The Ascent of Man (16 page)

Pythagoras was a philosopher, and something of a religious figure to his followers as well. The fact is there was in him something of that Asiatic
influence which flows all through Greek culture and which we commonly overlook. We tend to think of Greece as part of the west; but Samos, the edge of classical Greece, stands one mile from the coast of Asia Minor. From there much of the thought that inspired Greece first flowed; and, unexpectedly, it flowed back to Asia in the centuries after, before ever it reached Western Europe.

Knowledge
makes prodigious journeys, and what seems to us a leap in time often turns out to be a long progression from place to place, from one city to another. The caravans carry with their merchandise the methods of trade of their countries – the weights and measures, the methods of reckoning – and techniques and ideas went where they went, through Asia and North Africa. As one example among many, the mathematics
of Pythagoras has not come to us directly. It fired the imagination of the Greeks, but the place where it was formed into an orderly system was the Nile city, Alexandria. The man who made the system, and made it famous, was Euclid, who probably took it to Alexandria around 300
BC
.

Euclid evidently belonged to the Pythagorean tradition. When a listener asked him what was the practical use of some
theorem, Euclid is reported to have said contemptuously to his slave, ‘He wants to profit from learning – give him a penny’. The reproof was probably adapted from a motto of the Pythagorean brotherhood, which translates roughly as ‘A diagram and a step, not a diagram and a penny’ – ‘a step’ being a step in knowledge or what I have called the ascent of man.

The impact of Euclid as a model of mathematical
reasoning was immense and lasting. His book
Elements of Geometry
was translated and copied more than any other book except the Bible right into modern times. I was first taught mathematics by a man who still quoted the theorems of geometry by the numbers that Euclid had given them; and that was not uncommon even fifty years ago, and was the standard mode of reference in the past. When John Aubrey
about 1680 wrote an account of how Thomas Hobbes in middle age had suddenly fallen ‘in love with geometry’ and so with philosophy, he explained that it began when Hobbes happened to see ‘in a gentleman’s library, Euclid’s
Elements
lay open, and ‘twas the 47
Element libri
I’. Proposition 47 in Book 1 of Euclid’s
Elements
is the famous theorem of Pythagoras.

The other science practised in Alexandria
in the centuries around the birth of Christ was astronomy. Again, we can catch the drift of history in the undertow of legend: when the Bible says that three wise men followed a star to Bethlehem, there sounds in the story the echo of an age when wise men are stargazers. The secret of the heavens that wise men looked for in antiquity was read by a Greek called Claudius Ptolemy, working in Alexandria
about
AD
150. His work came to Europe in Arabic texts, for the original Greek manuscript editions were largely lost, some in the pillage of the great library of Alexandria by Christian zealots in
AD
389, others in the wars and invasions that swept the Eastern Mediterranean throughout the Dark Ages.

The model of the heavens that Ptolemy constructed is wonderfully complex, but it begins from a
simple analogy. The moon revolves round the earth, obviously; and it seemed just as obvious to Ptolemy that the sun and the planets do the same. (The ancients thought of the moon and the sun as planets.) The Greeks had believed that the perfect form of motion is a circle, and so Ptolemy made the planets run on circles, or on circles running in their turn on other circles. To us, that scheme of cycles
and epicycles seems both simple-minded and artificial. Yet in fact the system was a beautiful and a workable invention, and an article of faith for Arabs and Christians right through the Middle Ages. It lasted for fourteen hundred years, which is a great deal longer than any more recent scientific theory can be expected to survive without radical change.

It is pertinent to reflect here why astronomy
was developed so early and so elaborately, and in effect became the archetype for the physical sciences. In themselves, the stars must be quite the most improbable natural objects to rouse human curiosity. The human body ought to have been a much better candidate for early systematic interest. Then why did astronomy advance as a first science ahead of medicine? Why did medicine itself turn
to the stars for omens, to predict the favourable and the adverse influences competing for the life of the patient – surely the appeal to astrology is an abdication of medicine as a science? In my view, a major reason is that the observed motions of the stars turned out to be calculable, and from an early time (perhaps 3000
BC
in Babylon) lent themselves to mathematics. The pre-eminence of astronomy
rests on the peculiarity that it can be treated mathematically; and the progress of physics, and most recently of biology, has hinged equally on finding formulations of their laws that can be displayed as mathematical models.

Every so often, the spread of ideas demands a new impulse. The coming of Islam six hundred years after Christ was the new, powerful impulse. It started as a local event,
uncertain in its outcome; but once Mahomet conquered Mecca in
AD
630, it took the southern world by storm. In a hundred years, Islam captured Alexandria, established a fabulous city of learning in Baghdad, and thrust its frontier to the east beyond Isfahan in Persia. By
AD
730 the Moslem empire reached from Spain and Southern France to the borders of China and India: an empire of spectacular strength
and grace, while Europe lapsed in the Dark Ages.

