22 March 2024
Geometric symbol systems from the Medici Papal Library bear structural similarities to dynastic Egyptian notation separated by millennia and geography. The conventional explanation — coincidence — is not an explanation at all.
In the study of symbol systems, there is a category of finding that is simultaneously easy to observe and nearly impossible to discuss in professional settings. It is the observation that geographically and temporally isolated civilizations sometimes produce symbol systems that are, at the level of geometric structure, remarkably similar.
The standard response to such observations is “coincidence” — or, when the observer is being treated with slightly more courtesy, “convergent evolution.” Just as unrelated species may develop similar physical structures in response to similar environmental pressures (the eye of an octopus and the eye of a mammal, for instance), unrelated cultures may develop similar symbols because the range of simple geometric forms available to a human hand holding a marking instrument is finite. Circles, triangles, lines, crosses, spirals — there are only so many basic shapes, and it would be surprising if different civilizations did not produce overlapping symbol sets.
This argument is sound, as far as it goes. It goes less far than its proponents typically assume.
The argument from geometric limitation explains why multiple cultures independently develop circles, triangles, and crosses as basic elements of their symbolic repertoires. It does not explain why specific combinations of these elements — particular arrangements of lines and curves into compound symbols with consistent internal proportions — appear in systems separated by thousands of years and thousands of miles. The probability of two cultures independently producing the same simple shape is high. The probability of two cultures independently producing the same complex compound symbol, with the same internal geometric relationships, is considerably lower. The probability of two cultures independently producing dozens of structurally similar compound symbols is low enough that “coincidence” stops functioning as an explanation and starts functioning as a refusal to investigate.
This paper examines one such case: the structural similarities between symbol systems found in manuscripts from the Medici Papal Library (fifteenth and sixteenth centuries CE, Florence and Rome) and hieroglyphic notation from dynastic Egypt (primarily New Kingdom, circa 1550-1070 BCE). The systems are separated by approximately three thousand years and fifteen hundred miles. They belong to entirely different cultural contexts — one European Christian, the other ancient Egyptian. There is no documented transmission pathway between them. And yet, when the symbols are subjected to geometric analysis, the correspondences are difficult to dismiss.
I am aware that this territory is perilous. Symbol comparison across cultures has a long and unfortunate history of being conducted by enthusiastic amateurs who see what they wish to see, ignore what does not fit, and arrive at conclusions that range from the merely unfounded to the spectacularly irresponsible. I have no interest in contributing to that tradition. What I want to do is describe the geometric data as precisely as I can, acknowledge the limitations of my analysis, and ask whether the correspondences I have identified warrant further investigation by someone with more resources than I currently possess.
The Medici family's relationship with esoteric knowledge is well documented by mainstream Renaissance historians. Cosimo de' Medici (1389-1464) funded the translation of the Corpus Hermeticum — a collection of Greek texts attributed to Hermes Trismegistus, themselves a synthesis of Greek philosophical and Egyptian religious thought — commissioning Marsilio Ficino to produce the Latin translation that became one of the foundational texts of Renaissance Neoplatonism. Cosimo's grandson Lorenzo de' Medici continued the family's patronage of scholars working at the intersection of classical philosophy, esoteric tradition, and what would later be called “natural magic” — the study of hidden correspondences between celestial, natural, and human systems.
This patronage was not marginal to the Renaissance. It was central. The intellectual program that the Medici funded — the recovery and synthesis of ancient knowledge systems, including Egyptian, Greek, Hermetic, and Kabbalistic traditions — was the engine of Renaissance humanism. The Platonic Academy that Cosimo established in Florence was explicitly modeled on what its founders believed the ancient Alexandrian academy had been. The Medici were not collecting curiosities. They were attempting to reconstruct a knowledge system that they believed had been fragmented and lost.
Within the Medici collections — now dispersed across the Biblioteca Medicea Laurenziana in Florence, the Vatican Library (following the Medici papacy of Leo X and Clement VII), and several private collections — there exist manuscripts containing symbol systems that are typically categorized under the heading of “magical sigils.” These are geometric symbols associated with the invocation or communication with spiritual intelligences — angels, planetary spirits, and other entities within the Neoplatonic cosmological hierarchy.
The most relevant manuscripts for this analysis include:
Texts attributed to or derived from the tradition of Heinrich Cornelius Agrippa (1486-1535), whose De Occulta Philosophia systematized Renaissance magical practice and included extensive tables of sigils associated with planetary intelligences. Agrippa drew explicitly on earlier Arabic sources (particularly the Picatrix and the Ghayat al-Hakim), which themselves drew on late antique Hellenistic sources, which drew on — the chain becomes murky at this point, but the direction points consistently toward Egypt.
