In 1901 an extraordinary object was discovered in an ancient Roman shipwreck (dating to around 70 BC) off the Greek island of Antikythera. Now displayed in the Athens National Museum, the so-called Antikythera Mechanism, an intricate treasure constructed in Sicily some centuries earlier, consisted of a complex design of gears and wheels, of which 82 heavily encrusted bronze fragments were recovered. The sheer number of convolutions of the instrument and its sad state of preservation have meant that work on reconstructing the true form of the original has taken more than a century since its discovery. Recently, however, it has become possible to explain how the mechanism worked and what its purpose was. Amazingly, its moving wheels and displays were designed to indicate the changing positions of stars far in advance, so that its users might be able to predict celestial phenomena such as solar and lunar eclipses, and obtain calendrical information to calculate the timing of future athletic events such as the Olympic Games.

The Antikythera Mechanism not only provides a detailed representation of the astronomical knowledge of the era, it is a tour de force of engineering. Although Greeks of the Hellenistic Age (323–33 BC) are known to have designed devices such as early astrolabes and steam-powered automata, nothing as complex as the Antikythera Mechanism was to be produced by human ingenuity for more than a thousand years. An object of this kind — perhaps this very one — was known to the Roman statesman and orator Cicero (first century BC). In his treatise On the State, Cicero has a speaker ascribe the creation of what he calls a ‘globe’ to the famous Greek scientist and inventor Archimedes, who had lived and worked in Syracuse, the foremost city in Sicily, in the third century BC:

The Sicilian geometrician must have had a genius superior to anything we imagine in human nature…his invention was amazing: he calculated how with a single turn one could make unequal and different motions in different directions. [By moving the globe] one could track the relationship of the moon and sun using the same number of turns on the bronze device as the actual number of days. It showed the eclipse of the sun as one might see it in the sky, and the moon entering the earth’s shadow.

Despite Cicero’s detailed testimony to the existence of this invention, and even though the physical remains of the Antikythera Mechanism prove its operation, such an object remains a singularity in the known history of the ancient world. Where does innovation of this kind — or even innovation in general — fit into ancient thinking and experience? Throughout the centuries of antiquity, people passed their daily lives in much the same way as those before them had for millennia. They worshipped the gods of their ancestors, practised old-established social customs, ploughed their fields as had their forefathers, and fought wars face to face with their neighbours just as their predecessors had. This way of life survived for thousands of years after antiquity. The expression longue durée, the long time span, was coined by historians of the French Annales school to speak of the long-term historical structures that underlie the more oft-told story of rapidly changing events (histoire événementielle).

While it might be tempting to think that the Antikythera Mechanism was just the tip of an ancient technological iceberg, it is hard to substantiate such a view. While some attention was devoted to technology, innovation is most often found to have revolved around the creation of artillery weapons for the purpose of waging successful wars of conquest. Archimedes himself was known to be an exceptional inventor, as the designer of inventions such as the water-screw and the grappling hook, as the engineer of the giant ship Syracusia, and as the formulator of important mathematical principles and theorems. The evidence suggests that, with a few individual exceptions, the wider Greek world of the period, and indeed of the centuries prior and subsequent to Archimedes’ time, had little interest in or engagement with scientific novelties. In fact, in the history of classical scholarship, the ancient Greeks have usually been charged with a disinclination to all kinds of change and novelty. They have even been described as living ‘in the grip of the past’ (the title of a 1953 book about Greek cultural attitudes) and positively averse to innovation of any kind.

It is surprising, however, that such a stark view of ancient Greek traditionalism held sway as long as it did. The earliest term for ‘innovation’ is found first in texts from fifth-century BC Athens, in the word kainotomia. While this originally connoted ‘cutting a new vein’ in mining for metallic ores, it was soon extended to the more conceptual and artistic forms of innovation in which Greeks excelled. The fact is that despite their alleged aversion to the new, the ancient Greeks have long been acclaimed as the creators — particularly over the archaic and classical periods spanning five centuries from 800 to 300 BC — of a wide range of hugely significant cultural innovations. Among these, the invention of alphabetic writing, money, empirical medicine, lifelike sculpture, architectural forms, drama and historical literature, and the formulations of logic, philosophy, mathematical proof and political thought, are regularly cited.

