Hmm, I think you need to look more into the Antikythera device, Watchman. You've assumed it is just a chronograph which stolidly keeps track of time and the movement of celestial bodies. This isn't the case. The device is intended to accept input via the operator and then return a result. The operator sets the date and the device computes, using analog gears rather than digital electronics, a result which shows various things: the lunar cycle on that date, the solar cycle, the positions of the various planets in the sky and several other things. This is, by definition, the very essence of a computer - analog or digital. The fact that the Antikythera device uses gears to achieve what a digital computer does with electrons and binary manipulations doesn't detract from what it achieves. It accepts input and returns a result which would take many hours of mathematical work by hand. Same as any computer.

There's an article in The Economist about it, entitled appropriately enough for this discussion, The Clockwork Computer.

There's a wonderful article about it in the online version of Nature, called In Search of Lost Time.

And, of course, there is the actual research itself, represented on the web pages of the Antikythera Mechanism Research Project in Greece.