Manuscripts in the tradition of the Ars Notoria — a medieval system of “notory art” that employed complex geometric figures as objects of contemplation, believed to confer knowledge directly upon the practitioner through sustained visual engagement with the symbols. The Ars Notoria tradition predates the Renaissance and has roots in thirteenth-century Europe, but the Medici collections contain elaborated versions with geometric complexity that exceeds the earlier manuscripts significantly.
Sigil tables from various grimoire traditions preserved in the Papal Library collections — the institutional heir to significant portions of the Medici holdings. These tables present symbols organized by planetary and elemental correspondence, with each sigil consisting of a compound geometric figure constructed from lines, curves, circles, and angular elements arranged in specific proportional relationships.
I want to be absolutely clear about what these manuscripts represent within their own cultural context. They are magical texts. They belong to a tradition that mainstream scholarship classifies as “Western esotericism” — a category that is studied seriously by historians of religion and ideas (the field has produced excellent work, notably from scholars at the University of Amsterdam's Center for History of Hermetic Philosophy) but which is not typically examined for its geometric or structural content. The symbols are studied as cultural artifacts — expressions of Renaissance magical thinking — rather than as geometric objects with measurable properties.
This is, I believe, an oversight. Whatever one thinks of the metaphysical claims embedded in these manuscripts, the symbols themselves are physical objects with quantifiable geometric properties. They have proportions. They have angular relationships. They have internal structural logic. These properties can be measured and compared without reference to the metaphysical framework in which they are embedded, just as one can measure the acoustic properties of a cathedral without subscribing to the theology that motivated its construction.
I have discussed, in a previous paper on frequency encoding at the Karnak Temple Complex, a set of anomalous hieroglyphic sequences that resist standard linguistic parsing and whose geometric properties suggest a non-linguistic function — specifically, the encoding of acoustic frequency relationships. I will not repeat that analysis here. What I want to focus on is a subset of Egyptian symbolic notation that falls outside the standard hieroglyphic repertoire and which appears in contexts associated with what Egyptologists term heka — the Egyptian concept typically translated as “magic” but more accurately understood as the application of creative power through knowledge of hidden correspondences.
The relevant sources include:
The Coffin Texts and the Book of the Dead — funerary literature containing symbolic notation that accompanies but is distinct from the standard hieroglyphic text. Certain vignettes include geometric figures that are not hieroglyphs, are not purely decorative, and whose function within the funerary context is not fully understood. Egyptologists typically classify these as “protective symbols” or “magical diagrams” — designations that describe their presumed function without explaining their geometric structure.
Temple inscriptions at Dendera, Edfu, and Philae — late period temples whose walls contain symbol sets that, like the anomalous sequences at Karnak, do not resolve to standard linguistic readings. The Dendera ceiling, in particular, contains geometric arrangements that have resisted classification within the standard Egyptological framework.
Papyri from the Leiden and London collections — Greco-Egyptian magical papyri (PGM) dating from the second century BCE to the fifth century CE, representing the late period synthesis of Egyptian, Greek, and Jewish magical traditions. These papyri contain extensive symbol tables — known as charaktêres — that are neither Greek letters nor Egyptian hieroglyphs but compound geometric figures with consistent internal proportions.
The charaktêres of the Greco-Egyptian magical papyri are particularly relevant because they represent a documented point of contact between Egyptian symbolic traditions and the Mediterranean esoteric traditions that eventually fed into Renaissance magic via Arabic intermediaries. The transmission chain is: Egyptian temple tradition → Greco-Egyptian synthesis → Arabic translation and elaboration → medieval European reception → Renaissance systematization by figures like Ficino and Agrippa. At each stage, the metaphysical framework changed. The question is whether the geometric content changed with it, or whether something was transmitted through the frameworks that was not dependent on any particular framework.
I conducted geometric analysis of 142 sigils from the Medici-tradition manuscripts and 89 symbols from the Egyptian sources described above, using the same measurement methodology I developed for the Karnak frequency-encoding analysis: height-to-width ratios, angular relationships between major strokes, proportional spacing between component elements, and the presence or absence of specific structural features (enclosed spaces, radiating lines, bilateral symmetry, rotational symmetry, and connecting nodes).
I want to describe what I found, and I want to describe it carefully, because the data is genuinely strange and I do not want to overstate it.
Of the 142 Medici-tradition sigils analyzed, 67 (47 percent) share three or more structural features with at least one symbol in the Egyptian corpus. “Structural features” here means specific geometric properties: a circle enclosing a triangle, radiating lines from a central node at consistent angular intervals, parallel horizontal lines crossed by a diagonal at a specific angle range, and similar compound arrangements.
