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Saturday, March 13, 2010

Another story

There is always another side of looking at things and a Paradox to cause complete mayhem.One such story 'Hare and tortoise' with multiple interpretations caught my attention when I read about Zeno's paradox-The paradox of achilles and the tortoise,his paradoxes in essence were a not-so-subtle attempt to disapprove the very existence of motion while gave Sir Issac Newton his famous line of work.

A hare one day ridiculed the slow pace of the tortoise, who replied: “Though you be swift as the wind, I can beat you in a 100-metre race if I be given a 10-metre headstart.” The hare, believing this assertion to be a complete no-brainer, agreed. During the race the tortoise never for a moment stopped, but went plodding on with nary a halt in his stride straight towards the finish line. 


The arrogant hare, confident he would win in any case, decided to catch a little shuteye in between. At last waking up, he saw his opponent had almost reached the goal and, run as fast as he might after that, he was never able to overtake him. 


Now, only an idiot tortoise would challenge a hare to a race in the first place, right? So what was this famously slow moving reptile thinking when he decided to take on such a fleet-footed mammal? New studies have shown that there was no way the tortoise could have known the overconfident hare would take a short nap that would spell doom for him. Besides, when the historic event took place the proverb “slow and steady wins the race” hadn’t even been invented. 


Today scientists realise that actually the tortoise was exceedingly well-read in the ancient Greeks and was relying on something called Zeno’s paradox in order to outfox his opponent. He figured that if he had a 10 metres headstart then in order to overtake him the hare would first have to cover the 10 metres distance. 


But by that time he himself would have moved, say, a metre ahead. So the hare would have to then first cover that one metre. But by that time he would again be ahead by, say, a tenth of a metre which the hare would have to cover next and by which time he would be ahead by a hundredth of metre and so on. Forget overtaking the tortoise, the hare wouldn’t even be able to ever catch up with him. 


For hundreds of years thereafter people thought the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. 


In a recently held “rematch of the millennium” a much more modern hare who was well versed in calculus which has shown the paradox to be wrong, easily outran a deeply disappointed descendent of the original tortoise. In an interview later he mourned, “Mathematics just ain’t what it used to be.” 

Moral: All scientific progress comes at a price.

Think of it, all economic progress too comes at a heavy price.Paradox:Why does your most hateful job becomes the job close to your heart?

5 comments:

Anonymous said...

u reminded me good old days wen we use sit n jargonise the whole hare - torri story for lectures....

Karan said...

An interesting read and i for one did not know that there was actually a theory behind the story...

I for one am going through the archives of your blog :)

Anonymous said...

Good evening

Great share, thanks for your time

Anonymous said...

Hi,

I begin on internet with a directory

Stupidosaur said...

I had thought a little about this in the 'olden days'.

If we assume Hare's speed H and tortoise's speed T, and say tortoise has headstart dustance d. Then hare would cross turtle at time t

ht = d + Tt

In Zeno's paradox we are zooming into shorter and shorter time frames before t is reached. The lead distance of tortoise over hare gets smaller and smaller as it approaches 0. To cover it hare takes additional smaller and smaller time frames. As we go on adding these smaller and smaller timeframes to the total time hare is running, it goes on approaching t but never reaches it. And at the same time distance between hare and tortoise goes on approaching 0, but never reaches it.

I wonder why that doesnt actually happen in reality. Could it be that timeframes just cannot get smaller and smaller like we are assuming in the paradox? That there is a smallest or minimum time interval that has to pass in one go for reality to have meaning, or for time to exist? Just like we cannot go below an atom or molecule size without fundamentally losing the property of the concerned material?

Well it is not most scientific or logically derived thought, but well it is definitely one speculation that could be fodder for new scientific experiments :)

..that "time is not analog or continuous, but discrete or quantized"

You can think of it like how one by one images on movie screen makes things look in continuous motion. Similarly reality is shifting in one by one states, with no real continuity. Only it looks continuous because the difference between one frame of reality and next is very very very tiny?