Correction

I used to think Base 12 was all that, but I'm getting more partial to Base 3 on account of its optimal radix economy, and the existential appropriateness of a logical system that allows for "true", "false", and "some indeterminate third value."

I think this would resolve the Schrödinger's cat paradox by allowing us to classify the cat not as "alive" or "dead", but as in "some indeterminate state".  And you could do math on that, and everything.

I've looked for one of these on Ebay, but to no avail.  Doubt it would run Skyrim in any case...