{"id":87,"date":"2025-03-17T23:43:33","date_gmt":"2025-03-17T23:43:33","guid":{"rendered":"https:\/\/tracefleemangarcia.com\/trXiv\/?p=87"},"modified":"2025-03-18T23:38:46","modified_gmt":"2025-03-18T23:38:46","slug":"did-african-divination-lead-to-computer-science-probably-not","status":"publish","type":"post","link":"https:\/\/tracefleemangarcia.com\/trXiv\/2025\/03\/17\/did-african-divination-lead-to-computer-science-probably-not\/","title":{"rendered":"Did African divination lead to computer science? Probably not"},"content":{"rendered":"\n

Ron Eglash, a mathematician-cum<\/em>-anthropologist at the University of Michigan School of Information, makes an interesting claim: that geomancy, particularly the sort practiced by Ifa and Bamana diviners in Africa, is at the very origin of computer science.1<\/a><\/sup> Such a claim is intriguing, of course, especially given my own interest in astrology’s relation to computing — including through similar pathways that Eglash identifies, such as Llull and Leibniz.2<\/a><\/sup> However, Eglash’s history is lacking — and, it seems, easily disproven.<\/p>\n\n\n\n

Geomancy, or the science of the sand<\/h2>\n\n\n\n

To begin, a short description of geomancy is needed. Geomantia<\/em> is a Latin translation of the Arabic \u0639\u0644\u0645 \u0627\u0644\u0631\u0645\u0644 eilm alraml<\/em>, the “science of the sand”. Originally, a diviner would create a set of random arrays of points, without counting. Depending on whether or not these arrays were composed of an odd or even number of points, he would compose them into figures of four lines of one or two dots. When he has four of these figures, he treats them as “mothers” (Latin: matres<\/em>), using a basic sort of binary arithmetic to generate an entire divinatory “shield diagram,” which can be interpreted — of course — to predict the future or give information about a certain set of affairs.<\/p>\n\n\n\n

\"\"
A geomantic chart from The Geomancie of Master Christopher Cattan Gentleman.<\/em> This book (not this particular manuscript) may have been owned and annotated by William Oughtred, the inventor of the slide rule: the most widely-used analog computer until the invention of digital calculators.<\/figcaption><\/figure>\n\n\n\n

Eglash hypothesizes geomancy originated in Sub-Saharan Africa,3<\/a><\/sup> was transmitted to the Islamic world, where it made its way to Europe, inspiring the development of Llull’s ars generalis<\/em>, often cited as a forefather of modern computers.4<\/a><\/sup> Llull’s influence on Leibniz (who Norbert Wiener called “the patron saint of cybernetics” for his invention of mechanical calculating machines) is explicit in his doctoral dissertation De arte combinatoria<\/em>.5<\/a><\/sup> Thus, this portion of the genealogy is relatively well-founded.6<\/a><\/sup><\/p>\n\n\n\n

The first link in the chain (or perhaps scala geomantae<\/em>) is more tenuous, to say the least — Eglash claims that “geomancy is strikingly out of place in non-African systems” but seems to ignore the clear similarities between geomancy and Yijing<\/em> divination, the latter of which is attested centuries before the former. More importantly, there is clear evidence of mathematical knowledge being transmitted from China to the Muslim world, e.g. magic squares.7<\/a><\/sup> This is not to say that I believe there is evidence for a genetic relationship — personally, I believe an indigenous Arab invention most likely — but it as at least as likely, if not more so, than a sub-Saharan African invention. For the purposes of this article, though, the particular origins of geomancy are besides the point.<\/p>\n\n\n\n

Llull and geomancy<\/h2>\n\n\n\n

I will let Eglash speak for himself:<\/p>\n\n\n\n

\n

While Raymond Lull, like other European alchemists, created wheels with sixteen divination figures, his primary interest was in the combinatorial possibilities offered by base-2 divisions. Lull’s work was closely examined by German mathematician Gottfried Leibniz, whose Disseratio de arte combinatoria<\/em>, published in 1666 when he was twenty, acknowledges Lull’s work as a precursor. Further exploration led Leibniz to introduce a base-2 counting system, creating what we now call the binary code. While there were many other influences in the lives of Lull and Leibniz, it is not far-fetched to see a historical path for base-2 calculation that begins with African divination; runs through the geomancy of European alchemists, and is finally translated into binary calculation, where it is now applied in every digital circuit from alarm clocks to supercomputers.<\/p>\n<\/blockquote>\n\n\n\n