How could it be possible that such demonstrably innovative people as the ancient Greeks were averse to innovation? But equally, how could it be possible for an unquestionably traditional society, as by and large the Greeks and even the famously ingenious Athenians undoubtedly were, to come up with, foster and disseminate so many of the fundamentally novel disciplines, ideas and practices that are acknowledged to have originated with them? Numerous answers have been proposed to explain these apparent contradictions; and one answer must be that the circumstances in which the Greeks found themselves were particularly conducive to creativity.

For any kind of innovation to emerge and to be adopted, a key requirement is that favourable conditions — individual, social, or political — must prevail. The conditions for innovation include such things as the freedom to spend time thinking, an openness to different ideas and practices, the existence of incentives to innovate, the ability to take risks without fear of reprisal, and the wherewithal to disseminate and diffuse new ideas to a wide circle of recipients who are in a position to criticise and improve on their own and other’s efforts. It is rare in the historical record for such a combination of circumstances to be found. The independent citizen-states (poleis) of classical Greece benefited from unprecedented intellectual and social freedoms, while absorbing influences from cultures such as Phoenicia in the east (from whose writing system the Greeks developed their alphabet, the forerunner of the Latin alphabet) and Egypt to the south (the inspiration for Greek sculptural and architectural developments). For a while at least, a set of ideal conditions for innovation appear to have prevailed in the world of ancient Greece.

The stimulus to innovate is also related to a recognition of the benefits of doing something new, together with an understanding of how one might do so. Such a recognition is evident in ancient Greek texts, particularly in the areas of literary, artistic and musical production. The latter discipline provides explicit examples of the promotion of the new, as found in some surviving lines of lyric verse sung by a singer-songwriter called Timotheus. Timotheus, a native of the city of Miletus, was the most avant-garde musical performer of the late fifth century BC. He defiantly states in one of his songs: ‘I don’t sing the old songs, my new songs are better.’ Contemporary writings, as well as Timotheus’s rhythmically complex surviving lyrics, give us a sense of how he set about delighting and scandalising audiences in Athens. Notorious for being a redhead as well as a lyre player and composer with a taste for sensation and drama, he gained huge fame and popularity by spearheading the ancient equivalent of a pop revolution.

In addition to the bold rhythmical experimentation that can be heard in his lyrics (rhythmical patterns embedded in Greek words can be read as metrical units), Timotheus created new melodic possibilities by augmenting the number of strings used on the standard concert lyre, the kithara (the word from which ‘guitar’ derives). By combining this with use of a new lever mechanism (called strobilos) for altering the pitches of strings, he was also able to shift to melodies based around different tonal centres, modulating far more widely than performers who traditionally sang in a single key. The ‘New Music’, of which Timotheus was the foremost practitioner, had remarkably enduring appeal. The historian Polybius records that in this time (around 150 BC), boys in his native Arcadia (the central area of Greece’s southern peninsula, the Peloponnese) learned the songs of Timotheus along with that of another ‘new musician’, Philoxenus, to perform in annual festivals. An inscription from Asia Minor records that devotees of Timotheus were still performing his music more than 500 years after his death.

The novel sounds and styles that Timotheus employed and created laid the groundwork for the kinds of melodies and harmonies that filled people’s ears in the Roman and Christian eras. These sounds and idioms were, in turn, inherited and further developed by creators of music — troubadours and love lyricists as well as psalmists and church musicians — throughout Europe during the Middle Ages and the Renaissance. Arguably, therefore, Timotheus’s innovations might be thought to form some of the earliest examples of what was to become the European musical tradition. The details show an individual adapting against a known background — and, in this case, Timotheus sought to extend rhythmical, harmonic and melodic expressiveness by combining his musical ideas with novel technical initiatives and mechanical resources. The result demonstrated, to the displeasure of conservative observers such as the philosopher Plato, a deliberate challenge to and reversal of existing norms of musical sobriety and simplicity.

We thus see that three mechanisms of innovation might be derived from this example of musical inventiveness — adaptation, cross-fertilisation and reversal. These fundamental principles may be found, singly and in combination, in every kind of innovative endeavour. Together with the conditions that allow and foster the creation of novelty, they constitute what might be called the roots of new creation.

