Saturday, September 13, 2014

More math... Graphical Representation of Plato's Forms

      While in discussion on Thursday, I came up with a graphical representation of Forms that suits my fancy. We talked about a basketball being a poor representation of "roundness," for pure roundness is in itself intangible. Mrs. Quinet also talked about how mind-blowingly abstract graphs of lines were when you think about them. Combining the two thoughts, I considered each form to be a horizontal line. The line is infinite, therefore going along with the wholeness/pureness aspect of thinking of a Form by itself. Now define the basketball as a graph that intersects the horizontal lines representing "roundness," "orange," etc., and this produces a basketball. Because the basketball merely intersects each Form at a point, it will inevitably represent each Form poorly. Here's a picture I drew to clarify:
      Here, the green graph (the basketball) intersects three Forms: orange, bouncy, and round. Because the green graph only intersects each form, we can only glean a limited amount of information about "roundness" by looking at a basketball. Only when considering the entire horizontal line "y = roundness" will we be able to understand the abstract concept; however, we still cannot fully comprehend roundness because of the infinitude of the line.
      I will occasionally sit down and attempt to comprehend differing degrees of infinity. Though its not complicated to comprehend on paper, it still dizzies me that some infinities are larger than others. In brief, infinity is a hard thing to think about (which leads to epistemological questions), and that makes the graphical representation of Forms more complete.


Iris Mire said...

I greatly appreciate the math nerd spin you put on this. I agree with your idea that the basketball (green graph) results only in limited knowledge of each form because it only intersects each form at a single point. However, can you please explain why the basketball is considered infinite (indicated by the arrow on the green graph)? Is it because the basketball intersects an infinite number of forms?

Joe D said...

I drew it as continuing on "forever" because it intersects many more Forms than three. I'm sure there exists a limited number of Forms that define a basketball, so it would not be infinite. As in most analogies, it's not perfect. Another notable shortcoming is a definition of the space between horizontal lines (distances between Forms would be a frivolous consideration).