Free Induction

 F
ree induction occurs with only the effort required by random external data collection.
Its probability of accuracy is high. It requires much time because new percepts cannot be formed until all the 'buckets' they subsume have been filled.

Rationalization (forced induction) requires the greater mental effort of concentration.
Its probability of accuracy is low. It requires much less time because subsumed buckets are unfilled.
Note: 'Effort' is congruent with and is the identity of taking the mind out of its default state and putting it into a reflexible condition (see index "Nature of Existence").

The concept of speculation is a prominent part of rationalization. The low success rate of forced induction can be better understood by examination of this aspect.

First degree speculation is the choice of a solution from the first spectrum of possibilities.
Second degree speculation is the choice selected from the second spectrum which depends on the first choice .
Third degree depends on the second and so on.
By way of example, the probability of successful deduction to the 3rd level is 1/1000 if there are 10 possibilities in each spectrum. To insure successful free induction 1000 filled buckets are required.

Despite the low success rate of rationalization, when combined with empiricalization it provides the greater success rate.
In this manner:

If there are 10 possibilities in a spectrum, it is most probable that the correct answer will be obtained by 'trying' (testing by experiment) only five of them on average before the truth is found. The resultant success of forced induction is better than free induction by a factor 2^n where 'n' is the degree of speculation.

Recall also that the buckets 'tried' are unfilled.
Note: An unfilled bucket is not a percept. When identified as a member of a spectrum it is an 'idea', i.e. a candidate for percept formation.

Abstract principles once proven can be employed in other circumstances where they are logically constrained (deduction) without necessity of experimentation. It is therefore possible to 'learn' without verification from a 'teacher' resulting in a primarily deductive entity (a human).