Conjecture and Retrojection

As a murder mystery novel unfolds, detective and reader alike can
be visualized as assembling facts currently known to them into an
ever-developing story DAG. As this progresses, each will formulate
"conjectured nodes", or perhaps alternative conjectured nodes,
carrying facts or opinions which subsequent evidence may confirm or
refute. By this means, both try to solve the mystery.

In a scientific study, the scientist also formulates a conjectured
node -- a hypothesis -- and designs experiments to test it.

In these cases, the conjectured node is based on evidence available
at the time.

A retrojected node has some similarities. In contrast, however, it
is conjectured, or perhaps fabricated, to support a view which the
formulator wishes to propound. It is introduced into the story DAG,
perhaps replacing, modifying or serving as an alternative to a
non-supporting node, either:

    (a) at time t1, to explain or justify a fact at a later
        time t2,


    (b) at time t2, to fulfill an expectation or prediction
        from an earlier time t1, thereby trying to validate
        the later occurrence.

The reverse phenomenon also occurs. In the 1930s, for example, Leon
Trotsky was retrojectively expunged from the DAG of USSR history
because of his opposition to Stalin. In the term used by Orwell, he
became an unperson.

Some Examples

A simple example of (a) comes from the Book of Genesis.

At some point during the evolution of the book, perhaps as it was
first being written down (around the sixth century BCE), the sages
of the day ask: Why do the people of different regions speak
different languages?

They know of a very tall tower, a ziggurat, in Babylon, and they
propose an explanation:

                                  there is
                        A        a very tall
                         men build the
                B          ziggurat
                         claiming it
                        reaches Heaven
                        the Almighty
                C       regards this
                          as hubris
                         to prevent
                        worse hubris
                D       the Almighty
                E       people speak
                      different tongues

C and D form a retrojected subdag which "explains" the known fact, E.

We may observe here some new kinds of dependence between nodes:

    X justifies or explains Y
    X supposedly explains Y

and so on.

Many of the best examples of (a) will surely come from historic,
supposedly historic or biographical narratives. This is because
the key figures in these narratives, or their supporters, will
doubtless provide nodes or subdags to justify their actions.
("History is written by the victors.")

The most obvious of this type relates to Richard III.

Henry Tudor raised an army to fight Richard, who was killed in
battle, and Henry usurped the throne to become Henry VII. Popular
history, popularized by way of Shakespearian spin-doctoring,
portrays Richard as the epitome of evil:

    he was a coward,
    he was a hunchback (ipso facto evil, by popular belief of the day),
    he killed the Princes in the Tower.

Apparently, according to the latest evidence, he did indeed suffer
from some form of scoliosis, though this is no longer considered
relevant to his character. Other events, however, testify to his
bravery. And Henry himself may have had far more reason to kill the
Princes than Richard. If Edward V, one of the Princes, was still
alive at the time of the Battle of Bosworth, he was the rightful
successor to Richard, not Henry! Richard, on the other hand, had
become the Regent for Edward V at the time of his brother Edward
IV's death, and was now the acknowledged King.

In any event, the allegations became retrojected nodes, supplying
justification for Henry's actions.

Examples of (b) are a little more difficult to find, in that the
timings of t1 and t2 can be subject to differing opinion and,
depending on the precise formulation of the story DAG, can appear
to be of type (a).

We might expect to find examples of (b) in the following forms:

                event A is           event B
                predicted            occurs
                    \                 /
                     \               /
                      \          event B
                       \        is reported
                        \         /
                         \       /
                         event B is
                       is reported to
                         be event A

                event A is             event A
                predicted              occurs
               with features              /
                 P and Q                 /
                     \                  /
                      \             event A
                       \          is reported
                        \            /
                         \          /
                          \        /
                       event A is reported
                      with features P and Q

A simple case might arise in a revised version of the story of Snow
White, only child of the Monarch of Monochrome. Snow White's evil
stepmother, as we all know, arranges for her to be kidnapped and
fed to wolves. Years later, as the King lays dying, a woman arrives
with a hard-to-believe tale of being rescued by seven dwarves, and
claims to be the Princess. The King's heir presumptive, his fourth
cousin thrice removed, objects. He notes that the true Snow White,
like all oldest daughters of Monochrome Monarches, was tattooed on
her leg at birth with a black-and-white picture of a Monarch
Butterfly. The Snow White claimant, well-acquainted with this
custom, lifts her skirt to reveal just such a butterfly in full

Another example might be drawn from Shakespeare's Macbeth. In
Act IV Scene 1, Macbeth encounters an apparition summoned up by
the witches, who tells him:

        Be bloody, bold, and resolute; laugh to scorn
        The power of man, for none of woman born
        Shall harm Macbeth.

