A little lunacy is all right at this time of year, but you should have experienced at least a temporary respite during last night's total eclipse. Did Professor Gould ever make mention of anything that smacked of mathematics during his lectures last semester? We had a common student a few years ago who applied some interesting geometry to determine the shape of a sunken ship from the patterns of timbers "shaved off" by the water line, an application of slicing.
It certainly is true that the time dimension shows up in many circumstances connected with configuration spaces, and sometimes it seems to take over and dominate the discussion, but not always. The subtraction in the analogue of the Pythagorean theorem comes in because of the assumption that the speed of light is a constant, but that is not all that easy to present in an elementary way. I look forward to seeing more later.