February 10, 2023
Thanks to Alissa Simon, HMU Tutor, for today’s post.
In his book, Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter paraphrases Kurt Gödel’s Incompleteness Theorem as follows: “All consistent axiomatic formulations of number theory include undecidable propositions.” Although this is not where January’s Quarterly Discussion started, it is, perhaps, the “still point of the turning world” (if we want to borrow T.S. Eliot’s phrase). Hofstadter certainly thought so: he calls Gödel’s insight “the pearl.” In other words, Gödel had discovered that the very foundations of Principia Mathematica were unprovable. In creating a coded language to talk about math, Gödel demonstrated how difficult it is to prove the foundational precepts at the heart of mathematics. This in turn leads us to question how a system (any system) might be able to comprehend itself. Though I struggle to understand Gödel’s theorem itself, these larger implications drove me to include Hofstadter and Gödel in January’s Quarterly Discussion.
We paired a very short excerpt of Gödel, Escher, Bach with Book VI, Part Six of Aristotle’s Physics. This four paragraph excerpt also proved difficult, dense reading. In it, Aristotle represented “primary time” with the line ChRh. According to Aristotle, time depends upon motion, so anything that is not in motion does not exist in “primary time,” and therefore, not on the line ChRh. While notions of “primary time” remains a little unclear to me, we decided that it refers to the time in which change is happening. Using this definition, I am better able to understand how time intersects with both motion and change. Even so, I still wonder about the separation between these terms: for example, how might we describe the difference between motion and change?
In this short proof, Aristotle assumes that all time is divisible. This interests me profoundly. Can we take it as a given that all time is divisible? Can we take it as a given that time functions in a consistent manner, particularly when we define it based off of notions like change and motion? Wouldn’t it make more sense to speak of time in relation to a specific event? I believe that this is what Aristotle attempted to do by segmenting time in a linear nature. However, the assumption of time’s divisibility causes me to pause because of its profound implications.
As a group, we wandered through dense language and complex ideas. Notions of infinity and loops circled the conversation and appeared in many of the concepts that were discussed. Hofstadter added dimension to the conversation in the form of story, art and music. In this way, he literally imagines the way that a system might comprehend itself (or not comprehend itself).
Thanks to the wonderfully helpful participants who gave me most of the language for this blog. The next Quarterly Discussion will take place in April and focus on Imaginative Literature. Everyone is welcome. Contact Alissa, as****@hm*.edu, for more information.
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