In Act V Scene 8, he is engaged in a fight with Macduff for his
life, and the following exchange takes place:


        I bear a charmed life, which must not yield,
        To one of woman born.


                                   Despair thy charm;
        And let the angel whom thou still hast served
        Tell thee, Macduff was from his mother's womb
        Untimely ripp'd.

Essentially, Macbeth is pointing out to Macduff that, according to
prophesy, Macduff, being "of woman born", is not qualified to kill
him. Macduff, however, introduces a new node, perhaps true or
perhaps a fabrication to shake Macbeth's confidence, indicating he
is indeed qualified, because he was not "of woman born" in the
natural sense, but rather by Caesarian section! If this is untrue,
it is a retrojection -- added at this moment in order to validate
his role according to prophesy.

Among historic narratives, examples might be:

    the procedures involved by the Catholic Church in declaring
    someone to be a saint. This involves investigating, long after
    the supposed fact, (medical) miracles performed by the
    candidate after his/her death, which help to prove him/her
    qualified for sainthood.

    the history of the Old Pretender James, son of James II (of
    England, VII of Scotland). Since many of the English nobility
    wanted James II to be succeeded by his Protestant older
    daughter rather than his Catholic son James, they declared that
    the latter was not James II's son, but had been smuggled into
    his putative mother's bed in a warming pan! (By the way, a
    senior minister is now always present -- in current times, only
    symbolically -- at the birth of close potential successors.)

Both of the cases, these can be judged to be of type (a) or (b)
depending on how the story DAG is drawn.

Popular Beliefs and Superstitions

Similar to retrojected nodes of type (a), there is a class of nodes
sometimes invoked to explain the unexplained. We will call them "popular
beliefs". These are analogous to "moral principles" and, like them, may
be gathered in global or local databases. Some typical ones are:

    "It is bad luck to walk under ladders."
    "Beware the Ides of March."
    "If you go out in the rain without a coat, you will catch a cold."
    "Ne'er cast a clout, ere May be out."
        (This last, familiar in parts of England, cautions
         against switching to Summer clothing until June!)

and so on.

One example of their use might involve the following nodes:

    A: (popular belief) Going out in the rain without a coat
            might cause a cold.

    B: (medical belief) Close contact with someone having a
            cold might cause a cold.

    C: Johnny goes out in the rain without a coat.

    D: Johnny meets his friend Tom.

    E: Tom has a bad cold.

    F: Johnny catches a cold.

leading to two variant DAGs:

                            A   D   E   B
                             \  |  /   /
                              \ | /   /

where either the path (A, F) or the pair of paths (E, F) and (B, F)
is present, depending on one's point of view. Johnny's mother
firmly holds to the popular belief, and this leads to a strong

A similar DAG may be constructed in regard to the events surrounding
the death of Julius Caesar:

    A soothsayer warns Caesar that something bad will happen to him
    on the Ides of March. Caesar disregards the prophesy and goes to
    the Senate on the Ides. There he is murdered by his opponents.

Their dislike of him is no secret, and is one of the factors in his
demise. But, is the prediction another one?


For some reason, this calls to mind a joke:

    A rabbi heads out on the Day of Atonement carrying golf

    In Heaven, Elijah, who is watching this with the Almighty,
    says "He is going to play golf on the Holy Day. You should
    stop him."

    The Almighty responds "If he plays golf today, he will be

    The rabbi reaches the golf course and goes out to the first
    tee, where he tees up his ball.

    Again Elijah implores the Almighty to intervene, and again
    the Almighty responds "If he plays golf today, he will be

    The rabbi drives the ball. It soars high in the air, travels
    375 yards and rolls into the hole for a hole-in-one.

    Elijah turns to the Almighty and asks "Is that what you call

    "Who can he tell?" responds the Almighty.