> In effect your brain added 11+2 to get 13, then took away 12 to make it fit
Not my German brain. But mod 24, I'm with you again :) And don't let me start with the Russians, they did it in hardware:
https://en.wikipedia.org/wiki/24-hour_analog_dial#/media/Fil...
If it’s 11 o’clock and we agree to meet in two hours, you instinctively know I’m talking about 1 o’clock. But what you’ve just done is add two numbers mod(ulus) 12.
In effect your brain added 11+2 to get 13, then took away 12 to make it fit, and came up with the modulus (or remainder) of 1.
Modulus arithmetic is therefore sometimes known as clock arithmetic.