An orrery is a machine for predicting the movements of heavenly bodies.   The oldest known orrery is the Antikythera Mechanism, created in Greece around 2100 years ago, and rediscovered in 1901 in a shipwreck near the island of  Antikythera (hence its name).   The high-quality and precision nature of its components would indicate that this device was not unique, since the making of high-quality mechanical components is not trivial, and is not usually achieved with just one attempt (something Charles Babbage found, and which delayed his development of computing machinery immensely).
It took until 2006 and the development of x-ray tomography for a plausible theory of the purpose and operations of the Antikythera Mechanism to be proposed (Freeth et al. 2006).   The machine was said to be a physical examplification of  late Greek theories of cosmology, in particular the idea that the motion of a heavenly body could  be modeled by an epicycle – ie, a body traveling around a circle, which is itself moving around some second circle.  This model provided an explanation for the fact that many heavenly bodies appear to move at different speeds at different times of the year, and sometimes even (appear to) move backwards.
There have been two recent developments:  One is the re-creation of the machine (or, rather, an interpretation of it)  using lego components.
The second has arisen from a more careful examination of the details of the mechanism.  According to Marchant (2010), some people now believe that the mechanism examplifies Babylonian, rather than Greek, cosmology.   Babylonian astronomers modeled the movements of heavenly bodies by assuming each body traveled along just one circle, but at two different speeds:  movement in one period of the year being faster than during the other part of the year.
If this second interpretation of the Antikythera Mechanism is correct, then perhaps it was the mechanism itself (or others like it) which gave late Greek astronomers the idea for an epicycle model.   In support of this view is the fact that, apparently, gearing mechanisms and the epicycle model both appeared around the same time, with gears perhaps a little earlier.   So late Greek cosmology (and perhaps late geometry) may have arisen in response to, or at least alongside, practical developments and physical models.   New ideas in computing typically follow the same trajectory – first they exist in real, human-engineered, systems; then, we develop a formal, mathematical theory of them.   Programmable machines, for instance, were invented in the textile industry in the first decade of the 19th century (eg, the Jacquard Loom), but a mathematical theory of programming did not appear until the 1960s.   Likewise, we have had a fully-functioning, scalable, global network enabling multiple, asynchronous, parallel, sequential and interleaved interactions since Arpanet four decades ago, but we still lack a thorough mathematical theory of interaction.
And what have the Babylonians ever done for us?   Apart from giving us our units for measuring of time (divided into 60) and of angles (into 360 degrees)?
References:
T Freeth, Y Bitsakis, X Moussas, JH Seiradaki, A Tselikas, H Mangou, M Zafeiropoulou, R Hadland, D Bate, A Ramsey, M Allen, A Crawley, P Hockley, T Malzbender, D Gelb,W Ambrisco and MG Edmunds [2006]:  Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism.  Nature,  444 (30):   587-591.  30 November 2006.
J. Marchant [2010]:  Mechanical inspiration.  Nature, 468:  496-498.  25 November 2010.