Ignoring the Maths
In his book Cosmos, Carl Sagan described how a Greek
named Eratosthenes calculated the size of the earth almost 2,200 years back. He
started with the observation that at a certain time, the sun cast no shadow in
Alexandria. He inferred that this meant the sun was directly overhead. He then
wondered how it was possible that a stick could cast no shadow in one place
while at the exact same time, it could cast a substantial shadow at some other
place (Syene).
These observations
didn’t match a flat earth scenario. Instead:
“The only possible answer, he saw, was that
the surface of the Earth is curved.”
Eratosthenes then
applied maths to the problem:
“For the observed difference in the shadow
lengths, the distance between Alexandria and Syene had to be about seven
degrees along the surface of the Earth.”
He then asked a
man to calculate the distance between Alexandria and Syene: it was 800 km. If
seven degrees mapped to 800 km, how much does three sixty degrees (a circle)
map to? Eratosthenes approximated the maths to come to the answer: 40,000 km.
That’s the circumference of the earth, he said. A remarkably accurate number,
as it turned out!
Sagan then points
out something weird. Centuries later, Europeans wondered if there was a direct
route to the Indies (Japan, China and India) by going west instead of going around Africa and travelling east. But surely, says Sagan, knowing Eratosthenes
calculation of the size of the earth, they should have known better: the maths
should have told them that any westward route from Europe would be far too long
and not worth it.
In fact, it turns
out Christopher Columbus knew that. So what did he do to convince Isabella and
Ferdinand to fund his venture?
“He used the smallest possible
circumference of the Earth and the greatest eastward extension of Asia he could
find in all the books available to him, and then exaggerated even those.”
As Sagan pointed
out, here’s the irony of the situation:
“Had the Americas not been in the way,
Columbus’ expeditions
would have failed utterly.”
Was Columbus
crazy? Or did he just not trust the maps of the day (not an unreasonable
assumption in those times)? Or was he just someone who wanted the thrill of an
adventure? Or did his patrons let the lure of the possibility of an alternate
route to the Indies (and riches) cloud what the maths was telling them? I guess
we’ll never know for sure…
Very interesting!
ReplyDeleteNot only the Greeks estimate the circumstance of the Earth fairly accurately, they even knew precisely that Moon is close and Sun is far from the earth. They tried their hand to arrive at the Sun to Moon distance (from the Earth) ratio. They messed up some assumptions and ways; and their estimate was completely erroneous. :-( If their estimate were indeed true, the Earth would have evaporated into nothing pretty early, leaving our Solar system devoid a the life-bearer planter! :-)
About "Ignoring Maths" which Columbus did seems to have benefited the Colonizers tremendously! Probably they would be happy that Columbus actually decided to ignore the truth in order to sail to his heart's content!!
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Coming to the subject of Physics, I wonder if any physicist would even allow a fleeting glance at this 'preposterous' suggestion to "ignore maths"! Ever since Newton, the prime language of physics remains mathematics.
[After quantum mechanics and the theory of relativity it appears that mathematics firmly told physics, "Buddy, I don't need you. But, without me, you are nothing!"
I also understand, on hearing that, physics seems to have responded with, "If you didn't chip in to fit into our science, actually by now the whole world would have agreed with what school children say, "I hate maths!" We gave you great status! So, stop your boast; And come and help whenever I am in need of your help".]