What English Gardens Know About Education

Even over an essay collection that makes only occasional mention of his theory, Darwin’s shadow looms unignorably large. A recurring theme in it is the scientific endeavor to find concise descriptions for how patterns in Nature are generated, and this is an endeavor that has taken twisted and unexpected turns. Evolutionary theory tells us that our brains were shaped by a very particular kind of environment, sometimes called the “mesoworld” – one of breathtaking complexity, perched between the simplicities at macroscopic and microscopic scales – for which a deep appreciation of the cosmic and atomic mattered little for an organism’s survival. What scientists often find, therefore, is that when inquiring into the nature of things, we must learn to live with the limitations of our subjective judgments, and not dismiss a theory just because it runs counter to our intuition. As a result, the best theories currently on offer are not infrequently eerie and bizarre, beautiful only for their brevity. Our rationality, the jargon goes, is “bounded”.

The essays explore at least three such mental shortcomings, about locality, complexity, and causality. They the notoriously counter-intuitive features of quantum mechanics, by explaining how it relates to the more intuition-friendly classical physics. They shatter the misconception that there is a conservation law between simplicity and complexity, such that complex behavior must necessarily be underpinned by equally complex rules. They attempt to use models of the brain to explain findings within behavioral economics which suggest that humans make use of computational shortcuts that in certain contexts introduce maladaptive biases in how we attribute causes to events. For all of these things, humans need to relinquish their instinctive beliefs, and instead rely on man-made technologies – like the scientific method, statistics, and computer simulations – to more effectively torture Nature for its truths.

Darwin’s theory itself was, and in some places remains, controversial because it similarly violates our intuitions. Notice that we could hand-wavingly claim that “our minds did not evolve for it” to justify any absurd proposition, inflating this piece of reasoning into a meaningless “just so” story. However, in this case science has identified rather precise neurophysiological adaptations to account for why creationism feels natural as an explanation to the mesmerizing patterns we find around us. We have, for example, a well-documented tendency to “anthropomorphize” phenomena we perceive – to regard things like the wind and planetary orbits to be caused by conscious intention – and this may have disposed us to invoke a super-intelligent being in order to bring logic and comfort into the order and disorder of worldly happenings. Moreover, the human life-span is too short to observe the noisy, brute process of trial-and-error directly, so the fact that natural selection sits so uncomfortably within our belief system should be unsurprising.

Today, little in biology would make sense without natural selection, but the marvelous patterns in Nature are not just biological. In general, a pattern is a regularity of some form, and therefore cannot be localized in space and time – it has to be extended, either spatially, temporally, or both. The former includes the leopard’s spots, the ubiquity of the Fibonacci sequence in the plant kingdom, and the fractals of a fern or snowflake. The latter include the parabolic trajectory of a projectile, the elliptical orbit of a planet, and our notion of “causal relationships”, in which one event reliably predicts a subsequent event. To these we may add a third category of wondrous relationships, namely those of “fitness”, like how an organism is suited to its environment, how the constants of physics appear delicately tuned so as to make life possible, and the unreasonable effectiveness of mathematics in describing physical phenomena.

These categories could be whimsically compared to garden designs. Consider how patterns that are extended in space are central to the French tradition. Made famous by the gardens of Versailles, the French style is fond of labyrinthine shrubs in formal, symmetrical arrangements that don’t form spontaneously in nature. The pattern-ness of such, and consequently also its beauty, is appreciated instantaneously, made possible by how our visual system processes different parts of the retinal array in parallel. This makes the beauty of French gardens sensitively dependent on viewing angle, because from certain angles, its symmetries are lost.

By contrast, the beauty of an English garden is found not in unbroken regularities, but in the random-seeming placement of hills, trees, and shrubbery so as to conceal parts of the landscape. This topographical preference is innate and partly explained by how, during the Pleistocene epoch, our hunter-gatherer ancestors lived in tropical savannahs, where they evaluated potential habitats based on life-supporting cues like tree scatterings (for shade and protection), frequent undulations (as landmarks for navigation) and shrubbery about a meter high (so that food is available). The use of partial concealment also has a titillating effect of inspiring wanderlust and exploration, and the seductiveness of an English garden has important things to say about how brains process patterns that are extended in time.

Wanderlust is universal among complex animals, because by systematically exploring their environments the patterns they detect can be used to form an internal map to help navigate more efficiently in the future. Analogously, as seen in a child’s playful experimentation, they have an innate drive to intervene in the environment in order to explore its causal structure. Because these are both critical for survival, it is plausible that evolution has made sure that the neurochemicals associated with arousal are released whenever a gap or logical contradiction appears in either of these models, and that those associated with pleasure are released to reward its tidy resolution.

Just like how our curiosity compels us to explore what’s on the other side of a hill, we therefore have a general aversion towards conflict, ambiguity and unfinished business. In psychology, this drive surfaces under labels like “cognitive dissonance”, “need for closure” and the “Zeigarnik effect”. It explains our delight in a startling punch-line, and our dismay at an anticlimactic plot denouement. It is responsible for the slow-burning bliss from a well-crafted metaphor, and the haunting, intrusive thoughts following a truncated relationship (as well as many a pensive walk in an English garden to turn the latter into the former).

