The first computing machines used relays which are electromechanical mechanical switches. Current would flow into an electric magnetic and it would magnetize a

The first computing machines used relays which are electromechanical mechanical switches. Current would flow into an electric magnetic and it would magnetize a switch and close a loop thereby switching something "on." By placing these switches together into different configurations you could form equivalent logic gates. Sometimes insects or moths would get stuck in the relays which would screw up the system. This is the origin of the word "bug." Prior to incorporating logic into electronics, computing machines were hand cranked or motor cranked gear machines. See: https://www.youtube.com/watch?v=fhUfRIeRSZE https://www.youtube.com/watch?v=fhUfRIeRSZE. The YouTube video literally is a hand cranked portable calculator. The world you envision has already existed.