Forty-seven percent is high. It is higher than I expected. It is also, I must acknowledge, potentially inflated by the finite geometric vocabulary available to any symbol-maker working with straight lines, curves, and basic shapes. Some degree of overlap is expected.
However.
When I moved beyond structural features to proportional analysis — measuring the specific ratios between component elements within symbols — the correspondence pattern became more difficult to explain through geometric limitation alone.
In 31 of the 67 structurally similar pairs, the proportional relationships between component elements agreed to within 8 percent. This means that not only were the symbols composed of similar elements in similar arrangements, but the relative sizing of those elements — the ratio of the inner circle to the outer boundary, the proportion of the radiating line to the overall symbol height, the angular spacing between repeated elements — matched with a specificity that exceeds what random variation in the construction of similar shapes would predict.
Thirty-one symbol pairs with proportional agreement within 8 percent, drawn from systems separated by three thousand years.
I do not know what to make of this. I present the data.
The most unexpected finding concerns the angular relationships within compound symbols. Both the Medici sigils and the Egyptian charaktêres show a strong preference for specific angles between component lines: 36 degrees, 72 degrees, 108 degrees, and 144 degrees. These are all multiples of 36 — the angles of a regular pentagon and its associated star polygon (the pentagram).
In the Medici corpus, 61 percent of measurable angles between major strokes fall within 5 degrees of a multiple of 36. In the Egyptian corpus, 54 percent.
For comparison, I generated a control set of 200 random compound geometric symbols using a basic geometric construction algorithm (random line-and-curve combinations within bounded areas) and measured the same angular relationships. In the random set, 19 percent of angles fell within 5 degrees of a multiple of 36 — consistent with the mathematical expectation for random angles in a bounded space.
The Egyptian and Medici systems both show a pentagonal angular preference that is roughly three times higher than random chance predicts. They share this preference with each other. And the pentagonal geometry that generates these angles has a deep connection to the golden ratio (phi = 1.618...) — the same mathematical relationship that I have identified in the harmonic structure of Bach's cello suites and in the proportional architecture of the Karnak Temple Complex.
I am going to resist the urge to connect these threads prematurely. The data suggests a connection. The mechanism of that connection is unclear. Possible explanations range from the mundane (human visual preference for pentagonal symmetry, which is documented in perceptual psychology) to the extraordinary (a transmitted tradition of geometric construction that predates both the Egyptian and European systems and was independently preserved in each).
I present the data. The explanation is not yet mine to give.
The most economical explanation for the correspondences I have described is direct transmission — the Medici-era sigils were derived, through a chain of intermediate sources, from the Egyptian originals. This is not controversial in principle. Renaissance scholars explicitly claimed Egyptian ancestry for their magical traditions. Ficino translated the Corpus Hermeticum precisely because it purported to be Egyptian wisdom. Agrippa cited Egyptian sources. The entire intellectual project of Renaissance Hermeticism was an attempt to recover what its practitioners believed was ancient Egyptian knowledge.
The question is whether the transmission preserved geometric content — specific proportional relationships and angular preferences — across three millennia of cultural translation. The metaphysical content clearly transformed: Egyptian heka became Greco-Egyptian theurgy, became Arabic al-sihr, became medieval European magia, became Renaissance philosophia occulta. At each stage, the theoretical framework was reimagined to suit the receiving culture. But did the symbols themselves carry forward their geometric properties through these transformations, like a melody that survives translation into different keys?
If so, this would suggest that the geometric content of the symbols was understood, by at least some practitioners in the transmission chain, as distinct from and more fundamental than the metaphysical framework. The framework changed. The geometry persisted. This implies that someone, at each stage of the chain, recognized that the geometry mattered — that it was not merely decorative but carried information that needed to be faithfully reproduced even as the explanation for why it mattered was repeatedly reimagined.
There is an alternative possibility that I find more unsettling and more interesting: that the geometric correspondences are not the product of direct transmission at all. That the Egyptian and Medici systems arrived at similar geometric structures independently — not through coincidence and not through cultural contact, but because both systems were attempting to engage with the same underlying phenomenon, and the geometry they produced reflects the structure of that phenomenon rather than the structure of either culture.
This is, I recognize, a claim that I cannot substantiate with the data I have. It is a hypothesis. But it is a hypothesis that is consistent with the proportional correspondences, the angular clustering, and the pentagonal geometry that appears in both systems and that also appears in the acoustic architecture of ancient temples, in the mathematical structure of certain musical compositions, and in the resonant properties of certain natural materials — threads I have discussed in previous papers and which I am increasingly unable to consider in isolation from one another.