The scientific enterprise can be viewed as an epiphenomenon of this desire to complete patterns. While curiosity normally deteriorates with age, with scientific institutions it is kept artificially alive to sustain our quest to chart the causal structure of reality. Science is a technology for determining which temporal patterns are reliable, by quantifying our uncertainty as to whether the pattern is illusory. This is a slow and incremental process of assessing the quality of the predictions that a model generates, through carefully controlled experiments. If a model survives all the tests done to prove it inadequate, it becomes an assumption for a more specific model. This way, the growth of knowledge generally proceeds from general to specific – what Thomas Kuhn labelled “normal science” – punctuated by the occasional “paradigm shift” in which the current dominant theory is shown to be a specific instance of a more general one (for example, Newton’s equations were subsumed by Einstein’s).

Like natural evolution, normal science is slow and brute force. Progress is generally not very obvious to the experimenters binging coffee during late hours in the laboratory. The road to discovery is long and boring. Nevertheless, textbooks tend to introduce new concepts by first providing a historical overview of milestones and key contributors in this plodding process. Such an approach to organizing information is “bottom-up” in the sense that it presents the current state of science as a result rather than a starting-point.

Apart from equipping the student with trivia useful for faculty coffee-breaks, a historicizing approach also has the benefit of mitigating what psychologists call “hindsight bias” – the feeling of inevitability that obtains after a discovery has been made. Just like how we recall the denouement of a story better than the plot development, the geniuses of science often recount a middle-of-the-night epiphany as seminal to their theoretical contributions. This is probably an illusion stemming from how the emotional intensity of conflict resolution causes us to remember the end product of our thought processes better than the winding path of cognitions that led us to them.

There is, however, a high price to pay for the realism that comes from mingling history and concepts together. Cluttering our textbooks with context may distract the student from appreciating how concepts fit together into a general schema. Textbooks and school courses are consumed linearly, whereas science grows nonlinearly. It is not a one-dimensional sequence, but a tree branching out in all directions as researchers test different hypotheses in parallel. A bottom-up organization of scientific facts will have to choose a certain path in such a tree, and end up at an isolated tip, at which point the student’s exhausted working memory has forgotten what the point was with going there anyway.

What teachers may do instead is to trim off the tips and consider them in isolation, and try to unify them into a new internally coherent root, from which facts are then derived. In other words, begin with the most general representation of the current theoretical climate as possible, and then present experimental findings as a result of it, rather than vice versa. Crop the fruits of science’s most succulent concepts as they hang dangling on lonesome twigs, blend them, and let this juice power a cascade of inferences, like a crystal lattice in an oversaturated solution.

Conceptual integration is possible because scientific knowledge is not an amorphous assemblage of facts. Science is advanced by human brains that organize inputs into categories and concepts that are then combined and built upon in into increasingly complex structures. Like all complex adaptive systems, our knowledge therefore is near-decomposable, structured into relatively self-contained nodes. This is why we may reason about things like quantum field theory without literacy in any of the mathematical equations, as long as experts supply well-defined interfaces that specify what facts a certain theory assumes to be true (afferent dependencies) and what it results in (efferent dependencies).

A top-down approach would exploit this inherent structure of knowledge, and extricate concepts from context so as to purposively apply hindsight bias – focus on the state of the art, the research edge, the epidermis of the body of our laboriously accumulated insights. Then, given the freshest and finest understandings available, it would try to arrange them into a cohesive framework from which facts would fall like inevitable consequences. The arrangement would proceed radially from global to local, starting with an overview of how different topics relate conceptually, then breaking it down into smaller and smaller domains, with clear descriptions of how they interface with each other.

This makes a top-down approach pedagogically superior, for once we have a mental model in place we preferentially encode information that is relevant to that model. An individual’s body of knowledge grows in a hierarchical manner analogous to that of science, and just how the successes of science depend on the paradigms under which it labors, an individual’s understanding depends on what mental model he is initially taught. Recognizing this path dependence could accelerate a student’s learning immensely.

French and English gardens are both beautiful in their own right, but when it comes to their services as metaphors for education, a teacher has more to gain from latter. In the same way that the undulating hills of an English garden taps our need for cognitive closure, the top-down approach lays a conceptual landscape with a topography that has an overview (general schema), suggestions of paths to explore (domain interfaces), and the occasional landmark to aid navigation (curiosities and interesting thought experiments). This capitalizes on the positive aspects of intellectual ambiguity as a source of curiosity, while downplaying the discouraging influence it has when a student is forced to learn isolated pockets of facts without any foreground to help integrate them. Learning done right should feel like an evening stroll among the glistening trees in a pastoral piece of Cumbrian scenery.

By paying greater attention to how we present information, so as to involve the student’s biological reward system and make their thirst for understanding intrinsic and indefatigable, a lot of low-hanging fruit may be available when it comes to improving instructional practice. In these times when teachers are no longer needed as conduits of information, they are indispensable as garden architects thereof. Teachers and textbook authors must try harder to make connections between concepts explicit, to condense them into diagrams, and collapse them into larger categories, and to lay the groundwork for such a general schema is what this essay collection will attempt to do.

Darwin’s theory suggests that our brains may impose an ultimate limit on the extent to which we can represent theoretical abstractions in an intuitively gratifying way. Perhaps at some point in the future we can do no better than to face the formal stiffness of a French garden, to shut up and joylessly calculate. But until that day, let’s appreciate the flowers and greenery that Nature keeps on giving.