The Shroud of Turin and an Infinite Series

Having a somewhat skeptical bent and a long interest in pseudo-science An article on Medium about the Shroud of Turin caught my eye. For some background see Unraveling the Myths Surrounding the Shroud of Turin. The Shroud first appeared about 1355 A.D.:

The Shroud of Turin made its first appearance in a small country church built in Lirey, France, and by an aristocratic soldier Geoffroy de Charny. As soon as this relic was put on public display, it immediately became the subject of debate. Two local bishops declared the relic to be fake. In 1389, the bishop of Troyes, France, wrote a letter to the Pope denouncing the falsity of the relic and accusing the canons of the Church of Lirey of deliberate fraud. According to the bishop, the canons had commissioned a skilled artist to create the image, acting out of greed and taking advantage of people’s gullibility. The Pope responded by allowing the canons to continue exhibiting the cloth, but simultaneously obliging them to publicly declare that it was being displayed as a “figure or representation” of the true Shroud of Christ, not the original.

Attempts to “rehabilitate” the shroud and present it as a genuine relic of Jesus Christ began after 1453, when it was purchased by the House of Savoy. The controversy continues to this day.

The Medium article, Earliest Mention of the Shroud of Turin Claims it was “Lies Forged by Churchmen” is based on A New Document on the Appearance of the Shroud of Turin from Nicole Oresme: Fighting False Relics and False Rumours in the Fourteenth Century. Among the early skeptics of the Shroud was the well-known scholastic philosopher Nicole Oresme. This name rang a bell.

I am also reading Paul Nahin’s Hot Molecules, Cold Electrons: From the Mathematics of Heat to the Development of the Trans-Atlantic Telegraph Cable. This is a slow project since I am verifying all of the mathematical steps in it. Oresme was the first person to prove that the the harmonic series 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + ... + \frac{1}{n} + ... diverges. Nahin gives the proof, which is an example of the comparison test for infinite series. See Harmonic series (mathematics). Quite impressive for three centuries before calculus was discovered.

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