Core+philosophy

Like i had stated earlier, Zeno's four paradoxes are made up of 4 main points. The first is the arrow. Zeno states that at any time an arrow is at rest after it has been shot, it therefore can never move. The second is called the problem of the heap. If you have a pile of sand and you remove a grain of that sand, you still have a heap of sand (or x). If you keep doing this, eventually you would think there would be nothing left. If you thought this, then you are wrong. There will always be some sand present. The third is called the collumn marching. It states that if you have 2 collumns marching in the opposite direction at the same speed, eventually they will be going at 10 mph,which ends up to be twice as fast as they had started out. The one that stands out from all the others is Achilles and the Tortoise. Achilles and the Tortoise decide to race. Achilles can run twice as fast as the tortoise but they agree to give the tortoise a head start. Eventually Achilles catches up to the tortoise but at that same time the tortoise has moved ahead by half the distance that Achilles has ran. This keeps happening everytime Achilles "catches up" to the tortoise so the tortoise is still ahead. This all means one thing, Achilles can't catch up to Tortoise. The catch? Evntually Achilles does catch up, just not in the time frame allowed in the riddle. If you remember it never said that Achilles could NEVER catch the tortoise. The equation T = (d/s) (1 + 1/2 + 1/4 + 1/8....) can explain this perfectly. D represents Achilles and S represents this tortoise. If you follow the equation, everytime Achilles travels to the tortoise (or 1) the tortoise has doubled the margin and that margin keeps getting doubled.

Here is a picture of a Tortoise and Achilles. Zeno's philosophy of T = (d/s)(1 + 1/2 + 1/4 + 1/8....) is at work here because Achilles is trying to figure out why he cannot pass the tortoise.




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