Prof. Nishiyama – #4 – the math(s) of light switches.

For anyone who is not an electrician, the task of wiring-up a pair of interacting two-way light switches (say, for example at the top and bottom of a stairway) might seem decidedly non-trivial. Experienced electricians though may scoff at the perceived simplicity of this assignment – but what if the house had say, five floors, and needed an interconnected switch on each floor. Still too easy? Then how about an ‘unlimited’ number of floors? That’s when you’d need the assistance of someone versed in Boolean Mathematics. Like for example Professor Nishiyama of the Osaka University of Economics, Japan. The professor has written a paper for Osaka Kiedai Ronshu (vol. 59, #1) on just this very subject. Stairway Light Switches
Using a combination of truth tables, Venn diagrams, and Boolean algebra the professor shows (by way of a matrix which uses only simple three-way and four-way switches see note) that a circuit can be devised which can turn that lights on and off in a house with an infinite number of stories.

Note: Confusion sometimes arises over the differences in electrical switch terminology‘ways’, ‘poles’ and ‘throws’ – this paper is an example.

Also see: Previous Improbable notes regarding professor Nishiyama :  HereHere, and Here

Coming soon:  More research from professor Nishiyama .