John Dee, who lived from 1527 to 1608, was a court astrologer to Mary Tudor. At one point he was imprisoned for being a magician, but in 1555 they let him out again, presumably for not being one. Then he became an astrologer for Queen Elizabeth I. He devoted much of his life to the occult, both alchemy and astrology. On the other hand, he was also the author of the first English translation of Euclid's Elements, the renowned treatise on geometry. Actually, if you believe the printed word, the book is attributed to Sir Henry Billingsley, but it was common knowledge that Dee did all the work, and he even wrote a long and erudite preface. Which may be why it was common knowledge that Dee did all the work.

To the modern mind, Dee's interests seem contradictory: a mass of superstitious pseudoscience mixed up with some good, solid science and mathematics. But Dee didn't have a modern mind, and he saw no particular contradiction in the combination. In his day, many mathematicians made their living by casting horoscopes. They could do the sums that foretold in which of the twelve 'houses' -the regions of the sky determined by the constellations corresponding to the signs of the Zodiac - a planet would be.

Dee stands at the threshold of modern ways of thinking about causality in the world. We call his time The Renaissance, and the reference is to the rebirth of the philosophy and politics of ancient Athens. But perhaps this view of his times is mistaken, both because Greek society was not then as 'scientific' or 'intellectual' as we've been led to believe, and because there were other cultural currents that attributed to the culture of his times. Our ideas of narrativium may derive from the melding of these ideas into later philosophies, such as of Baruch Spinoza.

Stories encouraged the growth of occultism and mysticism. But they also helped to ease the European world out of medieval superstition into a more rational view of the universe.

Belief in the occult -magic, astrology, divination, witchcraft, alchemy -is common to most human societies. The European tradition occultism, to which Dee belonged, is based on an ancient, secret philosophy; it derives from two main sources, ancient Greek alchemy magic, and Jewish mysticism. Among the Greek sources is the Emeri Tablet, a collection of writings associated with Hermes Trismegist ('thrice master'), which was particularly revered by later alchemists; the Jewish source is the Kabbala, a secret, mystical interpretation of a sacred book, the Torah.

Astrology, of course, is a form of divination based on the stars and the visible planets. It may, perhaps, have contributed to the development of science by supporting people who wanted to observe and understand the heavens. Johannes Kepler, who discovered that planetary orbits are ellipses, made his living as an astrologer. Astrology survives in watered-down form in the horoscope columns of tabloid newspapers. Ronald Reagan consulted an astrologer during his time as American President. That stuff certainly hangs around.

Alchemy is more interesting. It is often said to be an early forerunner of chemistry, although the principles underlying chemistry largely derive from other sources. The alchemists played around with apparatus that led to useful chemists' gadgets like retorts and flasks and they discovered that interesting things happen when you heat certain substances or combine them together. The alchemists' big discoveries were salt ammoniac (ammonium chloride), which can be made to react with metals, and the mineral acids - nitric, sulphuric and hydrochloric.

The big goal of alchemy would have been much bigger if they ever achieved it: the Elixir of Life, the source of immortality. The Chinese alchemists described this long-sought substance as

'liquid gold'. The narrative thread here is clear: gold is the noble metal, incorruptible, ageless. So anyone who could somehow incorporate gold into his body would also become incorruptible and ageless. The nobility shows up differently: the noble metal is reserved for the 'noble' humans: emperors, royalty, the people on top of the heap. Much good did this do them. According to the Chinese scholar Joseph Needham, several Chinese emperors probably died of elixir poisoning.

Since arsenic and mercury were common constituents of supposed elixirs, this is hardly a surprise. And it is all too plausible that a mystic quest for immortality would shorten life, not prolong it.

In Europe, from about 1300 onwards, alchemy had three main objectives. The Elixir of Life was still one, and a second was finding cures for various diseases. The alchemical search for medicines eventually led somewhere useful. The key figure here is Phillipus Aureolus Theophrastus Bombastus19 von Hohenheim, mercifully known as 'Paracelsus', who lived from

1493 to 1541.

Paracelsus was a Swiss physician whose interest in alchemy led him to invent chemotherapy. He placed great store in the occult. As a student aged 14 he wandered from one European university to another, in search of great teachers, but we can deduce from what he wrote about the experience, somewhat later, that he was disappointed. He wondered why 'the high colleges managed to produce so many high asses', and clearly wasn't the kind of student to endear himself to his teachers. 'The universities,' he wrote, 'do not teach all things. So a doctor must seek out old wives, gypsies, sorcerers, wandering tribes, old robbers, and such outlaws and take lessons from them.' He would have had a high old time on Discworld, but would have learned a lot.

After ten years' wandering, he returned home in 1524 and became lecturer in medicine at the university of Basel. In 1527 he publicly burned the classic books of earlier physicians, the Arab Avicenna and the Greek Galen. Paracelsus cared not a whit for authority. Indeed his assumed name, 'para-Celsus', means 'above Celsus', and Celsus was a leading Roman doctor of the first century.

He was arrogant and mystical. His saving grace was that he was also very bright. He placed great importance on using nature's own powers of healing. For example, letting wounds drain instead of padding them with moss or dried dung. He discovered that mercury was an effective treatment for syphilis, and his clinical description of that sexually transmitted disease was the best available.

The main objective for most alchemists was far more selfish, sights were set on just one thing: transmuting base metals like lead into gold. Again, their belief that this was possible rested on a story. They knew from their experiments that sal ammoniac and other substances could change the colour of metals, so the story 'Metals can be transmuted' gained ground. Why, then, should it not be possible to start with lead, add the right substance, and end up with gold? The story seemed compelling; all that they lacked was the right substance. They called it the Philosopher's Stone.

The search for the Philosopher's Stone, or rumours that it had been found, got several alchemists into trouble. Noble gold was the prerogative of the nobility. While the various kings and princes wouldn't have minded getting their hands on an inexhaustible supply of gold, they didn't want their rivals to beat them to it. Even searching for the Philosopher's Stone could be considered subversive, just as searching for a cheap source of renewable energy now is apparently considered subversive by oil corporations and nuclear energy companies. In 1595 Dee’s companion Edward Kelley was imprisoned by Rudolf II and died trying to escape, and in 1603

Christian II of Saxony imprisoned and tortured the Scottish alchemist Alexander Seton. A

dangerous thing, a clever man.

The story of the Philosopher's Stone never reached its climax, alchemists never did turn lead into gold. But the story took a long time to die. Even around 1700, Isaac Newton still thought it was worth having a go, and the idea of turning lead into gold by chemical means was finally killed off only in the nineteenth century. Nuclear reactions, mind you, are another matter: the transmutation can be done, but is wildly uneconomic. And unless you're very careful, the gold is radioactive (although, of course, this will keep the money circulating quickly, and we might see a sudden upsurge of philanthropy). How did we get from alchemy to radioactivity? The pivotal period of Western history was the Renaissance, roughly spanning the fifteenth and sixteenth centuries, when ideas imported from the Arab world collided with Greek philosophy and mathematics, and Roman artisanship and engineering, leading to a sudden flowering of the arts and the birth of what we now call science. During the Renaissance, we learned to tell new stories about ourselves and the world. And those stories changed both.