Oldest operational computer

My vote, considering old technology would be for mechanical (and possibly pneumatic). Mechanical read-write memories have existed for a long time (think about the adjustable combination action on a pipe organ). Read-only memories are possibly even older (Jacquard looms, player pianos, music boxes). Mechanisms for performing addition and subtraction are also very old. By 1850, fine precision machining had progressed pretty far along. But Will's right--in 1906, electronics was very primitive, particularly in terms of controlling device characteristics. Remember that spark-gap transmitters overlapped the discovery of thermionic electronic devices by quite a few years, mostly due to--I suspect--power-handling capabilities and general reliability. Incidentally, I ran across a 2001 US patent for a mechanical bit- serial adder (6249485). Very clever. But could one have a computer that could execute conditional branches and modify its own program? Yes, I think so--consider program storage arranged as pins set in concentric circles on the surface of a rotating disc. One could certainly devise a method of skipping instructions until a certain pin had been encountered. Similarly, if a register could be implemented to hold a single instruction word, instructions could be implemented to store into it and execute it. For what little it's worth. Cheers, Chuck