Where Did the 12 Go?
A clock is not a 60–60 system. It is a 60–60–12 system.
Many people assume: minute hand is 1/60 of second hand hour hand is 1/60 of minute hand But this ignores a hidden structure: The hour hand is defined by 12 divisions, not 60. So the correct system is: second → 60 units minute → 60 units hour → 12 units Not a linear chain.
The mistake reveals a deeper principle:
Not all proportional systems are transitive.
Just because:
A relates to B by 60 B relates to C by 60
does NOT mean:
A relates to C by repeated chaining
because C may belong to a different structural partition (12 vs 60).
Everyone sees the 60. Very few people notice the 12.