his barometer and really collaborates with the mining administration: this includes the mining master, obviously, but also rank-and-file surveyors. The learned and the skilled could therefore interact when they met around common issues: How to best use instruments? How to control errors? How can quantification be applied in the natural world?
C: Who spoke Bergmannsprache? How did it first emerge and when did it fall out of use?
TM: The Bergmannsprache literally means the “language of miners”. We would describe it today as a German dialect–in fact a sociolect–used by communities of German-speaking miners and craftsmen all around Central and Eastern Europe, but also in Scandinavia and beyond. Its emergence is hardly documented, but its numerous verbs and nouns can already be found in documents from the from the Middle Ages. It developed in the Renaissance, as numerous innovations in mining emerged. Here’s an example: How do you name the cart used to transport mining ore? It’s obviously a mining hund (a dog), because of the sound the cart makes when pushed along underground rails.
Most of the early modern authors on mining, no matter in which language they write, provided their readers with dictionaries or glossaries. Christian Wolff, the famous philosopher and mathematician, advertised on the title page of his Mathematisches Lexicon (1716) that he had included “the dialects and idioms of mine surveyors”.
Contemporaries often criticised the mining dialect; it was found to be esoteric, or mystery-mongering. I try to reverse this perspective by providing some insight into its concrete use. One would not complain that a physicist or a biologist uses complex words: arts and science need their own concepts, because they deal with very specific objects. That is the same, I argue, with craftsmen and miners. Their Bergmannsprache was a codified, fast evolving language needed to deal with the challenges of mining.
C: What other projects are you currently working on?
TM: I recently moved from a French to a German university, so I am adapting to a new academic system, which is in itself interesting. It is a great place to continue working on early modern mathematical practitioners, and I am trying to expand the range of my research. I am trying to characterise the “slow rise of mathematics” in the Renaissance and beyond, among merchants, teachers, master builders, and so on.
The development of algebra, calculus and academic mathematics is fairly well-known. What interests me is rather how the culture of accuracy that I observed among miners developed in other contexts. How did common people learned to count and measure, and how did this change over time? In which ways were fairly basic arithmetic and geometry used in daily business, and which were the epistemic consequences? I am convinced that it is an inconspicuous, low-key movement that in the long run had a great impact on our modern understanding of numbers and quantification!