I. The Child Outside the Door

Leonardo da Vinci was born to parents who were not married.

It was 1452, near Vinci. His father, Piero, was a notary; his mother was named Caterina. He grew up within his father's family. He did not follow the paternal profession, nor receive a university education centred on Latin.

“Da Vinci” means “from Vinci.” The name points towards a place, bringing the later legend back to a child who grew up somewhere real.

As a young man he entered Verrocchio's Florentine workshop. Painting, sculpture and metalwork were not sealed departments there: a hand needed to understand pigment, but also weight, materials and tools. By 1472 he belonged to the city's confraternity of painters, the Company of Saint Luke.

The workshop was not knowledge's back entrance. It had disciplines, collaborators and standards of its own. Outside the university, he was learning to see in another kind of school.

Set him beside Li Bai and we may glimpse a freedom unwilling to follow only an assigned road. But birth outside marriage does not automatically confer freedom. Obstacles do not become gifts because a remarkable person later encounters them.

Du Fu repeatedly named his wish to serve and guide a ruler beyond Yao and Shun. On Leonardo's sheets, directions keep multiplying. A life may hurt because a road is blocked, or because there are too many roads. Commissions, money, war and the length of a lifetime were also real.

II. The Notebooks

Thousands of pages survive, often loosely described as about seven thousand.

Open them, and it is difficult to say what kind of book this is.

Anatomy. Bones, muscles, vessels, organs: he probably dissected some thirty human bodies, as well as many animals. To investigate the heart he brought drawings, models and flowing water together. How might eddies help a valve close? Brilliant insight sits beside errors inherited from the physiology of his time.

Water. Ripples, vortices, currents curling behind an obstacle. A river becomes more than a blue line: it is motion acting upon motion. The eye follows; the hand must find a way to keep that movement on paper.

Flight. Ornithopters, an aerial screw, a parachute. A wing can spread across a drawing while the power available to a human body remains insufficient to raise the machine. These are investigations of flight, not modern aircraft awaiting assembly.

War. Giant crossbows, an armoured vehicle, underwater equipment. His letter offering services to Ludovico Sforza devotes most of its space first to military skills, then turns to architecture, water engineering, sculpture and painting in peacetime, and proposes a bronze equestrian monument. The man remembered as a painter first asks a ruler to consider his bridges and weapons.

Light, shadow, perspective, colour. Shell fossils in the mountains and the past of the earth. Branches dividing into branches. Churches, bridges, urban waterways. Music, too: early biography preserves the image of a player of the lira da braccio.

Bodies and rivers, pictures and machines sometimes crowd the same sheet. Not every line announces a discovery. There are calculations, reminders, false starts and questions without answers.

He commonly wrote with his left hand, from right to left, in mirror script. A practised reader does not necessarily need a mirror. Nor did every sheet originally belong to the volume that holds it now: loose leaves were folded, bound and rearranged by later owners.

He planned treatises on painting, anatomy and other subjects, without systematically publishing these studies during his lifetime. After his death Melzi preserved and organised part of the papers; writings on painting eventually circulated in compilations including the Treatise on Painting. Other sheets disappeared or travelled into separate collections.

Images, comparisons and local arguments already make knowledge. But in the workshop that remains for us, many doors are still open.

III. Different Kinds of Unfinished

The unfinished is one way into Leonardo. It is not a stamp to press upon his whole life.

Few surviving paintings are generally accepted as his, and the precise count depends on attribution. Murals, collaborations and disputed works also make the list difficult to settle neatly.

The Last Supper, made from the middle of the 1490s to 1498. Working on dry plaster allowed him time to reconsider light and expression. He completed the painting; technique and environment caused early deterioration. Completion and preservation are different questions.

The Mona Lisa, begun around 1503, remained with him for years of further work. What we encounter is an intensely worked painting. Dates alone cannot tell us when he thought he had done enough.

The Battle of Anghiari, commissioned for Florence's town hall, left studies and echoes of its composition, but never became the complete mural intended. How much reached the wall, and precisely what happened there, remain debated.

The Sforza equestrian monument. He made a colossal clay model, but the bronze statue was never cast. In 1494 the bronze intended for it was diverted to cannon; after the French occupation of Milan in 1499, the model was destroyed. Technical difficulties belong here, but so do war and the fortunes of a patron.

Flying machines, the armoured vehicle, underwater apparatus: many proposals remained on paper. Anatomical and hydraulic research did not become the publications he envisaged. Unrealized plans and a painting damaged after completion are different problems.

Thousands of manuscript pages, a small surviving body of paintings, many interrupted undertakings. Beside them we must put commissions delivered, and long investigations not easily entered into either a success or a failure column.

He began much. Some things he made, others he repeatedly revised, others never reached their destination. What remains is not a blank record of accomplishment, but the friction between a life and its endings.

IV. Why Open Another Door?

Why is there always another undertaking?

We readily answer: distraction. Painting leads him to muscles, muscles to forces, forces to water and flight. The work on the table appears impossible to gather up.

Yet these directions also connect. To paint a turning body, look at how its bones turn; to understand blood inside a heart, look at swirling water. Curiosity can interrupt work, and it can take the work deeper.

In this series we might call that carving: something apparently familiar is opened again, exposing a question not yet asked.

Behind the doors are heart valves, circling currents, distant mountains fading through the air, the action of a bird's wing upon that air. Each asks for observation, and for the admission that an explanation may not yet be enough.

