“Yeah, it’s wrong, but it’s understandable!”
Learning at university sometimes feels like playing a slow and very joyless version of Tetris.
Long, dark revision weeks are spent in dim-lit dorms and reading rooms, flicking through lecture slideshows that never end, wearily trying to mentally twist, turn and rotate their contents into a form that, in time for exams, slots gracefully into our memory, or - failing that - is panickingly crammed into it as a holey heap of half-understandings.
How do we best rotate those rapidly gravitating Tetris shapes? What exactly is it that we do when we run highlighters down textbook pages and jot ballpoint marginalia on slideshow printouts? When our minds’ adhesive properties are worn off by hours in the library - when our intellect struggles like dried glue - what is it that makes information stick? What does it mean to extract an “essence” of a concept, as if the lecture notes contained some glistening liquid that could be pipetted, encapsulated, and implanted in our brains so that, when perturbed, it instantly would release an orderly avalanche of inferences, allowing us to enter an exam hall confident in our ability to answer every possible exam question?
These questions – about what a brain-friendly knowledge format looks like - have fascinated me ever since high school. That's when I first read about cognitive scientific theories on how our brains assimilate abstract concepts by mapping them onto concrete concepts from our visual and spatial experiences. The basic idea is that “understanding” occurs when our mind successfully, after a lot of unconscious processing, has stumbled upon a good analogy between the new concept and something we already know, derived from our daily interactions with the physical world. The theory hints at a tantalising possibility: any concept that is conceivable by a human mind must necessarily also be visualisable by a human mind. For every abstract concept out there, there is a metaphor lurking in our mental subterrain, waiting patiently to be unearthed.
A few years later I heard of German infographics pioneer Fritz Kahn who, operating in the first half of the 20th century, published popular science books in which he drew stunning, metaphor-laden illustrations of physiological processes in black and white. Kahn's illustrations accomplish what I imagine is every teacher's ultimate dream: inspiring in full-grown, hard-to-impress students some vestige of that same trance-like tingle they felt when as wide-eyed children they opened their favourite book.
Kahn's visualisations impel me to ask, when university presents me with new material to master: “How could the logic intrinsic in this concept be conveyed through a three-dimensional object, projected onto a two-dimensional image, and as independent of text as possible?”. Occasionally it happens that Kahn's work impels me to dip my own pencil into black ink in an attempt to wring some poetry out of a PowerPoint.
In reality this type of illustration is incredibly labour-intensive – less an ingenuous little pet project, and more like a socially isolating beast of a hobby. Visual analogies are hard to come up with, expensive to print and – should an error slip in - a Tipp-Exencrusted nightmare to modify. Realistically, verbal analogies will in most cases have to do.
But encouraging students to concretise and communicate the mental imagery they spontaneously generate upon acquiring new knowledge is probably still worthwhile. The reason for this is that when we reach a state of understanding, we tend to forget the winding path that took us there. What an “Aha”-moment ago seemed impenetrable becomes glaringly self-evident, and we lose access to our previous ignorance. All those mental transformations - unconscious metaphors, partial insights and near-intuitions – are flushed into oblivion, and because they were never preserved, the next student cohort is left with the same uninspired PowerPoint to grapple with, and an expert teacher who likely has forgotten what it is like to be baffled by his subject.
And this is why non-expertise is a valuable resource in the development of explanations. Learning at university is like Tetris because once the shapes mesh perfectly together - once all that knowledge has successfully been embedded, exams completed and flashcards binned - the limits of our collective repository of explanations return to what they were, as the knowledge representations of non-expert students are lost.
The infographics that follow are me trying to record how I rotated my Tetris tiles – how I mentally represent computing scientific concepts. Few of the included concepts were taught as part of my degree: rather they are concepts that I have looked up in order to make sense of course material I struggled with. My goal was to strip down computing science to its bare bones and understand how different parts of it - mathematical theorems, formal grammars, abstract automata, halting problems, Boolean algebra, logic gates and modern computer architectures – all interlock into a single, coherent tilework.
Without a doubt, the infographics are in places very flawed, naïve and typo-ridden. I am, after all, not an expert, and expect to re-do them many times in years to come – but how wonderful it would be if – despite these things - they evoked in some revisionweary mind out there the same excitement that Fritz Kahn’s infographics evoke in mine!