Class Summary For Tuesday Nov. 5th 2013

We started the class discussing about our previous homework which was to take a stand on how we prefer to view infinity, either from a rationalistic point of view or from an empirical point of view. Prof Hamman asked if anyone had difficulties choosing a stand. 50% of the class preferred to view infinity from a rationalistic point of view and the other 50% preferred the empirical.

Then, Prof. Carter continued on the topic of the different paradoxes. He started with the paradox of the arrow. He explained that the arrow can only travel as far as its length. And when it gets down to one instance, the arrow will be occupying a hundred percent of its space. And so this means the arrow is not moving at all for every given instance. Prof. Hamman tried to explain the concept behind Zeno’s paradox that there is no subdivision of time. This revealed a big difference between the first two paradoxes that suggest that, we cannot keep subdividing and the next two paradoxes that says if we cannot continue to subdivide, then we’ll get into trouble.

Another paradox Prof. Carter talked about was the stadium. The shortest distance the dogs can move is one length. They cannot move half a length. If the pandas are not moving while the dogs are moving next to each other passed the pandas, it will be discovered that we cannot tell when the last dog passed the second panda. From Prof. Hamman’s point of view, it was hard for him to understand this concept because we cannot think of a smallest unit of time. The next question that came up was whether we can divide time? If there is not a smallest unit to divide time, then we are going to have problem resolving this concept. At this point, it became clear that the paradox of the stadium got everyone more confused. The major challenge was unveiled, the rational is saying one thing and the empirical is saying another. Just as in the case of the dichotomy, it makes no sense theoretically that before an object can travel a given distance, it must travel half its distance. We all concluded that our individual perspectives still count in how we interpret these various concepts of infinity.

Prof. Hamman commented that Zeno was really clever to have imagined all these paradoxes. The class became curious to know how Zeno was able to come up with these concepts. Prof. Carter pointed out that Zeno might have been influenced by his friend who believed there is no space and there is no time.

In conclusion, Prof. Hamman commented on how Aristotle misinterpreted Zeno’s paradoxes and the great impact it had on the knowledge of infinity for a long period of time. At the end of the class, we were assigned our next assignment which is to create something that is a best representation of infinity. What a good way to end the class!