When Christianity came to win back Spain, the excitement of the struggle was on the frontier. Here Moors and Christians, and Jews too, mingled and made an extraordinary culture of dif­ferent faiths. In 1085 the centre of this mixed culture was fixed for a time in the city of Toledo. Toledo was the intellectual port of entry into Christian Europe of all the classics that the Arabs had brought together from Greece, from the Middle East, from Asia.

We think of Italy as the birthplace of the Renaissance. But the conception was in Spain in the twelfth century, and it is symbolised and expressed by the famous school of translators at Toledo, where the ancient texts were turned from Greek (which Europe had forgotten) through Arabic and Hebrew into Latin. In Toledo, amid other intellectual advances, an early set of astronomical tables was drawn up, as an encyclopedia of star positions. It is characteristic of the city and the time that the tables are Christian, but the numerals are Arabic, and are by now recognisably modern.

The most famous of the translators and the most brilliant was Gerard of Cremona, who had come from Italy specifically to find a copy of Ptolemy's book of astronomy, the Almagest, and who stayed on in Toledo to translate Archimedes, Hippocrates, Galen, Euclid — the classics of Greek science.

And yet, to me personally, the most remarkable and, in the long run, the most influential man who was translated was not a Greek. That is because I am interested in the perception of objects in space. And that was a subject about which the Greeks were totally wrong. It was understood for the first time about the year AD 1000 by an eccentric mathematician whom we call Alhazen, who was the one really original scientific mind that Arab culture produced. The Greeks had thought that light goes from the eyes to the object. Alhazen first recognised that we see an object because each point of it directs and reflects a ray into the eye. The Greek view could not explain how an object, my hand say, seems to change size when it moves. In Alhazen's account it is clear that the cone of rays that comes from the outline and shape of my hand grows narrower as I move my hand away from you. As I move it towards you, the cone of rays that enters your eye becomes larger and subtends a larger angle. And that, and only that, accounts for the difference in size. It is so simple a notion that it is astonishing that scientists paid almost no attention to it (Roger Bacon is an exception) for six hundred years. But artists attended to it long before that, and in a practical way. The concept of the cone of rays from object to the eye becomes the foundation of perspective. And perspective is the new idea which now revivifies mathematics.

The excitement of perspective passed into art in north Italy, in Florence and Venice, in the fifteenth century. A manuscript of Alhazen's Optics in translation in the Vatican Library in Rome is annotated by Lorenzo Ghiberti, who made the famous bronze perspectives for the doors of the Baptistry in Florence. He was not the first pioneer of perspective - that may have been Filippo Brunelleschi - and there were enough of them to form an identifiable school of the Perspectivi. It was a school of thought, for its aim was not simply to make the figures lifelike, but to create the sense of their movement in space.

The movement is evident as soon as we contrast a work by the Perspectivi with an earlier one. Carpaccio's painting of St Ursula leaving a vaguely Venetian port was painted in 1495. The obvious effect is to give to visual space a third dimension, just as the ear about this time hears another depth and dimension in the new harmonies in European music. But the ultimate effect is not so much depth as movement. Like the new music, the picture and its inhabitants are mobile. Above all, we feel that the painter's eye is on the move.