Euclid Writes an Algorithm: A Fairytale

How Euclid might have written and checked the correctness of his famous algorithm had he been a little further ahead of his time. Euclid of Alexandria was thinking. A traveler had that morning told him of a marvelous thing he had learned many years earlier from Eudoxus of Cnidus: a marvelous way to find the greatest common divisor of two numbers. But Eudoxus had not revealed the proof, and Euclid was wondering if it really was correct. He welcomed the distraction. Writing his Elements had become wearisome, and he was not sure he would ever finish. As Euclid idly scribbled in the sand, there suddenly appeared before him a beautiful woman wearing a diaphanous gown. “Who are you that disturbs my thoughts?” he asked. “I am a Fairy Godmother, but my friends call me FG.” “Wherefore have you appeared so abruptly?” “I am from 2300 years in the future, and I have come to take you there so you can write this algorithm that so intrigues you as it will then be written.” “What is an algorithm?” “There will be time to explain such things during our voyage. Come.” FG led Euclid into the temporal wormhole from which she had emerged, and they began their journey. As they traveled, she explained to Euclid what someone in the twenty-first century A.D. needed to know, including computers, programs, and mortgage-backed securities (which, in truth, Euclid only pretended to understand). After what seemed like a few weeks, FG said, “We have arrived in the year people now call 2010.” “Why chose you this year?” “It is the sixtieth anniversary of the birth of the computer scientist Professor Manfred Broy. In celebration, people are bringing him gifts. I have taken you here to write this algorithm so we can present it to him.” “He must be a wise and beloved man.” “Indeed he is. But there is no time now to speak of him. We must be off.” FG led him to a shopping mall where she bought a brand-new computer. “Let us now take it to my place and set it up,” she said. FG spent two hours setting up the computer, occasionally uttering expletives that were not Greek to Euclid. Euclid was puzzled. Finally, he said: “You have such wonderful devices. Why are they so hard to use?” FG replied, “We have made our computers so complicated that we can no longer understand them. We now suffer the consequences.” Euclid found this strange. But he was eager to begin writing his algorithm, so he let it pass. “How do I begin?” he asked.