Viz: Proof by Suc­ces­sive Contraindication

Begin the proof in front of a large atten­tive audi­ence. Lis­ten to the audi­ence reac­tion as you tran­scribe the proof onto the black– or white­board. When­ever the audi­ence makes con­traindica­tive noises above a pre­de­fined thresh­old, roll back the proof to the point where the noises began, and pro­ceed in a slightly dif­fer­ent direc­tion from there. Repeat as nec­es­sary, until the con­clud­ing point of the proof is reached, or a Socratic Ped­a­gogic Deficit [Cf.] is about to occur. If you detect that an SPD is about to occur, leave the remain­der of the proof to the audi­ence as an exercise.

Socratic Ped­a­gogic Deficit: In a les­son taught by the Socratic Method, the amount by which the pos­i­tive ped­a­gogic value of leav­ing the “real” answers ambigu­ous is exceeded by the con­fu­sion caused by leav­ing them ambiguous.