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The Antikythera, a Babylonian Astronomical Machine

"Two thousand years ago, a Greek mechanic (built a) clockwork mechanism that displayed the motions of the Sun, Moon and planets on precisely marked dials. By turning a handle, the creator could watch his tiny celestial bodies trace their undulating paths through the sky...  The Antikythera mechanism is by far the most technologically sophisticated artefact that survives from antiquity...  Scientists delving into the astronomical theories encoded in this quintessentially Greek device have concluded that they are not Greek at all, but Babylonian — an empire predating this era by centuries. "

Source: http://www.nature.com/news/2010/101124/full/468496a.html

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Other advanced pieces of equipment have been discovered as well which date back to the time of Ancient Babylon: for instance there was a terracotta jar thought to house the first primitive battery. An copper tube ran down into the pot, and there was the remains of an iron rod inserted into the tube. Archaeologists made a replica of it using new materials, and discovered when an acid was introduced- for the purposes of their observations, grape juice, the device gave off an electric current. It was discovered that by attaching copper wires between this "battery" and a small object made of base-metal, once could electro plate it, giving a gilded effect to the object.
Allegedly, archeologists have also found evidence of brain surgery from the same period.

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