Wednesday, March 01, 2006

Chad on Zeno and Black

I agree with Black’s position that mathematics alone cannot break the argument put forth by Zeno. Moreover, his argument examines the point that trying to count an infinite number of steps in a finite amount of time as impossible. In nature, it is true that the faster runner will overtake the slower runner. In my opinion the answer does not lie in trying to prove that it is impossible to count an infinite number of something in finite amount of time. The answer lies in the whole definition of infinity.
To my knowledge no one has ever proved infinity can exists. It is just simply an approximation used to put at an end of what the human mind is unable to conceive of. Human beings have been approximating nature since the beginning of time. As the centuries have passed since the time of Zeno our approximations have become better and better.
A good example is from the time of Isaac Newton. He invented calculus and applied it to celestial and earth bound mechanics. This new formulation explained everything from the distance a baseball could be thrown in a finite amount of time to the motion of planetary objects. Except, one thing was unable to be explained by Newton’s mechanics. The orbit of Mercury did not fit the calculations or any other explainable reason for its peculiar orbit. However, Newton’s approximations were close on nearly everything else in nature, but they were still approximations none the less.
Three centuries later Albert Einstein formulated his own approximations and clearly explained the orbit of Mercury. More in particular he defined that nature does have finite values for what was previously thought to be infinite. For example, Newton believed that the speed of light and gravity are instantaneous or at a speed of infinity. Einstein discovered that the speed of light in not instantaneous. Therefore, light travels a finite distance in a finite amount of time.
Two of the greatest minds in all of history understood that mathematics is invented as just approximations. It is the best tool we have and the approximations are used to explain how we believe nature works. Therefore, their arguments, including Zeno’s, still hold until a better approximation can explain them otherwise.


note: This post is Chad's despite the fact that it is not posted by Chad.

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