Fuzzyland, a tale of wisdom

by Arnold Neumaier

Once upon a time, the country of Fuzzyland had a leadership that was famous for its wisdom in governing the welfare of its people. The king spent mostof his time traveling through his kingdom to be up to date on the quality of life in his country. Every citizen was entitled and encouraged to present to him and his deputies: complaints about things that didn't go as smoothly as desirable; ideas about improving services, laws, or institutions; observations about faults and failures of public offices; examples of excellence that deserved imitation; and whatever else might benefit the development of the country.

The king listened, judged the quality and value of the cases presented, and then gave orders to his servants, couriers, and ministers. He saw the need for this, the desirability of that, the usefulness of this and the danger of that. And he passed on order by order, as he saw fit. Many different people presented their ideas and concerns, and the king responded with his heart, not caring whether or not his orders were consistent.

Other kingdoms had their rigid laws or self-centered rulers that left many dissatisfied, but Fuzzyland had something special that left the people happier than elsewhere and visitors from everywhere spread its fame. In those times, a king's word was a command that had to be obeyed, and whoever didn't obey risked his life. Plenty were the stories where wise men lost their life or position because they didn't or couldn't satisfy their ruler's many wishes. Not so in Fuzzyland.

Among the minister's advisors were some mathematicians who worked out a scheme to satisfy their king. The key idea was to translate the fuzzy statements of the king's orders into objective estimates of the surprise he'd feel should he find out how his orders had been followed. Then, equipped with the list of orders of the past, they employed an army of computer slaves to find the least surprising set of actions, and ensured that these actions were carried out properly and efficiently.

Whenever the king was impatient about a request not complied by to the letter, the ministers had data and diagrams to show him that by relaxing just a few of his requirements a little they were able to satisfy many other of his requests to a degree beyond expectation. And the king, whose primary concern was the welfare of the people, was satisfied and blessed his ministers and their wisdom. The country prospered, and the citizens of Fuzzyland blessed their king for his habit to decree the impossible but to be satisfied with the best compromise that could be found.


This is the prologue of my paper

For context and details, see: Uncertainty modeling in high dimensions

Another Fuzzyland story

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Arnold Neumaier (Arnold.Neumaier@univie.ac.at)