I debated whether to include this section. It moves the paper from the territory of unconventional scholarship into territory that most of my former colleagues would consider disqualifying. I include it because the data is relevant and because excluding relevant data on the grounds that it is uncomfortable is the exact methodological failure I have spent this paper criticizing.
In the course of my research into anomalous aerospace events — a subject I have addressed in a separate paper — I became aware of a case in which an individual with no background in ancient symbol systems, Egyptology, or Renaissance esotericism reported an anomalous encounter during which he observed, among other things, symbols displayed on what he described as the interior surface of a craft. The individual subsequently reproduced these symbols from memory. His drawings have been shared and discussed within the anomalous aerospace research community.
My interest was not in the individual's account of how he encountered the symbols — I have no means of evaluating that account and no opinion on it. My interest was in the symbols themselves, because when I first saw them, I recognized structural features that I had spent decades measuring on the walls of Egyptian temples.
I conducted the same geometric analysis on twelve of the reproduced symbols that I had applied to the Medici and Egyptian corpora. The sample is too small for statistical rigor. I acknowledge this. What I can report is the following:
Of the twelve symbols, eight share three or more structural features with symbols in both the Egyptian and Medici corpora. Five show proportional correspondences within 10 percent — a wider margin than I applied to the Medici-Egyptian comparison, reflecting the lower precision of symbols reproduced from memory versus symbols copied from manuscripts or carved in stone.
The angular clustering is present. The reproduced symbols show a preference for pentagonal angles (multiples of 36 degrees) at a rate of approximately 48 percent — lower than the Egyptian or Medici systems but substantially higher than the random baseline of 19 percent.
I do not know what to do with this. A man with no training in ancient symbol systems reproduced symbols that share geometric properties with notational traditions spanning three millennia. The symbols are not identical. They are not copies. But they exhibit the same geometric grammar — the same proportional preferences, the same angular clustering, the same compound structural logic — that appears in the Egyptian charaktêres and the Medici sigils.
If the individual fabricated the symbols — if he studied Egyptian and Renaissance sources and constructed his drawings to resemble them — then he accomplished a feat of geometric mimicry that implies a level of analytical sophistication he has never claimed to possess. If he reproduced what he actually saw, the question of why what he saw shares geometric properties with three-thousand-year-old symbol systems is one that I am not equipped to answer.
I present the data. I leave the interpretation to others. I note only that the conventional response — “coincidence” — has, by this point in the analysis, accumulated enough weight that the word has ceased to explain and has begun merely to obstruct.
I want to close with a speculation that I cannot prove and that I include because this paper would be incomplete without it.
If the geometric correspondences between the Egyptian, Medici, and anomalous symbol systems are not coincidental and not fully explained by cultural transmission, then one possibility remains: the geometry reflects something real. Not culturally real — physically real. A structure or pattern that exists independently of the cultures that have attempted to represent it, and that different cultures, encountering it through different means, have encoded using different metaphysical frameworks but consistent geometric language.
This is not as exotic a proposition as it may sound. We already know that certain geometric patterns appear repeatedly in nature — the Fibonacci spiral in shells and galaxies, the hexagonal geometry of honeycombs and basalt columns, the fractal self-similarity of coastlines and bronchial trees. These patterns recur not because they are culturally transmitted but because they are expressions of underlying physical principles. The geometry is in the world. Cultures that observe the geometry and attempt to record it will produce similar representations, not because they are copying each other but because they are copying the same source.
What if the symbols in question — the Egyptian charaktêres, the Medici sigils, the anomalous drawings — are records of an encounter with a geometric structure that exists outside the cultures that have recorded it? A structure that is perceptible under certain conditions, that different traditions have interpreted as spiritual, magical, or otherworldly, but that is, at its foundation, a pattern as natural and as real as a Fibonacci spiral?
I do not know whether this is true. I know that the geometry is consistent. I know that the consistency exceeds what coincidence explains. And I know that the geometry is connected — through pentagonal proportions and golden-ratio relationships — to the same mathematical structures that appear in acoustic architecture, in harmonic frequency relationships, and in the resonant properties of certain materials.
These threads are converging. I do not yet see the full pattern. But I see enough to know that the convergence is real, and that the conventional boundaries between disciplines — Egyptology, acoustics, materials science, symbology — are preventing anyone from seeing the whole.
I continue to look.
Correspondence: leh [at] 442423N1042233W.com
Note: High-resolution images of the Medici sigil corpus referenced in this paper are available upon request. The Egyptian source materials are documented in the published catalogs of the Leiden, London, and Cairo collections. I invite anyone with access to photogrammetric measurement tools and the relevant manuscript collections to replicate and extend this analysis.