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In 1901 Greek fishermen diving for sponges discovered a bronze device, long encrusted with sea life, buried in the wreck of an ancient Greek boat. Cleaning revealed a remarkable analog computer designed for calculating the positions of the sun, moon and the five visible planets as well as the four-year cycle of the Olympic games. Before discovery of this first or second century BCE device, known as the Antikythera mechanism, there was no evidence from either the historical or archaeological record that ancient Greek mathematics was sophisticated enough for the complicated calculations embodied in it, nor that they had the technology to produce it. Indeed, the Antikythera mechanism is the first known example of a mechanical model of the solar system, known as an orrery. It would be another two millennia, in the early 18^th century before modern orrery’s were invented. This mechanism is far too sophisticated not to have been preceded by more primitive devices. Yet this cultural and technological novelty and its antecedents seem to have disappeared, leaving no long-term impact. 

That the Antikythera mechanism was an invention with no impact should not be a surprise. In fact,  most inventions lead nowhere, just as most biological novelties do not lead to evolutionary success, or at least not immediate evolutionary success. Hence the need to distinguish invention (or novelty) from innovation. But the Antikythera mechanism raises some other interesting questions: How did the ancient Greeks discover the underlying mathematics and the required technology to construct the device? Why was the technology embedded in the mechanism not widely adopted? What happened to the mathematics required to build such a sophisticated analog computer? 

But there is a deeper question raised by the Antikythera mechanism, one that goes to the heart of how we think about novelties and innovations. Is there some process of search through an existing space of possibilities, or do some novelties and innovations construct new spaces of possibility? Some would take the existence of the Antikythera mechanism to mean that the whole space of analog computers, and possibly even their digital counterparts that we rely upon today, existed by the time of the ancient Greeks.

Grasping this issue requires a detour into the game of chess. The mathematician Claude Shannon once estimated that there were about 10¹²⁰ reasonable chess games that could be played – a number far larger than the number of atoms in the universe (a measly 10⁸⁰). Shannon’s number, as it is known, came from his estimate that there are about 30 reasonable moves from each position, and most games last about 40 moves. Even though 10¹²⁰ is a vast number it is not infinite, meaning that the number of possible games of chess is bounded. Moreover, the rules of chess determine the permissible actions of each of the pieces. And the rules do not change in the middle of a game (although pawns change their behavior when they are promoted upon reaching the end, or eight rank, of the board). Chess games also illustrate combinatoric explosions. At the outset of a game there are 20 different opening moves for white, and 20 for black, producing 400 different possible positions; after the fourth move there are some 121 million possible positions. Thus, we can imagine a chess game as unfolding within a vast space of possibilities with the structure of the space is determined by the allowable moves. But recall that Shannon restricted his estimate to ‘reasonable’ moves. Shannon’s number would be vastly larger if we added all the nonsense moves that any reasonably competent chess player would immediately discard. As the game proceeds some regions of the space become foreclosed and to an astute player, new opportunities appear. 

If the rules of chess had not changed substantially since the origin of the game in India in the 6^th Century, one might argue that the possibility space of chess games was created at the origin of the game. A space of possible chess games was established at the origin of chess, but those changing rules (movement of the queen, castling, and many others) have expanded and modified the possibility space. In other words, the space of chess games has been constructed and evolved over time. 

Back to ancient Greece. Viewing the Antikythera mechanism as reflecting an initial construction of a space for orreys, a small part of the space of analog computers ignores the questions that we are most interested in resolving: What were the social, cultural and technological circumstances that allowed generation of that device, and what circumstances, two millennia later, led to modern orreys? 

The evolution of life has been occurring in spaces far vaster than that those imagined by Shannon. For example, changes in how genes are controlled in developing animal embryo helped drive the early origin of animals. On a much smaller scale, when crabs acquired the ability to grow claws of different size an array of new styles of predation appeared. Early humans discovered the capacity for cumulative cultural change, language and eventually technology. Certain cultural changes represent novelties, opening new opportunities. A key objective in seeking to understand how the introduction of biological, cultural and technological novelties has changed the opportunities available as well as the rules through which those opportunity spaces are explored.

Douglas H. Erwin is a leading paleobiologist whose books include Extinction: How Life on Earth Nearly Ended 250 Million Years Ago (¿ìÉ«Ö±²¥) and (with James W. Valentine) The Cambrian Explosion: The Construction of Animal Biodiversity. He is an external faculty member at the Santa Fe Institute and was for many years a senior scientist and curator at the Smithsonian National Museum of Natural History.