MILAN — For a moment, I think of interjecting, “I’ve never read a word of Dan Brown,” but that might sound a bit sniffish.

I am at the convent of Santa Maria delle Grazie, and a smart young scholar is explaining a detail of Leonardo da Vinci’s “The Last Supper” — the youthful or feminine appearance of Saint John, the apostle immediately to Jesus’ right. The interpretation in Brown’s extraordinarily successful thriller “The Da Vinci Code” — that the image is Mary Magdalene — isn’t supported by evidence, the scholar says. And she’s right: There was a long-standing tradition in Western art of representing Jesus’ beloved John in androgynous style, and Leonardo was particularly fond of painting and drawing effeminate-looking young men.

Somehow, I’ve made it to see “The Last Supper” for the first time in my life without anything of Brown’s opus rubbing off on me. My guide’s caution, her polite reticence about Brown, suggests that his novel and the movie based on it have become part of the larger project of crowd control that is a daily fact of life at Santa Maria delle Grazie, where Leonardo painted his greatest work in the mid-1490s on a wall at the Dominican convent. There is the basic crowd control of timed-ticket entry, and the physical logistics of controlling how people enter and leave, to ensure stable atmospheric conditions in the room where the fragile painting has been in a state of decay for centuries. Then there’s the more complicated crowd control of making this a meaningful experience, something more than just a quick-hit addition to the bucket list of the tourist hordes that pass through the city on a daily basis.

I’ve come to the convent on Good Friday, just two weeks before the 500th anniversary of Leonardo’s death, which is this week. I’m lucky to have been given a little extra time at “The Last Supper” and even, for a few minutes, time without other tourists, and the experience is deeply moving. I’m surprised by this because “The Last Supper” is famous for being but a shadow of what Leonardo put on the walls about the same time Columbus sailed for America. Seen in reproduction, the work looks fuzzy and faint, the robes of the apostles in some cases retain only traces of their original color, their faces indistinct, and some of the key iconographic details, such as the salt cellar knocked over by Judas, are all but illegible.

Yet there it is, glowing on the wall, far more precise in its communication than anything I expected during a two-week trip looking at art in Italy. Even allowing for the myth of the painting, the “aura” of its celebrity and the tourist’s natural investment in having a memorable experience, the painting is magical. If nothing remained of it but the hands — touching, pointing, reaching and resisting — it would still be a formidable vision.

In reproductions, you aren’t necessarily aware of its placement on the wall, above a door, so that its figures seem to hover above you a bit like flickering figures on the silver screen. Or how the architecture of the room Leonardo depicts, with its walls receding in perspective to three windows at the back, integrates with the long, rectangular room for which the painting was created.

Nor can any reproduction render the contrast between Leonardo’s work and the painting opposite it, on the far wall — Giovanni Donato da Montorfano’s “Crucifixion.” The other painting was made about the same time, but in an older style, more brilliantly colored, better preserved and sounding a bit like a brass band in the distance while the Leonardo murmurs and whispers in another universe. Giovanni Donato’s painting is lovely in its own way, but it seems that he has assembled a teeming crowd of characters while Leonardo has captured a moment. One senses the difference between a group portrait in which everyone stares at the camera, and a snapshot of a family intimately engaged.

“The Last Supper” obviously won’t travel during the celebrations of Leonardo’s 500th anniversary, and so, like great architecture and natural wonders, it forces one into a painful confrontation with memory. I can’t help thinking of two related metaphors for memory, both of which involve the sense of touch: What of the world rubs off on us? What sticks? Those metaphors are particularly poignant in this room, where much of Leonardo’s paint didn’t stick, where restorations have overlaid new paint on the damaged surface and the most recent one involving a kind of rubbing off the previous efforts.

Within a few decades after Leonardo painted it — using a technique of egg tempera on a coated wall, which was a more flexible technique that yielded more fragile results — “The Last Supper” was already in bad shape. Around 1520, Giovanni Pietro Rizzoli, known as Giampietrino, made one of several copies (with possible contributions from another artist, Giovanni Antonio Boltraffio), a paint-on-canvas version that is roughly the same size though cropped at the top. When the Leonardo was restored over 20 years, beginning in 1979, this copy was used for guidance. It is brighter, bolder, with all the colors intact and many of the missing details (such as Judas’s salt cellar) fully present.

Yet Giampietrino’s painting doesn’t feel like a memory of the work, rather a document of it, or perhaps like someone’s cellphone snapshot of it, lost in time and disconnected from our own experience. One is happy to have it, but it stands apart from a contemporary experience of the Leonardo.

The clarity and sheen of Giampietrino’s painting also underscores how much the meaning of Leonardo’s original is now bound up with its poor condition. Its decay becomes a metaphor for the transience of the moment depicted, which emphasizes the larger transience of Jesus’ life, showing us the shock and dismay of the realization that he will be betrayed, will die, will leave this group of beloved disciples. I am glad that Giampietrino left us a clearer vision of Saint John, whose youth and beauty becomes one more marker of the ephemeral presence and loss embedded in Leonardo’s conception of this brief biblical drama, but I am also very glad to have seen Leonardo’s Saint John physically fading on the wall above me.

Then I leave the room with everyone else, not certain whether I’ll ever see this work again, wondering what will stick with me. At home, a day later, too jet-lagged to think straight, I watch the “Da Vinci Code” movie for the first time. Now, I remember some silly flapdoodle about vessels and chalices and secret societies, but not much else. Nothing, it seems, rubbed off on me.