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…

Comments

  1. Ramiah KumarJanuary 9, 2019 at 11:28 AM

    Very interesting!

    Not 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!!

    ---------------------

    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".]

    ReplyDelete

Post a Comment

Popular posts from this blog

Student of the Year

Image
As a toddler, my daughter loved Alia Bhatt’s songs, esp. the ones from Student of the Year . (That movie did have many good songs and well-choreographed dances). Fast forward to present day, when she is 12 yo. She rarely watches Hindi movies now, but one of the few ones she likes of late, Raja aur Rani ki Prem Kahani has, yes, Alia Bhatt.   If I had any hopes that there was anything to be read in the name of her toddler-time favorite ( Student of the Year ), they have been dashed. Our conversations come exam time are perfectly captured by this photo and its caption: In fact, the pic below captures how she and I look at her answer sheets – me intently, she with an expression of “It’s over, so why are you even looking at it?”   Of late, we pull her leg and tell her that she isn’t showing any signs of academic prowess, she’d better find a rich guy to marry. Some time later, she showed us this meme on the Internet: “Me No Study, Me No Care Me Go Marry Millionaire If He Die
Read more

The Retort of the "Luxury Person"

Image
Coming up with biting and witty retorts. It’s something we dream of, but rarely manage to pull off. Worse, the more we stew over the offending remark, the more likely we are to come up with that dream retort, as Calvin ruefully points out: During our last holiday at the Taj Resort, seeing my wife carrying towels to our poolside chairs, one of the kids there mistook her for a member of the staff and asked for a towel. When my wife narrated this to us, I did not imagine that my 8 yo daughter would come up with her own retort. But a day later, my daughter recapped the incident, an incident that didn’t even involve her in the first place , and said, “You know what I’d have told that kid who asked for the towel?”. And without waiting for an answer, she told us anyway: “I don’t work here. I too am a luxury person who is living at this resort. Go get your own towel.” We were highly amused by the phrase she had coined: “luxury person”. It certainly captures the kind of holid
Read more

Animal Senses #7: Touch and Remote Touch

Instinctively, we think touch is based on contact. Not entirely true, explains Ed Yong in Immense World – there’s a more important aspect than contact: “These incredible feats are possible through movement. If you rest a fingertip upon a surface, you can get only a limited idea of its features. But as soon you’re allowed to move, everything changes. Hardness becomes apparent with a press. Textures resolve at a stroke.” As you run your fingers over a surface, they hit the tiny peaks and troughs and set off vibrations in the mechanoreceptors at their tips.   At the tip of its snout, the star-nosed mole has many pairs of hairless appendages. It uses them to touch things around itself. Alive or dead? Food or ignore? It does these movements at an insane speed. In the time it takes to blink our eyes, the star-nosed mole can probe, identify and swallow its food. “Light may be the fastest thing in the universe, but light sensors have their limits, and the star-nosed mole’s sense of
Read more