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On the one hand, Europeans knew about the roundness and size of our planet since Eratosthenes (third century BCE). The measurement was extraordinarily precise (~1% error).

On the other hand, the eastbound ground distance to India was known at least since the Romans.

Taking these two pieces of information together, Christopher Columbus could have estimated the distance going westbound. However, he underestimated it dramatically.

Why was it so?

WoJ
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    Short answer was that he was a believer in what I call The Unscientific Method: Think up a fact you want to be true, then cast about for evidence that supports it, discarding any that doesn't. – T.E.D. May 29 '23 at 18:14
  • Columbus problem was that he used an Italian/Roman Mile (1,479 meters) instead of the Arabic mile (1,973 meters) for the 56⅔ miles miles per degree calculation. Had this been known by the Spanish court's mathematicians at the time, they would have used that as the reason why they thought that Columbus calculation was wrong. But they didn't, so I assume that this knowlage had simply been 'forgotten'. – Mark Johnson May 29 '23 at 20:18
  • See: What did Native Americans know, or speculate, about the Old world? – Mark Johnson May 29 '23 at 20:18
  • @T.E.D.: Rounding that thought out: Many have speculated that rumours of the Grand Banks may have circulated around the Mediterranean for a decade or more before Columbus. If accurate, and Columbus had heard those, the "answer" he reverse-engineered might have been just an excuse to find what lay south of the rumoured fishing grounds. It just seems more than coincidental that the distances are quite close. – Pieter Geerkens May 30 '23 at 00:23
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    @MarkJohnson - Well, my point was sort of that his problem was that he wanted it to be a small distance so his idea would be feasible. Which miscalculation he found or came up with to get that small number he wanted was really beside the point for him. – T.E.D. May 30 '23 at 01:32
  • @T.E.D. And my point is: Columbus (as did the Spanish court's mathematicians) knew and used the 56⅔ miles degree of longitude along the equator. But both had 'forgotten' that the mile used was the Arabic mile. Had they known this, they could had easily refuted Columbus claim. There is,however, no meantion that they used this argument. This seems to me to be far more plausible than the wishful thinking approach to this question. – Mark Johnson May 30 '23 at 04:46
  • Does anybody have a PDF copy of Pierre d’Ailly’s Imago mundi (1410), which is where Columbus got the 56⅔ miles per degree from. It would be interesting to see if only the term 'miles' was used or was more specific that it was not a Roman mile. An image showing this text would be interesting. – Mark Johnson May 30 '23 at 05:14
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    @MarkJohnson - The Spanish Monarchs referred Columbus' claims to a committee of experts. Whatever exact argument they used, they did in fact confidently report back to the monarchs that he'd grossly underestimated the size of the earth. That didn't end up mattering for political reasons (the Portugese had just rounded the Cape) that had nothing to do with the quality of anyone's math. – T.E.D. May 30 '23 at 15:23
  • @T.E.D. And? Depending on how the 56⅔ miles per degree statement in Pierre d’Ailly’s Imago mundi (1410) was written (with or without an expliced statement that it was not Roman miles), his error can be explained easily. The Spanish court's mathematicians came to their conclusions seperatly that tge result was wrong. I see no justification in your claim (made as a statement of fact) based on your The Unscientific Method. Everyone has a soft spot for their pet projects, there is nothing spectacular or new in that. – Mark Johnson May 30 '23 at 15:59
  • @T.E.D. A Sample from 1999: How NASA Lost a Spacecraft From a Metric Math Mistake | SimScale. Also a wrong measurenent unit error. – Mark Johnson May 30 '23 at 16:03

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