The formulation of an idea of ‘the roots of creation’ is first found in the philosophy of a Greek thinker who lived two centuries before Archimedes. In the early fifth century, Empedocles of Acragas (modern Agrigento in Sicily) built on philosophical predecessors to challenge sixth-century thinkers, such as Thales and Anaximenes (both from Timotheus’s native city, Miletus), who had argued that the universe arose from a single ‘originating principle’ (archê) such as water or air. Empedocles proposed that there were four eternal roots of the physical cosmos: earth, fire, air and water. From the interchange of these elements, combining and separating through love and strife, the perceived universe arose. The roots themselves must be eternal, Empedocles argued; they could not have sprung into being from nothing.

The recognition that nothing new can arise without a pre-existing substrate is of great importance to the notion of innovation. It was to be stressed by the great fourth-century BC philosopher Aristotle in his analysis of change in the Physics. The proposition corrects a popular misapprehension of the meaning of ‘radical’ innovation, which is sometimes taken to mean ‘new roots and all’. Such a thing, Aristotle insisted, cannot logically exist: what is new must have roots in the old. An innovation that was wholly unrelated to the past would simply be unrecognisable; so ‘radical’ innovation must properly mean ‘new from the roots up’. Once this is recognised, various elements or mechanisms of innovation come into play, operating on the existing material to transform it – specifically the processes of adaptation, reversal and combination.

Greek antiquity is a rich source of stories that illustrate these processes employed both deliberately and unconsciously. They serve to explain how the Greeks became notable innovators. The ‘invention’ of the alphabet, for instance, adapted from the letter-symbols used by the Greeks’ Eastern neighbours, the Phoenicians, was not so much an invention as a cultural adaptation of great significance which allowed Greeks to commit their own ideas to writing using 24 phonetic symbols. The Phoenicians had named their ‘a’ after ‘alif ’, meaning ‘ox’ — the shape of the letter showing the pointed nose of the ploughing animal ahead, with the horns trailing behind – and the Greeks formalised the shape as their a[lpha]; similarly, they adapted Phoenician ‘bet’ (house), the plan of a house with two rooms, to make their b[eta]; and so on for the whole alphabet.

Another overseas people, the Egyptians, were the inspiration for the earliest Greek representational statues of the sixth century BC. These initially followed the rigid style and contours of their models. But by combining sculptural techniques with an understanding of muscles and sinews as regularly viewed in athletic games, and informed by surgical practices developed to treat those wounded in battle, Greek sculptors transformed their statues into the fluid lifelike figures familiar from fifth-century Greek art.

The battlefield connection provides a further illustrative tale of innovation. Ancient battles between city states tended to follow a predictable pattern, with the strongest fighters stationed on the right wing of the phalanx. Once this column broke through their opponents, the battle was won, and the highly trained Spartans seemed invincible in such encounters. In 371 BC, however, at the Battle of Leuctra, the Theban commander Epaminondas reversed the standard procedure by putting his best fighters, reinforced by a column 50 men deep, on the left wing. The toughest of Spartans could make no headway, and their army, though much larger than that of the Thebans, was thrown into confusion. Epaminondas became master of the field through this simple reversal of the usual practice.

The intellectual and technical roots of the Antikythera Mechanism are lost to the historical record, but history records the Eureka moment of Archimedes, which may have resulted from his solution to the question of why a colossal ship (which he was commissioned to produce by the tyrant of Syracuse) should be able to float: that is, his formulation of the Archimedes principle. That story demonstrates a condition of innovation familiar to individual thinkers and inventors. Archimedes found his solution not at his desk or in front of his diagrams, but when he was relaxing in the bath.

Would-be innovators recognise the value not only of focusing intently on the problem in hand, but of taking time to switch off and allow a solution to emerge before immersing themselves once again in the intricate operation of making their solution work in practice. The questions raised by the existence of the remarkable Antikythera Mechanism seem likely to remain forever a mystery. But the conditions for intellectual illumination that the Archimedes Eureka story may demonstrate, as well as the other fundamental mechanisms and strategies that can be detected in so many stories of innovation from Greek antiquity, remain central to our understanding of how people and societies have come up with new ideas, and how we may continue to generate them.