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‘The Quijote‘ allows many readings, from the medical remedies that appear there to the plants, passing through gastronomy, mythological characters and even mathematics. And it is that Miguel de Cervantes he used them as a backbone in more than one scene.
—Perhaps one of the best known takes place when Don Quixote orders Sancho to whip himself so that Dulcinea can be freed from the enchantment that has turned her into a villager, in exchange for this ordeal he will receive what he has in his bag. Namely, 3,300 cuartillos, a quarter of the real.
—With this plot base, Chapter LXXI of Part Two is developed, where the following dialogue between Don Quixote and Sancho Panza takes place:
“Tell me, your grace, how much will you give me for each spank you give me?”
—Take your time what you have mine, and put a price on each whip
“They,” replied Sancho, “are three thousand and three hundred and something; of them I have given myself up to five: the others remain; let these five enter among the many, and let us come to the three thousand and three hundred, which is a cuartillo each, that I will not take less even if everyone sends me, they make three thousand and three hundred cuartillos, and they are the three thousand, one thousand and five hundred real means, which make seven hundred and real counts; and the three hundred make one hundred and fifty half-reales, which come to seventy-five reales, which together with the seven hundred and fifty, are eight hundred and twenty-five reales for all…
Sancho makes an ingenious calculation without having to make the initial division: 3,300 quarts: 3,300/4= (3,000 + 300) / 4 = 3,000/4 + 300/4= 750+75=825.
Decimals and math errors
In Cervantes’ work we find several examples of decimal fractions, which suggests that the Spanish population would be accustomed to using this type of terminology: “a third part to the person who will accuse him improved by a third and a fifth” (chapter XXI, First Part), «we have to come out improved in third and fifth» (chapter XXXI, Second Part), «three quarters of a league had traveled» (chapter XXIX, First Part), «and since the night was almost in the two parts of its day» (chapter XLII, First Part) and «he sent the duchess up to half a bushel» (chapter LII, Second Part).
In chapter IV of the First Part we find a mistake in a multiplication: “the farmer lowered his head and, without answering a word, untied his servant, to whom Don Quixote asked how much his master owed him. He said nine months, at seven reais each month. Don Quixote did the math and found that they amounted to seventy-three reales, and he told the farmer to pay them out immediately, if he did not want to die for it».
paradoxes and equations
Another of the best-known episodes, and one that is closely related to logic, is the so-called paradox of the hanged man, which takes place during the period of time in which Sancho was governor of the island of Barataria.
A foreigner arrived there who affirmed that a river divided two terms of a manor and on the river there was a bridge and also a gallows. The law of the region agreed that if someone passed over the bridge he had to swear first where he was going and what he was going to, if he told the truth he would be allowed to pass and otherwise, if he lied, he would be hanged.
On a certain occasion it happened that a man went to cross the bridge swearing that he was going to die on that gallows. If he was allowed free passage, he would lie on his oath and therefore he should be hanged. However, if he hanged her he would have sworn the truth and, for that reason, he would have to be set free.
Sancho, after remaining thoughtful before such a curious dilemma, decides that if it were up to him he would leave the man alive, since whatever he did he would break the law.
In ‘Don Quixote’ we find certain numerical extravagances, for example, in which the knight errant incurs in chapter VIII of the First Part when estimating the length of the arms of the giants:
“What giants?” said Sancho Panza.
“Those you see there,” replied his master, “with long arms, which some of almost two leagues usually have.”
At that time the Castilian league was equivalent to 6,350 m, which means that the arms of the giants would exceed twelve and a half meters in length.
In the Cervantine novel we can also enjoy the beauty of the principle of equivalence for equations (chapter XXXIII of the First Part): «if we remove equal parts from two equal parts, the remaining parts are also equal». In other words, if “a” equals “b” then “ac” must equal “bc”.
Pedro Gargantilla is an internist at El Escorial Hospital (Madrid) and the author of several popular books.
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