sockillogical

1. the absence of logic pertaining to socks
2. an adjective to describe the lack of logic
3. painful undertakings, as in "psychological torture" or " sockillogical torture" when trying to pair socks after doing the laundry
4. bad dress sense; poorly matching clothes.

a. Looking for matching socks in the morning is sockillogical.
b. The businessmen in the photograph were mostly sockillogical in that 3 out of 5 had mismatching socks.