Advanced Gear-based Calculation (the Antikythera Mechanism)
In a sense, this technology was lost twice: First, when the ship that carried it sank two millennia ago and, second, when historians, unmoved by hard-to-read X-rays of the day, left it to languish for more than a century after it was brought back to the surface in 1900-1901.
It was worth the wait. Once scholars sussed out what this laptop-sized object was — a gear-based machine for correctly modelling the movement of the planets, moon and sun — it changed the way we thought of Greek gear technology, to say nothing of the precision of mathematical calculation the device implied. It's all there in the gears: For example, one gear's 235 teeth match the number of months in 19 solar years (the shortest time in which solar and lunar cycles line up). The inventor might have inherited this idea from the ancient Mesopotamians, who used the 235-month cycle and built up great tables that tracked the sky's movements with remarkable accuracy. Other gears and ratios tracked lunar motion, even taking into account hitches caused by the moon's elliptical orbit [sources: Marchant, PBS, University of Puget Sound].
Since the decipherment of the so-called Antikythera Mechanism, some have quibbled over whether a planetarium qualifies as a computer, but it performs calculations that reveal when eclipses will occur, down to the hour — decades in advance. Lunar cycles were vital to the Greeks, who relied on them to cycle farming practices, time religious festivals, schedule payments and plot tactical advantages [sources: Marchant, PBS, University of Puget Sound].
Europe would have to wait until 1642 before an effective, geared mechanical calculator, the Pascaline, would be invented by French mathematician, inventor and philosopher Blaise Pascal. Cousin devices to the Antikythera Mechanism may have cropped up here and there in the medieval world, but true astronomical clocks would not reappear in Europe until the 14th century [source: Marchant].