Mathematical Approach to Spiritual Discernment [ © 1997]
A Mathematical Approach to Spiritual Discernment
by José Becerra
The scientific method is a recursive process of inductive and deductive reasoning whereby we observe, infer and make statistical comparisons in order to assess causation. In the inductive phase, structured observations lead to explanatory models of reality. In the deductive phase, these models are used to predict expected observations. Discrepancies between the expected and the actual observations are used to refine the explanatory model(s) leading to subsequent predictions and observations.
This scientific process of inquiry can also be described in terms of the spiritual disciplines of Observation, Recognition and Revelation. We train ourselves in the discipline of spiritual observation in order to recognize patterns of events in life. These creatively discovered or “discerned” patterns “reveal” causal or synchronistic relationships among events to be tested by future experimentation.
The fundamental context of any observation, as experienced by ordinary human consciousness, is dual. The very act of observing defines the basic duality of self (Observer) and the not-self (observed). Moreover, ordinary observations are always reducible to simple statements of empirical truth or falsity.
If we assume that Truth, Goodness and Beauty are absolute attributes of Reality, then a scientific observer is constantly faced with decisions to accept or reject the truth, goodness or beauty of inferences drawn on evidence produced by the act of observation. The four possible options may be portrayed thus:
If an observer always accepts true propositions [Te=0], we conclude that such observer has perfect sensitivity to ascertain the Truth. Likewise, if an observer always rejects false propositions [Fe=0], we conclude that such observer has perfect specificity to ascertain Falsity. An observer with both perfect sensitivity and perfect specificity has attained perfect spiritual discernment: a very significant milestone in the evolution of human consciousness on Earth. It should be noted that such attainment would imply an unfathomable perfection to the ordinary rational mind, a division by zero. Spiritual disciplines define this stage as having attained true harmlessness: “perfect poise, a completed point of view and divine understanding.”
Short of this attainment, imperfect spiritual discernment may be mathematically defined as the ratio of two proportions: first, the proportion corresponding to correctly accepting true statements [Tc/(Tc+Te)]; and second, the proportion corresponding to incorrectly accepting false statements [Fe/(Fe+Fc]. This ratio may called the Discriminant Ratio (DR).
The greater the difference between Truth and Falsity in a given empirical proposition, the easier it would be to develop cognitive skills of adequate sensitivity and specificity to discern between them.
More commonly, however, in situations where the difference between Truth and Falsity is small, the observer needs to optimize the relationship between sensitivity and specificity in order to minimize errors of judgment. Many spiritual disciplines encourage the practice of “evening reviews” in which the observer reviews the experience of the day. One practical aspect of this systematic exercise is to empirically ascertain the DR applicable in different situations. The end of cycles or projects may also afford unique opportunities to brood on these transcendental matters.
Short of the state of relative perfection, human consciousness relies on probability statements to quantify the uncertainty or doubt inherent in decisions made with imperfect empirical knowledge. Although gambling has been documented as early as in the Gambler’s Lament of the Rig-Veda, it was not until the late 17th and early 18th centuries that the mathematical theory of probability was first developed and established. To date, no consensus exists in regard to the subjective or objective nature of probability statements. However, for the purpose of this essay, probability will be defined in its subjective dimension as the degree of an observer’s belief in the truth or falsity of a given proposition.
The foremost exponent of the subjective approach to probability has been Thomas Bayes (1707-1761). Spiritual discernment, as previously defined in terms of the DR, may be mathematically related to the observer’s beliefs by a derivation of Bayes’ Theorem of conditional probabilities:
(Precedent Belief) x (Discriminant Ratio) = Subsequent Belief
Belief is an attitude of mind in regard to explanatory models of reality. Beliefs also influence the way we structure consciousness to ascertain “facts.” Beliefs, in the Bayesian sense, are attitudes that can be evaluated in a continuous scale from zero (meaning impossible) to 1 (meaning certainty). Short of perfect convictions (i.e., beliefs with values of either 1 or 0), human consciousness relies on empirical evidence tested against models of reality to render judgments about events and their circumstances. This is the epistemological basis of the scientific method.
When it is “reasonable” to believe in a “probable” cause? Is credible, preponderant or “clear and convincing evidence” enough to ascertain truth, or should we believe something only when it is “beyond reasonable doubt”? These are instances in the field of law where these considerations are also relevant.
The scientific method is useless wherein certainty reigns. If a group of people is definitely convinced about the falsity of a proposition (precedent belief = 0), no empirical evidence or test whatsoever could possibly be produced to change their minds (subsequent belief = 0). This explains why ecclesiastical authorities would refuse to even look into Galileo’s telescope in the Middle Ages. History has proved them wrong but their action was consistent with Bayes Theorem. Likewise, there are people today who deny any truth in alternative healing, astrological influences or extrasensory perception. They may be right or wrong, but scientific evidence would prove them nothing because, in their minds, such events cannot possibly happen! Period.
The usefulness of the Bayes approach may also be illustrated by the analysis of the extreme attitudes of credulity and skepticism. The gullible attitude of mind leads to indiscriminate acceptance of both true and false propositions. The precedent belief is set high and the sensitivity far surpasses the specificity (rendering the DR close to 1). On the other hand, the skeptical attitude of mind leads to indiscriminate rejection both false and true propositions. The precedent belief is set low and the specificity far surpasses the sensitivity (rendering the DR close to 1). In both cases the individual lacks spiritual discernment (DR=1) and does not benefit much from empirical evidence “Tested” beliefs would just mirror preconceived ones. Not much has been learned from the observation process.
The observer needs to constantly calibrate the DR or spiritual discernment according to the circumstances at hand. These circumstances include both the past experience of the observer and the context of the events. In some circumstances, an experienced observer may also rely more on precedent beliefs than on “partial” or “biased” empirical evidence. But there is a well-known danger in taking the position that “the empirical evidence is wrong and I am right.” The difference between a fanatic and an expert is, in a sense, very simple: both have the same attitude of mind, but one is supported by the Truth and the other is not. Many have lost their way by their inability to discern this subtle but most vital difference.
The greatest practical usefulness of the Bayesian approach and the conventional scientific method is reserved for agnostic observers. For an agnostic observer, the precedent belief in a proposition is defined by a 50:50 chance. According to the Bayes’ Theorem (2), if such an Observer is faced with scientific evidence that favors one of two choices by a 99:1 margin (DR=99), then the agnostic individual is entitled to believe in the proposition with a 99% chance of being correct ([1:1] x [99:1] = [99:1]). Further scientific evidence may always adjust, or even reverse, such decision though.
As we grow in the experience of Truth, Goodness and Beauty, we learn to scientifically and spiritually discern the better from the worse in events and circumstances. We grow in humility as each new “conviction” opens unplowed fields of uncertainty. We also learn that the better of today may be the worse of tomorrow. We may thus grow in tolerance and compassion towards those who hold today our beliefs of yesterday, as we also grow in recognition of those who know today what we may believe tomorrow. And so on, until we truly know.