Tale of Hansel and Gretel

¶ … tale of Hansel and Gretel

Once upon a time, there was an honest woodcutter with two children named Hansel and Gretel. The woodcutter told the children that if it was a mild winter, many people would not want to buy logs and kindling, and the family income would very likely decrease. Sure enough, there was no snow, and few people needed wood for their fireplaces. Given that the demand for firewood was dependent upon the probability of a warm winter, the little family grew hungrier and hungrier. Despite the desperation of the family, the woodcutter remarried. The children's stepmother was wicked and jealous. "See reason," she told the woodcutter. "Our survival and the children's are mutually exclusive events. We can make enough money to feed ourselves, or feed the children but our budget does not allow for the outcome of our collective survival: a principle as simple as the addition principle in probability. Either A, we survive, or B, the children survive, but A and B. cannot occur simultaneously."

The stepmother convinced the woodcutter to lead the children away into the woods and abandon them in a clearing. "Perhaps they will survive there, and fend for themselves," she said. So one day, the woodcutter took Hansel and Gretel on one of his journeys. He left them in a clearing alone and headed home without telling his son and daughter. However, Hansel, who had sensed that something was afoot before he left the family cottage, had scattered stones as the children walked, so they could find their way back along the path. Hansel's stones were unusual: bright pink stones he had gathered from the family garden. By deploying sequential counting techniques and leaving a stone every fifth step, the children were able to retrace their paths. The children found their way back easily: "the presence of a path, even a path of stones ensures we can find our way," said Hansel. "The presence of a path is a complementary event to being lost: without a path one can never lose one's bearings."

However, the next time the children were not so fortunate. Hansel's father took away the stones from the boy, and so the children only had scraps of bread to scatter on the path, to find their way back. The hungry birds in the sky pecked away at the bread. The presence of the birds was an independent event unrelated to the travails of the children: it could not be foreseen and would have not made getting loss more or less probable if Hansel had used stones. But with bread, alas, that was not the case.

"Don't the leaves of the trees look strange?" said Gretel. The conifers of the evergreen trees around the children were organized in perfect Pascal's triangles. The strangeness of the land of probability was confirmed when they came upon a gingerbread house covered with chocolate shingles and lollypops in every permutation of the colors of the rainbow (Hansel and Gretel calculated the possible combinations). Had the children been less hungry and weary they would have further calculated a subset of probabilities that the individual who owned such an abode was likely to be a witch, and that the outcome of events was likely to be ugly, but they were too hungry and simply dug in to the bounty before their eyes.

Even the theoretical probability that the house was owned by a witch was high, given its curious ability to remain perfectly intact, despite rain, insects, and other likely outdoor events that should crumble its cinnamon-sprinkled surface. And sure enough, witch popped out her head, and demanded the children pay for the shingles of peppermint and the windowpanes of spun sugar they had ripped from the structure of her home.