Combinatorial art

Combinatorial art is the systematic production and examination of possible combinations, presented in the novel as a bridge between Renaissance mnemonic schemes, early calculating machines, and modern computers. Its promise is to organize scattered signs into a decipherable whole; its danger is that the capacity to connect everything can make coincidence appear conclusive and invention seem real.

From historical method to imagined machine

The concept enters the characters’ reconstruction of how the Jesuits might have pursued the Templar map. Diotallevi argues that they understood what the Templars of Provins and the Baconian camp had not: the map could be reconstructed through ars combinatoria, a procedure anticipating electronic computation. He connects this method to Father Kircher’s reading of combinatorial treatises extending back to Lullus and to Kircher’s Ars Magna Sciendi. The claim does not merely assign the Jesuits a store of secret documents; it gives them a way to process accumulated information systematically.

Belbo dismisses the resulting diagrams as resembling a crochet pattern, but Diotallevi insists that they represent all possible combinations. He links their operation to factor analysis, the Sefer Yesirah, and temurah, the permutation of letters. The proposed method thus moves between mathematical enumeration and esoteric interpretation: permutations are at once a calculable procedure and a key to concealed meaning.

The narrative distinguishes an abstract model from an instrument capable of executing it. Conceiving a map from a polar projection is one task; determining how many trials would be needed to find its solution is another. Listing every possible combination is not the same as building a mechanism to carry them out. Kircher and his disciple Schott are therefore imagined as constructing devices with perforated cards—“computers ante litteram,” or binary calculators. The sequence makes the historical claim vivid while exposing its recursive logic: modern computing is projected backward into old combinatorial schemes, which in turn acquire new authority from the resemblance.

The Jesuit computer and its comic names

The characters turn the supposed machinery into a series of computer-age puns. IBM becomes lesus Babbage Mundi and lesum Binarium Magnificamur; AMDG, conventionally expanded as Ad Maiorem Dei Gloriam, is recast as Ars Magna, Digitale Gaudium; and IHS becomes lesus Hardware & Software. These playful expansions fuse Jesuit devotion, combinatorial art, and digital technology into a single imagined genealogy.

The jokes do more than decorate the hypothesis. Their confidence and ingenuity enact the very operation under discussion: familiar letter groups are recombined until they seem to disclose a hidden history. The transformations make the proposed link between religious orders and modern technology feel both irresistible and patently manufactured. Combinatorial art is therefore shown not only as a method attributed to the Jesuits but also as a narrative technique by which the characters produce evidence for their own theory.

From combinations to universal conspiracy

That technique expands beyond machines and historical records into a total theory of society. Casaubon describes a secret organization whose worldwide branches conspire to spread the rumor that a universal conspiracy exists. The formulation folds the suspicion back on itself: even belief in a plot becomes evidence of a plot to make people believe in plots. It offers an explanation for why patterns seem to multiply without requiring any single, verifiable central plan.

The characters state the method’s premise with deliberate extremity: if even one fact in the universe does not reveal a mystery, hermetic thought is violated. The Templars consequently become the universal connector, the order said to have something to do with everything. This is combinatorial reasoning released from any stopping rule. Rather than testing which associations hold, it treats the possibility of another link as a reason to continue linking.

The Plan gives that procedure a practical and disturbing consequence. The men admit that they began by making unwarranted associations and regarded their work as a parody of the Diabolicals’ logic. Yet repeated research and the habit of connecting everything altered their thinking. The narrator recognizes that pretending to believe can become indistinguishable from belief. He describes the three men’s different trajectories: he was becoming addicted, Diotallevi corrupted, and Belbo converted. What began as a consciously playful method had trained its practitioners to lose the distinction between resemblance and identity, metaphor and fact.

Fabrication, belief, and the empty secret

The method’s most consequential demonstration is the Plan itself. The men invent a nonexistent scheme, but others accept it as real and identify fragments of their own confused mythologies as episodes in its logical web of analogy, resemblance, and suspicion. Once those believers act on the supposed scheme, invention acquires effects in the world: the Plan exists socially because people behave as if it exists. The book’s combinatorial procedure has not uncovered a concealed master design; it has helped create one by giving disparate materials a structure that its audience wants to recognize.

Casaubon’s reflections on conspiracy explain why such a structure takes hold. Frustration and guilt invite the invention of an enemy who can be blamed for failures that would otherwise seem accidental or self-produced. Competing groups attribute their own designs to one another, and their accusations can encourage mutual collaboration in sustaining the imagined plot. The resulting pattern is self-reinforcing: suspicion supplies the connections, while each new connection appears to confirm the suspicion.

The final account of Belbo’s secret brings the method to its sharpest limit. His refusal to disclose a secret persuades his captors that it must be immense; his insistence that he has none makes them more certain that he does. Their search, sustained across centuries, has bound them together, yet disclosure threatens to disappoint them and to abolish the mystery that gives their group meaning. The sought-after secret is therefore not a final piece of information waiting at the end of a successful calculation. It is an empty secret whose apparent depth increases as it remains unavailable. Combinatorial art can keep generating connections indefinitely, but the novel’s bleak conclusion is that an inexhaustible search for meaning may produce not knowledge of a hidden whole, but a whole made persuasive by the search itself.