He did construct. He drew, compared, devised experiments, arranged arguments; he could return to one question for years. But a local construction often opened onto another problem, resisting closure into a book ready to be delivered.

Beside him we can place Newton: the public argument of the Principia alongside investigations spreading across Leonardo's sheets. Newton also pursued many subjects; Leonardo also sustained concentrated work.

To give the contrast a momentary shape: one erects a building others can enter beyond the door; the other still hears something in the next room. He sets down the line he has just drawn. He wants to go and look.

V. Leonardo and the Others

Carving and construction are two lights this series casts upon people, not two kinds of citizenship.

Socrates questions; Plato gives continued conversation a form and builds philosophical arguments; Aristotle organises knowledge. Newton's mathematics, Bach's counterpoint, Qin Shi Huang's imperial projects and Kant's critiques then give construction very different weights.

Leonardo stands among them, now asking, now making. He will not remain inside one craft, yet never leaves craft behind. Eyes and hands must answer for the new question.

Socratic questioning prevents an answerer from settling too easily; Leonardo's curiosity prevents him from settling. “There is another door.” We hear that in the papers: it is our phrase, not a recovered quotation.

Darwinian variation offers another association: many possibilities, outcomes not known beforehand. But human designs have intentions; biological variations do not prepare answers for future needs. The resemblance illuminates only the uncertainty of exploration.

Leonardo did not pack the Wright brothers, modern medicine and the Navier–Stokes equations into his notebooks in advance. Later aviation and science had their own problems, evidence and collective labour. They were not merely waiting to understand a prophet's plans.

What moves us is not that every attempt was right. It is his willingness to make uncertainty so specific: how the wing attaches, how the water turns, how the hand rises. A line that can be wrong can also invite the next question.

VI. Those Few Paintings

Return to the paintings. Do not let the unfinished hide what has already happened there.

The Last Supper, the Mona Lisa, the Virgin of the Rocks, the Lady with an Ermine. The disturbance around a table, gestures between rocks, an animal in a woman's arms: each establishes a world we can enter again.

The Mona Lisa's smile is particularly elusive. Leonardo brought sfumato to extraordinary refinement, using thin layers of paint to make contours pass gently into one another. As our gaze shifts between mouth, eyes and face, the expression seems to shift too.

Not every viewer must report the same illusion. What matters is that the painting does not fasten an expression to a face like a label. Having seen it, we want to look once more.

In this series' vocabulary, it resembles remainder. Nothing needs to hide outside the painting: relations already painted make “she is smiling” feel insufficient. Zhuangzi's Hundun echoes from a distance. Some things lose their animation when we insist on cutting every boundary sharply.

This is not simply a mouth left unpainted. Softness is a choice achieved through labour; an unsettled experience can belong to finished art. The expression that refuses to be carried away in a sentence is itself a form.

Gödel has invited us elsewhere to think about the limits of formal systems. What returns here is only a reader's reluctance to close things too quickly. A smile is not governed by a theorem about arithmetic proof. It needs no mathematical guarantee to make us pause.

VII. Mirror

Writing from right to left can look as though the page has turned to the other side of the world.

It is a metaphor we may borrow, not a key that unlocks genius.

A tree draws his attention to branching relations; a river to water travelling around an obstacle; a person to the cooperation of muscle and bone. Looking at a painting, he returns to the light that illuminates a face.

He has not left the visible world to possess a final answer concealed behind it. Within the visible, he looks for relations an ordinary glance may miss.

Kant can enter this comparison, but a dissection knife cannot refute him. Once observed, the body's interior is still an object of experience, not a philosophical thing-in-itself finally caught in view.

Kant asks after the conditions and boundaries of our knowing. Leonardo asks how this particular thing works. Neither question replaces the other; together they make the word “seeing” less simple.

Having seen, he draws. A drawing is not the waste left over from perception: it tests that perception and offers it to someone else. Beside the mirror script, the lines still turn towards another reader.

He continued working during his last years in France, and died at Clos Lucé near Amboise in 1519, aged sixty-seven. He did not have five hundred years. Nor did the papers on his table turn themselves into a finished book that day.

VIII. One More Door

Now let us invite him to this series' imagined bridgehead.

Paint on his hands, ink too, and perhaps the marks of tools and models. Hands that have worked for a long time.

Socrates stands. Laozi has disappeared; Confucius waits. Du Fu weeps and Li Bai flies. Bach listens, Beethoven clenches his fist, Sima Qian carries books, Rumi turns.

Leonardo looks about him. How does the bridge carry its weight? Why does the water curl back just there? Someone turns in the crowd: how do shoulder and arm move together? How does that bird hold itself in the wind?

He walks a few steps, stops, takes out paper, draws a few lines. When someone has finished speaking, he may still be looking at the movement of their mouth.

These steps differ from Rumi's turning. Again and again they lead towards another object; each pause may become a door.

He began so much.

Some observations were right, some guesses mistaken, some questions passed to the next page. Work directed towards truth does not require an unbroken record of being correct.

No one can say how many more years would have let him finish everything. Answers would have produced new questions. Even five hundred years is not a schedule we can calculate.

He had sixty-seven. Within them, he gave things we might otherwise pass by the time of an attentive gaze.

His hands at the bridgehead still bear its traces. He did not touch everything. He makes us feel that anything might deserve another look.

The Mona Lisa is smiling. The painting is there; the looking has not ended.

He wants to open one more door.

Han Qin (秦汉) · @hqinjarsy · Great Lives