In this proselytising religion, the science of the conquered nations was gathered with a kleptomaniac zest. At the same time, there was a liberation of simple, local skills that had been despised. For instance, the first domed mosques were built with no more sophisticated apparatus than the ancient builder’s set square – that is still used. The
Masjid-i-Jomi (the Friday Mosque) in Isfahan is one of the statuesque monuments of early Islam. In centres like these, the knowledge of Greece and of the east was treasured, absorbed and diversified.

Mahomet had been firm that Islam was not to be a religion of miracles; it became in intellectual content a pattern of contemplation and analysis. Mohammedan writers depersonalised and formalised
the godhead: the mysticism of Islam is not blood and wine, flesh and bread, but an unearthly ecstasy.

Allah is the light of the heavens and the earth. His light may be compared to a niche that enshrines a lamp, the lamp within a crystal of star-like brilliance, light upon light. In temples which Allah has sanctioned to be built for the remembrance of his name do men praise him morning and evening,
men whom neither trade nor profit can divert from remembering him.

One of the Greek inventions that Islam elaborated and spread was the astrolabe. As an observational device, it is primitive; it only measures the elevation of the sun or a star, and that crudely. But by coupling that single observation with one or more star maps, the astrolabe also carried out an elaborate scheme of computations
that could determine latitude, sunrise and sunset, the time for prayer and the direction of Mecca for the traveller. And over the star map, the astrolabe was embellished with astrological and religious details, of course, for mystic comfort.

For a long time the astrolabe was the pocket watch and the slide rule of the world. When the poet Geoffrey Chaucer in 1391 wrote a primer to teach his son
how to use the astrolabe, he copied it from an Arab astronomer of the eighth century.

Calculation was an endless delight to Moorish scholars. They loved problems, they enjoyed finding ingenious methods to solve them, and sometimes they turned their methods into mechanical devices. A more elaborate ready-reckoner than the astrolabe is the astrological or astronomical computer, something like an
automatic calendar, made in the Caliphate of Baghdad in the thirteenth century. The calculations it makes are not deep, an alignment of dials for prognostication, yet it is a testimony to the mechanical skill of those who made it seven hundred years ago, and to their passion for playing with numbers.

The most important single innovation that the eager, inquisitive, and tolerant Arab scholars
brought from afar was in writing numbers. The European notation for numbers then was still the clumsy Roman style, in which the number is put together from its parts by simple addition: for example, 1825 is written as MDCCCXXV, because it is the sum of M=1000, D=500, C+C+C= 100+100+100, XX=10+10, and V=5. Islam replaced that by the modern decimal notation that we still call ‘Arabic’. In the note in
an Arab manuscript, the numbers in the top row are 18 and 25. We recognise 1 and 2 at once as our own symbols (though the 2 is stood on end). To write 1825, the four symbols would simply be written as they stand, in order, running straight on as a single number; because it is the place in which each symbol stands that announces whether it stands for thousands, or hundreds, or tens, or units.

However, a system that describes magnitude by place must provide for the possibility of empty places. The Arabic notation requires the invention of a zero. The words
zero
and
cipher
are Arab words; so are
algebra, almanac, zenith
, and a dozen others in mathematics and astronomy. The Arabs brought the decimal system from India about
AD
750, but it did not take hold in Europe for another five hundred
years after that.

It may be the size of the Moorish Empire that made it a kind of bazaar of knowledge, whose scholars included heretic Nestorian Christians in the east and infidel Jews in the west. It may be a quality in Islam as a religion, which, though it strove to convert people, did not despise their knowledge. In the east the Persian city of Isfahan is its monument. In the west there survives
an equally remarkable outpost, the Alhambra in southern Spain.

Seen from the outside, the Alhambra is a square, brutal fortress that does not hint at Arab forms. Inside, it is not a fortress but a palace, and a palace designed deliberately to prefigure on earth the bliss of heaven. The Alhambra is a late construction. It has the lassitude of an empire past its peak, unadventurous and, it thought,
safe. The religion of meditation has become sensuous and
self-satisfied. It sounds with the music of water, whose sinuous line runs through all Arab melodies, though they are based fair and square on the Pythagorean scale. Each court in turn is the echo and the memory of a dream, through which the Sultan floated (for he did not walk, he was carried). The Alhambra is most nearly the description
of Paradise from the Koran.

Blessed is the reward of those who labour patiently and put their trust in Allah. Those that embrace the true faith and do good works shall be forever lodged in the mansions of Paradise, where rivers will roll at their feet … and honoured shall they be in the gardens of delight, upon couches face to face. A cup shall be borne round among them from a fountain, limpid,
delicious to those who drink … Their spouses on soft green cushions and on beautiful carpets shall recline.

The Alhambra is the last and most exquisite monument of Arab civilisation in Europe. The last Moorish king reigned here until 1492 when Queen Isabella of Spain was already backing the adventure of Columbus. It is a honeycomb of courts and chambers, and the Sala de las Camas is the most
secret place in the palace. Here the girls from the harem came after the bath and reclined, naked. Blind musicians played in the gallery, the eunuchs padded about. And the Sultan watched from above, and sent an apple down to signal to the girl of his choice that she would spend the night with him.