Let’s go play outside! Dawning summer brings the allure of outdoor study breaks that add an additional element to our matrix of procrastination. But it doesn’t have to all be guilty romps through sunny avenues. We can recharge our scholarly batteries at the intellectual level in several ways by stepping, proverbially, outside the bounds of our usual ways of thinking. To think better we have to think differently, and in ways that our chosen academic discipline might not even consider.
What could be more universal than logic? It seems to apply everywhere, at least in theory. Kurt Godel (1906-1978) was a logician who concluded that even the arid moonscape of mathematical certainty resists the finality of proof and understanding. Logic is a theory system meant to map an a-theoretical world, after all. While “logic permits the use of any argument that carries conviction”, mere certitude is often not enough to convince others of what we are saying (Heijenoort 349). Even an airtight explanation leaves wiggle room because it has an outside. And it’s the outside that counts most if we are to understand why our perfectly rational calculations meet with resistance. Sometimes different people have different truths filtered through the reality of their different experiences; our own experiences are inevitably personal—such that empathy involves imagining how it would feel to feel what one does not actually feel at the time. In other words, to step outside oneself.
The reality that every system of knowing (epistemology) has limits became known as Godel’s Incompleteness Theorem. It states that: “in any formal system there exists an undecidable formula-that is, a formula that is not provable and whose negation is not provable” (Heijenoort, 352). Godel’s “fundamental results showed that in any consistent axiomatic mathematical system there are propositions that cannot be proved or disproved within the system and that the consistency of the axioms themselves cannot be proved” (Heijenoort, 352). As with numbers, so with humans: if we state that we are too exhausted to study no one can disprove the fact and thus our nap becomes a practical part of our academic regime for that day. If we are to put our studies in perspective and return to them with renewed vigour from our breaks, it also helps to remember that what we are studying has limits and therefore is within our grasp to understand and even master.
Godel goes on to explain that every system encounters a paradox when it purports to be able to illuminate the world. The system will encounter a wall; if it could explain everything it would be everything rather than just far enough outside its objects of study that it needs to be to sort and organize them.
When something doesn’t naturally fit into a system the system has means to try and make it fit, with varying results. Some outliers just can’t be accommodated. To allow for this discrepancy between explainable and unexplainable situations,“we have to introduce a distinction between ‘true’ and ‘provable’.” (Heijenoort, 352). Systems have limits to what they can explain. Beyond these bounds some truths may resist explication until we think outside our previous methods. Think of the phrase pictures or it didn’t happen.
The True and the Provable
The other day a crow flew over my head carrying a squiggling snake. Clearly still alive and on its way to doom at the hands of this juvenile murder (of crows), the scene carried a certain poetic pathos as well as a natural scientific curiosity. So did it really happen? In my mind it certainly did. Had I snapped a photo it would have been true to anyone who trusts their eyes (and distrusts that I’d have learned to use photoshop). Likewise, if I’d written of my experience and posted a letter to a relative that too would carry an element of my truthful experience. Even writing a poem or song about the crow and its slithery dinner might (were I talented enough) incite similar or identical synaptic and emotional responses on the part of an audience. But what if I’d only dreamed I saw the crow and snake? We know that our minds create dreams outside of themselves, as it were, and yet we have no way to record them objectively. A dream is experientially true and yet its contents are not empirically provable.
In his time, Godel claimed that “The human mind surpasses all machines” (Meyer, online). The magic of existence, human existence, includes the ineffable realm that resists empirical understanding. To truly comprehend being human we have to think outside of our technology and what we can prove with our creations; we have to investigate that for which we have no measure. As Blaise Pascal famously said ‘the heart has reasons that reason knows not’. As students seeking motivation it helps to take a break and think of our lives and coursework differently. After all, there will always be blind spots in our ways of thinking and perceiving. Artificial Intelligence researchers have even suggested that our species is at a dead end in the quest to create machines that correspond to our human ways. Andrew Moore, dean of computer science at Carnegie-Mellon University, recently claimed that AI at present still contains “no magic” (Moore, online). Like a dream explained through a brainscan but without knowing what caused its contents, efforts to replicate humanity in technology have not re-created humans quite as we are.
How can we get outside of our humanity to see what we don’t know about ourselves? Maybe it’s like imagining how to photograph a dream. A photo can only speak in photographic language and, it would appear, computers have limitations built into the nature of their ontology too. “We have pretty much stopped trying to mirror human thinking out of the box. We are focusing on engineering [what has already been invented” (Moore, online). So, instead of thinking like a machine when it comes to experiencing our course material, it helps to think like a human, even when being all-too-human feels suspiciously like indolent procrastination. Productivity includes an outside to itself—one without which its process would be impossible. After all, if we were hard at work all the time how would we know that we were? We’d have nothing to compare our glorious toil to!
Study breaks recharge our brains and daydreams fertilize our minds. Even if their productivity appears invisible in our final essays or exam results their empirical invisibility on the page does not mean that they lack value. They simply aren’t reflected within the ways we think of measuring our progress; their impact may resist measurement on the page yet exists in the ether of how we wrote what we wrote.
In fact, recent neurological studies show that the spaces between stimuli are when the action really happens:
Ingvars Birznieks and Richard Vickery developed a unique way to control the neural information that’s presented to the brain. Essentially, they delivered short mechanical taps to the fingertips of study subjects…Birznieks and Vickery ensured that each tap generated a corresponding nerve impulse to a neuron in the brain. By triggering the sense of touch — which the brain registers from vibrations along the ridge of our fingertips — the scientists were able to monitor how nerve impulses encoded the information. (Controneo)
At the neuroscience level, it turns out that the gaps really are what matter most. Neuroscientists traditionally believed that at the moment of a stimuli the brain would be most responsive. Neuron bursts were supposed to occur in direct correlation to the inputs being generated in the external environment. “Instead, it was the silent period between bursts that best explained the subjects’ experiences” (Moore, online). The study realized what we know from our study breaks: a mental jaunt away from our usual beliefs and expectations can reap benefits and increase our success at AU. So besides enjoying being outside in summer let’s also remember to refresh our minds by imagining the unimaginable.