Learning. Simple.


By Daniel Cabrera

The concept of complexity, particularly complex adaptive systems, have taken over the discussion in many areas of our society, from social networks, to management theory to education; even this blog has discussed the theories of complexity and how to manage it. At the same time as the discussion on complexity-related disciplines has exploded, the importance and the teaching of simplicity have faded. In this post, I discuss basic concepts about simplicity, its relation with understanding and complexity and why is important to learn to achieve simplicity in education.

The concept of simplicity originates from numerous domains of human knowledge (e.g., religion, philosophy and science) and is widely considered to be of theoretical virtue and value, justified by metaphysical, naturalistic and probabilistic arguments. Traditionally we equate simplicity to ontological simplicity, also known as parsimony or roughly the number and complexity of things postulated. Ontological simplicity is commonly understand and described by Occam’s Principle:

“Entities should not be multiplied unnecessarily” OR
“When you have two competing theories that make exactly the same predictions, the simpler one is the better”

Complexity and simplicity co-exist and need each other. From a learning theory perspective, simplicity can be defined as the process of knowing and understanding a complex idea or concept. This process of understanding is framed as reducing (simplifying) the complexity of the idea to the point that the elements contained in the idea are describable by a small formula (i.e., minimal formula), understood in the realm of Kolmogorov complexity. For example:

The set containing the items apple, peach, banana and orange can be   simplified to the formula fruits; a minimal formula of minimal complexity, while

The set containing a87984bfbdsjh3298%4gh++5934bbx5&*(2344@#43534543234 can only be described as with a a87984bfbdsjh3298%4gh++5934bbx5&*(2344@#43534543234; a minimal formula of maximal complexity (no compression or simplification is possible)

From an education perspective, the teaching and learning of complexity/simplicity has been dominated extensively by exemplar theories championed by Nosofsky. According to this theory, humans learn new concepts as a function of comparing a new idea with a previous stored category of ideas, judging on similarities and dissimilarities and the learning occurring as the new idea is assimilated with previously known concept framework, adapting it and modifying it as it happens. The learning process is focused on comparing and storing patterns instead of abstracting the intrinsic simplicity or essence (minimal formula) of the conceptual object.

In a learning model that uses exemplar theories, the amount of complexity reduction is minimal, failing to achieving the ideal of simplicity. Feldman argues that this type of approach is only appropriate for an early or basic stage of learning. Complex minimization is more appropriate for advanced concept learning.

Achieving simplicity is not only important from a romantic idea of elegant and parsimonious thinking, but also from a cognitive and operational economic perspective. Exemplar category creation can be expensive from a brain operations perspective, utilizing multiple elements in a difficult to predict pattern. In contrast, complexity minimization is cognitively difficult, but adopts a predictable model that is reproducible to a certain extent. In other words, exemplars are complicated and expensive, while complexity minimization is complex but economical.

Managing vast amounts of information and learning difficult new concepts is at the core of the learning process of clinical learners. Exposure to repetitive patterns and dynamic variations of concepts (exemplars) is of fundamental importance in concept learning; however, the ability of extracting simplicity from complexity (complexity minimization) allows learners to engage complicated systems even when no obvious pattern emerges or when difficult problems with no obvious solutions are placed in front of them.

When a learner is facing a new concept, he or she should try to assimilate or understand this new idea using a mechanism that allows him or her to decrease the complexity to a point where the amount of information necessary to describe the concept is elegant, parsimonious, familiar and reproducible. When this goal is achieved a learner understands the concept. From a mechanistic perspective Nosofsky proposes the RULEX (RULe and EXception) model, where concept learning happens when a new idea is subjected to a series analysis until an appropriate RULEX is found. The hierarchy of these rules is

– Rule that discriminates perfectly between classes using a single attribute (Exact)

– Rule that discriminates fairly well between classes using a single attribute (Imperfect)

– Rule that discriminates fairly well between classes using multiple attributes (Conjunctive)

– Exceptions to the rule (Disjunctive)

When an appropriate RULEX explaining the phenomena is obtained, the understanding of the problem is complete enough that permits making inductions, inferences and predictions. This facilitates the building of a scaffold via semantic meaning, where new and complex concepts can be build upon. It is superior to a “storage bin,” where similar things are (attempted to) fit together (i.e., exemplar).

The challenges we face, as Clinician Educators, are to understand how we learn and craft processes to explain these mechanisms. There is much we still don’t know. While we teach and model for our learners to assimilate patterns into illnesses scripts we don’t dedicate as much time teaching how to abstract the core essence of a phenomena and apply it to the complex decision making process required of clinical medicine.

Perhaps we should dedicate less time to the storage of information and more time to the assignment of meaning of information, to compress complexity into simplicity.

Sources and further reading

  1. Maeda J. The Laws of Simplicity. MIT Press; 129 p.
  2. Baker A. Simplicity. In: Zalta EN, editor. The Stanford Encyclopedia of Philosophy [Internet]. Fall 2013. 2013 [cited 2015 Feb 17]. Available from: http://plato.stanford.edu/archives/fall2013/entries/simplicity/
  3. Feldman J. The Simplicity Principle in Human Concept Learning. Current Directions in Psychological Science. 2003 Dec 1;12(6):227–32.
  4. Nosofsky RM. The generalized context model: an exemplar model of classification. Formal Approaches in Categorization [Internet]. Cambridge University Press; 2011. Available from: http://dx.doi.org/10.1017/CBO9780511921322.002
  5. Charlin B, van der Vleuten C. Standardized assessment of reasoning in contexts of uncertainty: the script concordance approach. Eval Health Prof. 2004 Sep;27(3):304–19.
  6. Nosofsky RM, Palmeri TJ, McKinley SC. Rule-plus-exception model of classification learning. Psychological Review. 1994;101(1):53–79.

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