These claims are repeated in his TED talk<\/a>, though without mention of Llull. Likewise, this claim has been repeated in both popular media and in other academic works. In short, however, this entire paragraph is emphatically incorrect.<\/p>\n\n\n\n

In an earlier version of this chapter published in American Anthropologist<\/em>,8<\/a><\/sup> Eglash makes his source for these ideas explicit: the occultist and professor Stephen Skinner.9<\/a><\/sup> Skinner’s own hypothesis, however, is much more subtle. Rather than painting Llull as a geomancer, he posits that the “possibilities of combining Lullian wheels with geomancy might in fact prove a fruitful field for speculation”, given that some of Llull’s sixteen-chambered figures appear agreeable to the sixteen geomantic figures, and that later geomancers have used circular diagrams which resemble Llullian wheels, such as that of the 17th century author Henry de Pisis, who devised a volvelle (a paper wheel) to produce the four matres<\/em>. Skinner’s own hypothesis is the inverse of Eglash: it was Llull who inspired geomancers, rather than vice-versa. Indeed, Skinner notes that Llull was no fan of geomancy: though Llull “talks slightingly of the art of geomancy”, his wheels “are of interest to the geomancer.” Llull criticizes geomancers in Arbre de la ci\u00e8ncia<\/em> and provides a refutation in Tractatus novus<\/em>:<\/p>\n\n\n\n

\n

He observes that a man may set out on a journey to buy wheat, spending many days before reaching the market. Naturally, this man passes under the influence of many constellations before reaching his destination. Suppose that, at the end of his travels, this man inquires of a geomancer what he is planning to purchase and the sage, after casting points, suggests “iron or silver.” If geomancy were an absolute science, the man would have to change his purpose and buy something other than wheat, which is clearly not the case. He suggests the real purpose behind these false prophets is lucre: “per so que los p\u00fascan enguanar e d’\u00e9ls dines aver”.10<\/a><\/sup><\/p>\n<\/blockquote>\n\n\n\n

One should note that Eglash consistently refers to Llull as an alchemist, despite Llull’s well-documented distaste for alchemy. The historical Llull actively argued against the transmutation of metals, but his later students did not accept this and seemed to have authored a number of alchemical and magical works in his name, such as the immensely popular Liber de secretis naturae seu de quinta essentia<\/a><\/em>.<\/p>\n\n\n\n

\"\"
Pseudo-Llullian wheel employed for alchemy in a 1498 manuscript of Liber de secretis naturae seu de quinta essentia<\/em><\/figcaption><\/figure>\n\n\n\n

Thus it seems that Eglash is taking the pseudo-Llullian alchemical corpus at face value.11<\/a><\/sup> Though I have found no pseudo-Llullian works which mention or discuss geomancy, they may exist. This being said, in any case, Leibniz was no geomancer, and almost certainly did not view Llull as one, either. I have only found one mention of geomancy in Leibniz’s work, which occurs in the Discourse on Metaphysics<\/em>, in which he passingly calls it a “ridiculous art.”<\/p>\n\n\n\n

Leibniz and the (alleged) Chinese origin of binary<\/h2>\n\n\n\n

If not geomancy, then where did Leibniz get binary arithmetic? From a strictly historical view, it was an independent invention — and Leibniz was not the first, being preceded in this in the West by Francis Bacon, John Napier, and Juan Caramuel y Lobkowitz.12<\/a><\/sup> However, Leibniz himself did not believe he invented binary. Per Sypniewski, “he thought that his binary number system was a rediscovery of a system known to the ancient Chinese, but forgotten or corrupted by them over the course of the ages”, as discussed in his Discourse on the natural theology of the Chinese<\/em>, perhaps inspired by his reading of the Jesuit-produced Confucius sinarum philosophus<\/em>:13<\/a><\/sup><\/p>\n\n\n\n

