Michigander in Mass

A couple days ago I walked by someone wearing a t-shirt only a mathematician, logician or philosopher could truly appreciate. The front of the shirt read "The statement on the back of this shirt is true." So what did the back of the shirt read? "The statement on the front of this shirt is false," of course. It was very ironic, as the chapter of The Universe and the Teacup by K.C. Cole I was reading that day was dealing with that very same issue: paradoxes.

Gödel was probably the first person to really recognize the limitations of mathematics to describe reality. To illustrate his insight, Cole gave us the sentence "This sentence is false" as an example. If it's true that it's false, then isn't it really true? And if it's false that it's false, isn't it in fact then true? (Whoa, hold on, gotta take another toke on the bong...) Gödel suggested that the sentence is only paradoxical if we focus on its internal validity and try to describe in mathematical terms the logical consistency of its self-references. If we can break out of the feedback loop, so to speak, we can judge the sentence's validity from another perspective.

Truth, the reader begins to realize, depends on your perspective. Your context. She then turns to computer logic, and specifically, language recognition. Take these two sentences:

"Time flies like an arrow."
"Fruit flies like a banana."

Although you and I might have to think twice about these sentences when we hear them together like this, taken in the context of a conversation, we have no trouble understanding their meaning. Computers don't have such an easy time. How easy is it to determine the subject, verb, object, etc., without access to a complex set of rules and some amount of contextual information (e.g., prior discussion of either bugs or the aerodynamics of fruit)?

Paradoxes come about because we apply (usually binary) logic to situations and expect them to be neatly categorized. I think one of her points is that this is not always necessary or true. What we think is the truth may in fact be limited by our perspective. We try to impose a schema on the world that aligns with how we perceive the world. But looks can be deceiving. A line isn't always a line, for example. A two-dimensional plane looks like a line to someone looking on edgewise. A three-dimensional sphere looks like a circle to someone unable to perceive depth.

Our brains have been designed to perceive things in a certain manner. Two extremely important functions that our brain must perform are filtering and categorizing. "Pay attention to this," "ignore that." "Friend, foe." "Food, preditor." I would argue that the binary numbering system that anyone familiar with computers takes as so fundamental arises from our built-in preference for such very simple but critical (at least for our initial survival and development) logic. But could our perspective be wrong? Are we looking at the problem edgewise?

My next science/philosophy excursions will explore some other interesting points she makes on how numbers can be deceiving and the nature of time and symmetry. Then I might go off on my own tangent on how our basic survival skills and mental coping mechanisms have skewed our perspective. And perhaps I'll find some more silliness to focus on too, lest we take ourselves too seriously.