Umberto Eco is like the grandparent who tries to be interested in videogames, but just doesn’t get it. On page two of his new book, “On Literature” (Harcourt, 334 pages, $26), he writes, “I am told that there is now a generation of digital hackers who, not having ever read a book in their lives, have now enjoyed Don Quixote for the first time thanks to the e-book.” He does so in good fun – but not, realistically, in good faith. Hackers are nerds, and no one enjoys Don Quixote as their first book.

The author whose “Foucault’s Pendulum” famously contains, on a single page, the plot of “The Da Vinci Code,” is quite given to networks, to conspiracies, to patterns. His embarrassing avidity for new technologies represents an admirable optimism. For Mr. Eco, people change, and paradigms really do shift. Indeed, they shift more for him than they do for the rest of us.

Mr. Eco’s “History of Beauty” (Rizzoli, 438 pages, $40) co-authored with Girolamo de Michele, is like an art history textbook organized around an offbeat history of ideas rather than periods or schools. “In Renaissance culture and mentality, there came into being centrifugal forces whose thrust was toward a disquieting, nebulous, and surprising Beauty … a process that only briefly and often only apparently crystallized into set, clearly defined figures,” as his co-author writes.

Thus Mannerism – think Durer’s self-portrait as Jesus – for example, “expresses a thinly veiled conflict within the soul,” born between “the impossibility of rejecting the artistic heritage of the previous generation and a sense of extraneousness to the Renaissance world.” Mannerism is, then, not a brief set of artists working between the Renaissance and the Baroque, but an antithetical thread woven throughout the whole epoch.

Mr. Eco’s totalizing imagination seizes upon the Middle Ages. His chapter on “Beauty as Proportion and Harmony,” savors the “grand theory” of proportion, in which everything is related to everything else. “Medieval culture started from an idea of Platonic origin (which, moreover, was also being developed at the same time within the Jewish mystical tradition) whereby the world is seen as a huge animal, and therefore as a human being, while a human being was like the world.” Mr. Eco traces numerical correspondences between macrocosm and microcosm, which, he says, were also aesthetic correspondences.

This is patently the vision of the semiotician, who must observe synchronicities across languages and read human meaning in etymologies. But in his new collection of occasional essays, Mr. Eco belabors the epistemological fantasy – of arcane networks, of library as universe and vice versa – that animates his fiction and complements the semiotician’s mind.

In the essay “Betweeen La Mancha and Babel,” Mr. Eco imagines a “Magnum Opera,” a situation in which angels would write a daily book of each man’s thoughts, which would be cross-referenced with already existing divine books. These catalogs would be employed by “Defending Angels” at Judgment Day. Different angels would make different connections, and compendia and miscellanies – new books – would proliferate, until “We will have an astronomical infinity of books, each of which hovers between different worlds, and the result will be that we regard as fictitious stories that others have considered true.”

To common sense, this stupendous result undermines Mr. Eco’s premises just as a too-high sum might indicate faulty computation. To Mr. Eco such a vision is a validation of his wonder and curiosity. It gives a prized sensation of vertigo, a high, a thrill. Borges is not far away, but neither is Dan Brown.

An essay defends Dante’s “Paradiso” against the great Italian critic De Sanctis, who admired “the throngs of splendors” but found there were no real characters in them, and that “the songs of the souls are devoid of content.” This would also be our critique of Mr. Eco’s visions of infinite pattern. He casts this argument, somewhat disingenously, as the belief “that poetry exists only in representations of the carnal passions and those of the heart, and that poetry of pure understanding cannot exist.”

He has, quite justifiably, identified a real prejudice. Yet what is this “poetry of pure understanding”? Mr. Eco’s history of art is organized around changing concepts of beauty. He refuses to take art for granted as a self-responsible phenomenon. He insists on telling the story of paintings in terms of ideas. Typically, he explains that color replaced form as the “cause of beauty” in “the century in which Roger Bacon was proclaiming that optics was the new science destined to solve all problems.”

By always pointing his pen toward “pure understanding,” rather than toward the paintings themselves, Mr. Eco has produced an exquisite book of reproductions that are neglected by the accompanying texts. To further distress his pages, Mr. Eco supplies tiny columns of philosophical excerpts, by Nietzsche or Plato, printed in cobalt blue on white. To put the poetry of pure understanding into context for “young readers,” he calls the “Paradiso” the “apotheosis of the virtual world, of nonmaterial things, of pure software, without the weight of earthly or infernal hardware.”

Mr. Eco’s ideas of technology are indeed superlunary. Repeatedly, his eagerness to see a Borgesian dream manifested in the World Wide Web – or in medieval codices – undermines his credibility as a social analyst.

Italo Calvino, a near contemporary of Eco’s in Italian literature, identified Borges’s representations of infinity as the source of the Argentine’s sway with generations of Italians. Calvino wrote that, “In every text he writes, in any way he can, Borges manages to talk abut the infinite, the uncountable, time, eternity or rather the eternal presence or cyclical nature of time.” Calvino associated this persistence of Borges’s with his “maximum concentration of meanings in the brevity of his texts.”

In other words, Mr. Eco’s literary master considered the idea of infinity within a style of economy. But Mr. Eco uses ideas of infinity in a self avowedly “baroque” way, multiplying into tedium.

In his own essay, “Borges and My Anxiety of Influence,” he writes that where Borges was a minimalist, he is a maximalist. And where Borges used a “defamiliarization” technique; Mr. Eco makes the unknown familiar. “I take a reader from Texas, who has never seen Europe, into a medieval abbey … and make him feel at ease.” Mr. Eco remembers that before Italian structuralism took up Borges, the Argentine was unfashionable: He “wrote in a classical style, worked on the signifieds,” where as everyone else worked on signifiers.

Fans of Mr. Eco, from Texas and elsewhere, who have been brought closer to European arcana by “The Name of the Rose” or “Foucault’s Pendulum,” will likely not enjoy his occasional essays, mostly papers from academic conferences, which hover at a level of “pure understanding” that has little to do with “signifieds.” “The History of Art” will serve as an idiosyncratic reference for those who wish to see which artworks contemporary texts can be clustered with sections like “Ladies and Heroes” or “The Beauty of Monsters.”

Both these books are ancillary to Mr. Eco’s main work, in fiction and in semiotics, and they partake of his eccentricities but not of his power as an entertainer.