## THE MANDELBROT MONK
While Udo himself is little-known, one of his works is far more familiar. This 13th century German monk was the author of a poem called The first clue to Udo's undiscovered skills was found by mathematician Bob Schipke, a retired professor of combinatorics. On a holiday visit to Aachen cathedral, the burial place of Charlemagne, Schipke saw something that amazed him. In a tiny nativity scene illuminating the manuscript of a 13th century carol, Discovered in 1976 by IBM researcher Benoit Mandelbrot, the Mandelbrot set is the most famous fractal (a mathematical object with the property of infinite detail). Only the advent of fast computers made feasible the repeated calculations involved - or so it was thought. [*4] "I was stunned," Schipke says. "It was like finding a picture of Bill Gates in the Dead Sea Scrolls. The colophon [the title page] named the copyist as Udo of Aachen, and I just had to find out more about this guy." Schipke visited Bavaria, where the poems, "Although it had been discovered in the 19th century, it had promptly been filed away again," Schipke says. "The local historian who found it was clearly no mathematician, and dismissed it as obscure theology. But it yielded several major surprises." In a recent paper, Schipke and Eberhardt report on Udo's discoveries. [*5] The first chapter, The second part, Schipke continues: "What was interesting at this point was that we looked back at the words of More was to come. In the final and longest chapter, Initially, Udo's aim was to devise a method for determining who would reach heaven. He assumed each person's soul was composed of independent parts he called "profanus" (profane) and "animi" (spiritual), and represented these parts by a pair of numbers. Then he devised rules for drawing and manipulating these number pairs. In effect, he devised the rules for complex arithmetic, the spiritual and profane parts corresponding to the real and imaginary numbers of modern mathematics. In When Schipke saw the translation, at once he saw it for what it was: an allegorical description of the iterative process for calculating the Mandelbrot. In mathematical terms, Udo's system was to start with a complex number z, then iterate it up to 70 times by the rule z -> z*z + c, until z either diverged or was caught in an orbit. [*4] Below the description was drawn the first crude plot of the Mandelbrot, which Udo called the "Divinitas" ("Godhead"). He set it out in a 120x120 frame he termed a "columbarium" (i.e. a dovecote, which has a similar grid of niches) and records that it took him nine years to calculate, even with the newly imported technique of ‘algorism', calculation with Arabic numerals rather than abacus. "It tends to be taken for granted," Schipke says, "That the Mandelbrot is too calculation-intensive to be done without computers. What we have to remember is the sheer devotion of the monastic life. This was a labour of faith, and Udo was prepared to work for years. Some slowly-converging pixels must have taken weeks." Why did the work of this gifted mathematician go unnoticed for so long? Schipke blames, in part, specialisation. "When the Codex was unearthed in 1879, only a non-mathematician got to see it, and he didn't know what he was looking at. It's a common enough story. Take Hildegard of Bingen, whose accounts of her visions were taken as pure mysticism, but neurologist Oliver Sacks instantly recognised them as accurate descriptions of migraine symptoms. Likewise, literary critics dismissed Edgar Allan Poe's final work, "But there were also contemporary reasons why Udo's knowledge didn't make it into the mainstream. His basic belief - that salvation and damnation could be determined in advance - was heretical, and his use of Arabic numerals was thought a bit of a black art. And there was the disagreement with Thelonius." Despite the borderline nature of his work, Udo impressed his abbot at the monastery of Sankt Umbertus near Aachen. Life for a 13th century monk wasn't necessarily austere: the scurrilous But Udo and his helper, Thelonius, ran into instant disagreement. Udo had always interpreted the Mandelbrot as signifying God. Thelonius took the opposite view: that it represented the Devil. Numbers that escaped to infinity, he argued, were souls flying free to heaven, and those caught in an orbit had fallen into the pit of Hell. Like many theological collaborations, they had a schism on their hands. Udo noted that their differences brought all work to a halt, and finally the two were reprimanded by the abbot for coming to blows in the refectory. "Sadly I write," says Udo on the last page of the Codex Udolphus, "that on pain of excommunication I must lay down my dice and my numbers. I have seen into a realm of heavenly complexity, and my heart is heavy that the door is now closed." Bob Schipke comments: "It's a pity that personal differences ended research that could have moved mathematics forward by centuries. But fortunately, Udo couldn't leave the subject alone. By dropping clues into the |

## miércoles, 26 de marzo de 2008

### Mandelbrot

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## 2 comentarios:

Caramba, Mandelbrot era un Profeta !!

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