8.  P l a u s i b l e   R e a s o n i n g
     (Previous sections may need to be read to understand references in this section)

Probability is the degree to which an object behaves predictably in a future complex system. Its measure is usually a value expressed as a number between zero and one (a percentage). Probability theory is traditionally divided into two categories, physical and evidential. For millennia, physical probability, also known as frequentist theory, has been associated with games of chance. It deals with events like flips of a coin that tend to occur at a persistent rate, or relative frequency, in a long series of trials. Frequentist theory predicts that the probability of a coin toss coming up heads is 50 percent, not because there are only two possible outcomes but because over a large number of trials repeated into infinity, the frequency of heads and the frequency of tails both tend to mathematically converge at 50 percent. In other words, physical probability is based on experiment—a large number of repetitive trials.

In the eighteenth century, probability theory was redefined by Thomas Bayes (1703–1761), but it was not until the 1950s that Bayesian theory was applied to a wide range of applications. Bayesian theory is based on a partial belief rather than on frequency. Bayes evidential probability theory is a subjective method of determining plausibility, or the degree to which an object’s behavior is supported by available evidence. Bayes’ rule is used to update the degree of a belief according to the validity of posterior information. For example, when Jane was on trial for pilfering CIA equipment, a judge was inclined to believe new evidence in light of the veracity of prior evidence. Thus evidential probability is based on the subjective assessment of the validity of information—we might also say the confidence in that information.

The difference between physical and evidential probability was clarified by David Hume (1711–1776), a historian, economist, and philosopher who wrote extensively on human rationality. Hume noted that there were two ways to validate information: relating ideas and referring to the real world of facts. He proposed that the relation of ideas can only validate other ideas and nothing more beyond their related contexts. The proposition that “an equilateral triangle has three sides of equal length,” which orthodox philosophers (notably Plato and Descartes) have deemed a logical statement, was, Hume thought, detached from reality, because its truth depends on the ideas of geometry, not on an actual triangle in the real world with sides of equal length, which does not exist—at least not to an infinite degree of precision. Therefore Hume concluded that the relation of ideas cannot validate information. Moreover, he also thought that real-world facts can never be certain because of the fallibility of human interpretation. This proposition has become known as Hume’s fork.

Thomas Bayes and David Hume seem in part to agree, but they also seem to disagree. Bayes’s theory of evidential probability adheres to Hume’s real world of facts, but it does so through human subjective interpretation, which Hume distrusts. Removing human fallibilities from the equation, however, may reconcile the differences between the two thinkers.

In our uncertain real world, the plausibility of a future event is a human common-sense measurement inhibited by our cognitive biases and by our limitations in gathering, selecting, and analyzing information. For example, just before the pitcher threw the third pitch, Casey figured it would probably be a fastball, but he was not 100 percent sure. As he pounded his bat on the plate, he thought about the several possibilities. During the game the pitcher had thrown 60 percent fastballs, 30 percent curveballs, and 10 percent changeups. With two strikes on a batter and fewer than three balls, he had thrown a curveball 80 percent of the time, however to the last two hitters, he had thrown third-strike fastballs. Of course, Casey did not mathematically compute this information. He could not recall exactly how many fastballs, curveballs, and changeups had been thrown for strikes during the game, but his prediction was more than 50 percent sure, based on a hunch of the most recent information. He expected the third pitch to be a fastball (actually he was about 130% sure due to his overconfidence); he swung at it and missed.

Although similar to the human cognitive process for predicting the future, NF conforms to formal rules of plausible reasoning and remains unswayed by the emotional ambivalence of human thinking. It adheres to nine fundamental principles:

1. Generic software that requires no modifications to use with any application.
2. Dedicated, focused, and uninhibited as it gathers and processes cue data.
3. Qualitative evaluation of information measures magnitude
4. Quantitative evaluation of information codifies and counts similar events.
5. Events are decayed with age, giving due weight to the greater relevance of recent events.
6. Fast and frugal heuristics find the best forecast and expedite decisions.
7. Subjective method of rating information is based on Bayesian probability theory.
8. Confidence from one-hundred to one-hundred-and-twenty percent is attributed to event ratings.
9. Represents the degree of objects’ plausible behavior in real-world values.

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