Class Summary November 19, 2013

Class Summary- November 19, 2013

“If you stare too long into an abyss, the abyss will stare back into you”

At the beginning of the class, we first had a discussion about a number line and that no matter what number you choose on it, it will always be in the middle. This statement was made based on the concept of transformation, the shifting of coordinates, in mathematics. 

Then, we transitioned into the significance of a paradox and defined it. Professor Hamman gave an example of a simple paradox: “This Statement is False”. This is a paradox because this sentence is technically written correctly, yet the content within the sentence makes it false. Therefore, a contradiction occurs making it neither true nor false.

Afterwards, we then discussed Zeno’s Paradoxes in depth. Many of us were confused about the Arrow and Stadium paradox. Professor Carter provided the class with an analogy of a camera for the Arrow paradox to help the class understand it. He said that when you capture a moment with a camera-the faster the shutter speed, the less time the object has to move. Eventually, the object will not move. However, there is always time between the moment of when it is taken and when it is being exposed.

 

Next, we looked at possible solutions for Zeno’s paradoxes, but then realized that when one solution is made, it would contradict with another paradox, which then made the paradoxes unsolvable. For the dichotomy and Achilles paradoxes, we said that there could be a solution by creating an ending point to the dividing. However, when we made a solution for the arrow and stadium paradoxes, taking away the “Zeno” or time/space in between the object, it would contradict with the dichotomy and Achilles paradox.  

Lastly, we viewed the various manifestations and compared them to Zeno’s paradoxes. One of the manifestations that we mentioned was the mirror image and how it is similar to the dichotomy because the mirrors appear to be getting smaller (half the size) in the distance.