I think a good analogy to make this seem less mysterious would be the various methods of determining an average. E.g. we have no problem saying the "average fam

I think a good analogy to make this seem less mysterious would be the various methods of determining an average. E.g. we have no problem saying the "average family" has 2.4 children despite the impossibility of any family having 2.4 children. The number is just useful in other calculations for income, expenses, etc. From there it's not hard to imagine that the -1/12 result could be useful and justifiable as an intermediate step in other calculations despite being an "impossible" destination on its own.