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Retroactive clairvoyance is an effect of hindsight bias, whereby one retrodicts alleged predictions or prophecies. That is, after an event has occurred, one claims that a psychic had predicted it, albeit in language or signs too vague or obscure to have been understood prior to the event in question.
Advocates of the prophetic abilities of Nostradamus are experts at retroactive clairvoyance, as are those who defend the notion that the Bible contains a prophetic code. It was only many years after the rise of Hitler, for example, that the following verse from Nostradamus was interpreted to be a prediction of Hitler's rise to power:
Beasts mad with hunger will swim across rivers,
Most of the army will be against the Lower Danube.
The great one shall be dragged in an iron cage
When the child brother will observe nothing.
It took over two millennia for some statisticians to discover that hidden in the words of the Bible are all kinds of meaningful messages. Others have applied the same formula to such books as War and Peace and The Skeptic's Dictionary and found similar odd results, indicating that humans have an uncanny ability to find meaningful patterns where none were intended.
A common ploy of psychics when a child goes missing is to provide police with tips based on their "visions." The psychic typically "sees" something like a dark car, the letter S, the number 5, a torn shirt, water, a man with a beard, trees, a shallow grave, and other "clues." Later, actual evidence is retrofitted to match these "clues" (hindsight bias). The tips that don't fit are conveniently forgotten (selective thinking) or facts are distorted, exaggerated, and embellished (retrospective falsification).
Some police officers actually fall for these tricks, like the sheriff who made Phil Jordan a deputy for his alleged help in the Tommy Kennedy case. In 1975, a six-year old boy got lost in the woods and the police invited Jordan to help find him. Jordan's version of the story is that he visualized a map of the area the night before he was called out and that he led the search team to the boy. The case has been investigated by Joe Nickell and Ken Feder. Jordan's map was vague and erroneous. It was of little use in the search. Jordan intentionally went to an area of the woods that hadn't been searched. He was in a ravine when others located the lost child, whom they'd heard yelling for help.
The process of finding specific meaning in vague or ambiguous words, letters, initials, numbers, and so on is called subjective validation. It is the key to understanding cold reading, as well as retroactive clairvoyance and all kinds of divination.
books and articles
Feder, Kenneth L., and Michael Alan Park. 1994. The mythologized psychic detective: Phil Jordan. In Nickell 1994, 115–129.