\n

Fohi,14<\/a><\/sup> the most ancient prince and philosopher of the Chinese, had understood the origin of things from unity and nothing, i.e., his mysterious figures reveal something of an analogy to Creation, containing the binary arithmetic (and yet hinting at greater things) that I rediscovered after so many thousands of years, where all numbers are written by only two notations, 0 and 1.<\/p>\n<\/blockquote>\n\n\n\n

Interestingly, Leibniz claims that \u4f0f\u7fb2 F\u00fax\u012b had “knowledge of the science of combinations” — I cannot find the original (presumably Latin) text of this work, but I would assume his verbatim description is ars combinatoria<\/em>. Thus, Leibniz more likely saw an affinity between the Llullian art and the Yijing<\/em> rather than with geomancy.<\/p>\n\n\n\n

Conclusion<\/h2>\n\n\n\n

To conclude this short diatribe, I agree with Skinner that Llull has something to offer geomancers, and this can be a fruitful inquiry — I will continue to scour the pseudo-Llullian corpus for discussions of geomancy. And to a certain degree, I agree with Eglash: computer science is at least partially rooted in medieval and Renaissance occultism. However, his more particular claims are problematic, if not easily-refuted.<\/p>\n\n\n\n

There is something to be said, however, about the nature of historical genealogy here. The great semiotician, novelist, and historian Umberto Eco wrote in one of his several accounts of Llull15<\/a><\/sup> that<\/p>\n\n\n\n

\n

…the Ars<\/em> thus became a calculus with meaningless symbols. This is a state of affairs that shows how much progress Llullism has made, providing tools for our contemporary theoreticians of artificial and computerized languages, while betraying the pious intentions of Ramon Llull. And that to reread Llull today as if he had had an inkling of computer science (apart from the obvious anachronism) would be to betray his intentions. All Llull had in mind was speaking of God and convincing the infidel to accept the principles of the Christian faith, hypnotizing them with his whirling wheels. So the legend that claims he died a martyr\u2019s death in Muslim territory, though it may not be true, is nonetheless a good story.<\/p>\n<\/blockquote>\n\n\n\n

Insofar as Llull is an ancestor of modern computer science — and through him, Ifa, the zairja, the shih, or whatever mystic art truly inspired him — then in an age of meaningless generative large-language models which continually belt out mass-produced slop, the plot has truly been lost. For the ancient babalawo, Ifa is divine communion with the Yoruba pantheon. For the medieval adept of the \u4e09\u5f0f sanshi<\/em> “three boards”, calculation, ritual, and artifact are fused in a single microcosm of the astral plane. For Llull, his ars<\/em> was a divinely-inspired missionary tool that would unite the world under Christendom. To read any of these figures as computer scientists is to betray their intentions. <\/p>\n\n\n\n

