A Math Error


In 1491, a noted Spanish ship’s captain and seaman made a math error when calculating the circumference of the earth. At the equator, a line drawn all the way around our planet is about 25,000 miles long. This has been known and verified by various forms of mathematics since the time of ancient Egypt. But Christopher Columbus was convinced based on his own calculations that this number was 15,000 miles. That is a 10,000-mile difference and the reason he was sure he could reach China by sailing westward from Spain. If he had been correct, it would have been an easy sail. The error appears to have come from Columbus using the wrong value for a degree of longitude when looking at Chinese maps. It is even possible he used the distances as shown on Ptolemy’s maps, which were also far off.

At this time, the rivalry between Portugal, who had a painfully long but known route to the Orient around Africa, and Spain was intense. The Spanish monarchs were willing to do just about anything to find their own entry into the incredibly profitable trade. Many of us have heard the tale of Columbus convincing Queen Isabella that the earth was round by using an orange. There is no chance that really happened as just about every educated person in Europe already knew it was round. Columbus’ math error explains why the advisers to Ferdinand and Isabella all opposed financing his expedition. It wasn’t because they thought the earth was flat; it was because they had checked the sailor’s calculations. The learned men of Spain’s greatest court opposed financing the explorer because they had determined his math was wrong . . . and it was.

Even so, the Spanish monarchs decided to take a chance and in 1492 supplied three rather small ships to the mathematically challenged seaman. Or maybe it seemed a cheap way to just get rid of him after he had lobbied them for months on end. And so the rest is, as we say, history. Columbus sailed in the Nina, Pinta, and Santa Maria. Eventually, and rather heroically, he discovered the New World. Or at least he found a few islands in the Caribbean. The real importance of this being that Columbus showed everyone that something was there.

Incidentally, Columbus made another mistake while on his journeys. But this one was more fun. He mistook manatees for mermaids and recorded the finned women’s presence in the newly found waters.

Believing his own math was vindicated, the captain called the native peoples “Indians” and called the islands he finally landed on the “Indies.” Columbus died poor and would be amazed at how he has been revered today. He also might be a little upset to find out just how wrong he was. This math error may have been for Spain and Europe the most serendipitous mistake of all time. It brought the Spanish crown two centuries of plundered wealth and power while opening two continents to Europe.

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