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Three minds acting on the nullsome, onesome, twosome, threesome, foursome, fivesome, sixsome, sevensome.

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 Viewed in this way, however, the learning triad is revealed to be a relatively weak learning algorithm. There is no provision for "backtracking" -- for going back up a node, retreating from a sequence of modifications that has not borne sufficient fruit. In order to backtrack, one would like to actually erase the previous modification to the thought process, and look for another child node, an alternative to the child node already selected.
An elegant way to view backtracking is as going around the loop the wrong way. In backtracking, one is asking, e.g.: What is the thought that gave rise to this action? Or, what is the action that gave rise to this percept? Or, what is the percept that gave rise to this thought? In algebraic language, one is asking questions that might be framed
THOUGHT * ACTION = ?
ACTION * PERCEPT = ?
PERCEPT * THOUGHT = ?
In going backwards in time, while carrying out the backtracking method, what one intends to do is to wipe out the record of the abandoned search path. One wants to eliminate the thought-process modifications that were chosen based on the percept; one wants to eliminate the actions based on these thought modifications; and one wants to eliminate the new percept that was formed in this way. Thus, speaking schematically, one wants to meet PERCEPT with -PERCEPT, ACTION with -ACTION and THOUGHT with -THOUGHT. Having annihilated all that was caused by the abandoned choice, one has returned to the node one higher in the search tree. The natural algebraic rules for backtracking are thus:
THOUGHT * ACTION = - PERCEPT
ACTION * PERCEPT = - THOUGHT
PERCEPT * THOUGHT = - ACTION
Backtracking is effected by a backwards movement around the learning triad, which eliminates everything that was just laid down.
Ben Goertzel. On the Algebraic Structure of Consciousness#1223
1996

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