Footnotes<\/h2>\n\n\n
  1. Eglash, R. (1999). African fractals: Modern computing and indigenous design<\/em>. Rutgers University Press. \u21a9\ufe0e<\/a><\/li>
  2. Fleeman Garcia, T. (2025). Astral computers in Asia<\/a><\/em>. \u21a9\ufe0e<\/a><\/li>
  3. Interestingly, Eglash does not seem to reference Abayomi-Cole, a Sierra Leonean doctor and minister who insisted on the complex mathematics of Ifa divination as an Indigenous African science a century before him. See Bos, C. (2022). John Augustus Abayomi Cole and the Search for an African Science, 1885\u20131898. Isis<\/em>, 113<\/em>(1), 63\u201384. https:\/\/doi.org\/10.1086\/718388<\/a> \u21a9\ufe0e<\/a><\/li>
  4. Sales, T. (1997). Llull as computer scientist or why Llull was one of us. In M. Bertran & T. Rus (Eds.), Transformation-Based Reactive Systems Development<\/em> (pp. 15\u201321). Springer. https:\/\/doi.org\/10.1007\/3-540-63010-4_2<\/a> \u21a9\ufe0e<\/a><\/li>
  5. Leibniz, G. W., Mugnai, M., Ruler, H. van, & Wilson, M. (2020). Leibniz: Dissertation on the combinatorial art<\/em>. Oxford University Press. \u21a9\ufe0e<\/a><\/li>
  6. Eco, U. (with Oldcorn, A.). (2014). From the Tree to the Labyrinth: Historical Studies on the Sign and Interpretation<\/em>. Harvard University Press. https:\/\/doi.org\/10.4159\/9780674728165<\/a> \u21a9\ufe0e<\/a><\/li>
  7. Wilson, R., & Watkins, J. J. (Eds.). (2013). Combinatorics: Ancient & Modern<\/em>. Oxford University Press. \u21a9\ufe0e<\/a><\/li>
  8. Eglash, R. (1997). Bamana sand divination: Recursion in ethnomathematics. American Anthropologist<\/em>, 99<\/em>(1), 112-122. \u21a9\ufe0e<\/a><\/li>
  9. Skinner, S. (1980). Terrestrial Astrology: Divination by geomancy<\/em>. Routledge-Kegan Paul. \u21a9\ufe0e<\/a><\/li>
  10. Lucas, J. (2003). Tempting Fate: The Case against Astrology and the Catalan Response. Catalan Review<\/em>, 17<\/em>(2), 123-139. \u21a9\ufe0e<\/a><\/li>
  11. Normally this is commendable, but he does it unconsciously. Ramon Llull as a complex, contradictory, even ghostly figure, existing in a web of social relations which produce the figure of the doctor illuminatus<\/em>, writing long after his death in magical apocrypha, is far more interesting to me than a stringent focus on a historical man whom little is known about for certain. \u21a9\ufe0e<\/a><\/li>
  12. Ares et al<\/em> call Leibniz the “self-proclaimed inventor of the binary system” and accuse him of plagiarizing the Spanish Caramuel, but it is hard to see this as anything other than a nationalistic rant — given the authors are all based at Spanish universities and the fact that Leibniz explicitly attributed binary to none other than the mythical sage-king \u4f0f\u7fb2 F\u00fax\u012b as discussed. See Ares, J., Lara, J., Lizcano, D., & Mart\u00ednez, M. A. (2018). Who Discovered the Binary System and Arithmetic? Did Leibniz Plagiarize Caramuel? Science and Engineering Ethics<\/em>, 24<\/em>(1), 173\u2013188. https:\/\/doi.org\/10.1007\/s11948-017-9890-6<\/a> \u21a9\ufe0e<\/a><\/li>
  13. Sypniewski, B. P. (2005). China and Universals: Leibniz, Binary Mathematics, and the Yijing Hexagrams. Monumenta Serica<\/em>, 53<\/em>, 287\u2014314. \u21a9\ufe0e<\/a><\/li>
  14. An older transliteration of \u4f0f\u7fb2 F\u00fax\u012b. \u21a9\ufe0e<\/a><\/li>
  15. Eco, U. (with Oldcorn, A.). (2014). From the Tree to the Labyrinth: Historical Studies on the Sign and Interpretation<\/em>. Harvard University Press. https:\/\/doi.org\/10.4159\/9780674728165<\/a> \u21a9\ufe0e<\/a><\/li><\/ol>\n\n\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    Ron Eglash, a mathematician-cum-anthropologist at the University of Michigan School of Information, makes an interesting claim: that geomancy, particularly the sort practiced by Ifa and Bamana diviners in Africa, is at the very origin of computer science. Such a claim is intriguing, of course, especially given my own interest in astrology’s relation to computing —…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"pagelayer_contact_templates":[],"_pagelayer_content":"","footnotes":"[{\"content\":\"Eglash, R. (1999). African fractals: Modern computing and indigenous design<\/em>. Rutgers University Press.