Connecting this with the article about the person who smelted his own sword, I wonder if it's possible for one person to single-handedly build a computer starting from Stone Age technology and raw materials?
http://lists.canonical.org/pipermail/kragen-tol/2010-June/00... are some thoughts about possible low-tech digital logic techniques. https://github.com/kragen/calculusvaporis has some thoughts about how to build a reasonably practical non-bit-serial CPU out of only about 1000 NAND gates (or the equivalent.) I think that with the height-field approach described in the kragen-tol post, you could probably make it out of 1000 moving parts — although most of them would have to be machined to fairly tight tolerances. I think the level of mechanical difficulty is similar to a 1960s V6 engine (fewer parts, but much higher force and demands on precision), or a little higher than that of a Curta calculator (600 parts for Type I).
The Clock of the Long Now uses steel gears on stone and ceramic bearings. It contains some mechanical binary calculation (and the prototypes are the most beautiful machines I've ever seen) but it's not a programmable computer.