The Long Now Project clock details...

Time calculations

Options considered for the part of the clock that converts time source (for example, a pendulum) to display units (for example, clock hands) include electronics, hydraulics, fluidics, and mechanics.

A problem with using a conventional gear train (which has been the standard mechanism for the past millennium) is that gears necessarily require a ratio relationship between the timing source and the display. The required accuracy of the ratio required increases with the amount of time. (For instance, for a short period of time the count of 29.5 days per lunar month may suffice, but over 10,000 years the number 29.5305882 is a much more accurate choice.)

Achieving such precise ratios with gears is possible, but awkward; similarly, gears degrade over time in accuracy and efficiency due to the deleterious effects of friction (which is to say, they get smaller. Smaller gears move faster, throwing precise calculations seriously out of joint). Instead, the clock uses binary digital logic, implemented mechanically in a sequence of stacked binary adders (or as Hillis, their inventor calls them, serial bit-adders). In effect, the conversion logic is a simple digital computer (more specifically, a digital differential analyser), implemented with mechanical wheels and levers instead of typical electronics. The computer uses a 28-bit number representation, with each bit represented by a mechanical lever or pin that can be in one of two positions. This binary logic can only keep track of absolute time, like a stopwatch; to convert from absolute to local solar time (that is, time of day), a cam subtracts (or adds) from the cam slider, which the adders move.

Another advantage of the digital computer over the gear train is that it is more evolvable. For instance, the ratio of day to years depends on Earth's rotation, which is slowing at a noticeable but not very predictable rate. This could be enough to throw the phase of the Moon, for example, off by a few days over 10,000 years. The digital scheme allows that conversion ratio to be adjusted, without stopping the clock, if the length of the day changes in a different way than expected.