\",\"id\":\"c1646c56-7d2d-4306-ba09-efef71a83944\"},{\"content\":\"Fleeman Garcia, T. (2025). Astral computers in Asia<\/a><\/em>. \",\"id\":\"c24157f9-6d06-463e-8255-cc1ce58b0332\"},{\"content\":\"Interestingly, Eglash does not seem to reference Abayomi-Cole, a Sierra Leonean doctor and minister who insisted on the complex mathematics of Ifa divination as an Indigenous African science a century before him. See Bos, C. (2022). John Augustus Abayomi Cole and the Search for an African Science, 1885\u20131898. Isis<\/em>, 113<\/em>(1), 63\u201384. https:\/\/doi.org\/10.1086\/718388<\/a>\",\"id\":\"c8fae92b-f909-4165-a2ac-8b2105bf06b4\"},{\"content\":\"Sales, T. (1997). Llull as computer scientist or why Llull was one of us. In M. Bertran & T. Rus (Eds.), Transformation-Based Reactive Systems Development<\/em> (pp. 15\u201321). Springer. https:\/\/doi.org\/10.1007\/3-540-63010-4_2<\/a>\",\"id\":\"7d7db728-7d73-4406-a015-2b242f7f7af3\"},{\"content\":\"Leibniz, G. W., Mugnai, M., Ruler, H. van, & Wilson, M. (2020). Leibniz: Dissertation on the combinatorial art<\/em>. Oxford University Press.\",\"id\":\"5a17374e-8ee2-4e3d-b720-9a4f39fd2398\"},{\"content\":\"Eco, U. (with Oldcorn, A.). (2014). From the Tree to the Labyrinth: Historical Studies on the Sign and Interpretation<\/em>. Harvard University Press. https:\/\/doi.org\/10.4159\/9780674728165<\/a>\",\"id\":\"e7decfc9-b325-42d7-88dc-4625055d4a95\"},{\"content\":\"Wilson, R., & Watkins, J. J. (Eds.). (2013). Combinatorics: Ancient & Modern<\/em>. Oxford University Press.\",\"id\":\"5be73f9e-e62a-4aa6-a24d-2b353a006b32\"},{\"content\":\"Eglash, R. (1997). Bamana sand divination: Recursion in ethnomathematics. American Anthropologist<\/em>, 99<\/em>(1), 112-122.\",\"id\":\"addede0d-3b44-44d9-ba0c-bf0d85c0a8a6\"},{\"content\":\"Skinner, S. (1980). Terrestrial Astrology: Divination by geomancy<\/em>. Routledge-Kegan Paul.\",\"id\":\"5b5bc180-2b33-4523-876e-a6a8a56c8ef0\"},{\"content\":\"Lucas, J. (2003). Tempting Fate: The Case against Astrology and the Catalan Response. Catalan Review<\/em>, 17<\/em>(2), 123-139.\",\"id\":\"8c528d7b-ad99-4b13-9df8-a10f2e22b44f\"},{\"content\":\"Normally this is commendable, but he does it unconsciously. Ramon Llull as a complex, contradictory, even ghostly figure, existing in a web of social relations which produce the figure of the doctor illuminatus<\/em>, writing long after his death in magical apocrypha, is far more interesting to me than a stringent focus on a historical man whom little is known about for certain.\",\"id\":\"acc38e6d-7f0b-49ec-939c-fbda06e126f6\"},{\"content\":\"Ares et al<\/em> call Leibniz the \\\"self-proclaimed inventor of the binary system\\\" and accuse him of plagiarizing the Spanish Caramuel, but it is hard to see this as anything other than a nationalistic rant -- given the authors are all based at Spanish universities and the fact that Leibniz explicitly attributed binary to none other than the mythical sage-king \u4f0f\u7fb2 F\u00fax\u012b as discussed. See Ares, J., Lara, J., Lizcano, D., & Mart\u00ednez, M. A. (2018). Who Discovered the Binary System and Arithmetic? Did Leibniz Plagiarize Caramuel? Science and Engineering Ethics<\/em>, 24<\/em>(1), 173\u2013188. https:\/\/doi.org\/10.1007\/s11948-017-9890-6<\/a> \",\"id\":\"7b09eb38-e0e8-49c8-97e6-4e36c8f9c409\"},{\"content\":\"Sypniewski, B. P. (2005). China and Universals: Leibniz, Binary Mathematics, and the Yijing Hexagrams. Monumenta Serica<\/em>, 53<\/em>, 287\u2014314.\",\"id\":\"16ece51c-ed86-40ff-be1a-59e38e9be326\"},{\"content\":\"An older transliteration of \u4f0f\u7fb2 F\u00fax\u012b.\",\"id\":\"03fe559e-e1af-4298-89cf-e1fe2c2ff03f\"},{\"content\":\"Eco, U. (with Oldcorn, A.). (2014). From the Tree to the Labyrinth: Historical Studies on the Sign and Interpretation<\/em>. 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