1 Tools of Description

From a practical point of view, the concepts of complexity and simplicity can only be regarded as useful linguistic tools. In the hands of scholars and artists, they are the equivalent of what a ladder or a pair of pliers are for a craftsman. Hence, complexity and simplicity also often appear in this volume as operational, functional terms with no clear ontology behind them. Without these concepts, we would not be able to describe a diverse range of phenomena and structures, whether in the natural sciences or the humanities. These terms therefore turn out to be indispensable for organizing and categorizing knowledge in specific disciplines of science and art.

The undeniable tendency to arbitrarily classify phenomena as either simple or complex is largely due to our cognitive limitations. We experience only a very limited slice of reality, and within that narrow spectrum, we make seemingly obvious distinctions between the simple and the complex. We then project these categories, often unconsciously and automatically, onto other parts of reality. Thus, these concepts are not just transparent tools of description, but rather become necessary means of co-creating reality.

2 The Emergence of Meaning

The concepts of complexity and simplicity allow for the relatively easy, though not always meaningful, superposition of structures that previously had little in common. As an exercise, the reader may choose random occurrences of complexity and superimpose them on top of each other in a search for meaning. For example, let us consider ideas taken from the present volume: the complexity of harmonic relations in music, the complexity of a straight line, the complexity of new media, the complexity of philosophical discourse, the complexity of information, the complexity of emotional experience, the structural complexity of amino acids, or the complexity of the movement of the Sun. Their very juxtaposition stimulates the imagination and drives the archetypal content of complexity. Moreover, thanks to such contents, we can make – more or less sensible – mappings of patterns from one conceptual space to another.

The strength of the Complexity and Simplicity project lies precisely in the fact that, even before any planned scientific investigation, we can juxtapose the complexity of emotional experience with the structural complexity of amino acids, if only as an exercise. We can, for a moment, impose the order of emotional experience on the order of amino acids and consider whether anything meaningful emerges. Perhaps the adaptation of the structure of emotions to the structure of amino acids, or vice versa, will lead to a creative discovery, the emergence of new meanings or perhaps it will serve as a basis for artistic creation. Of course, it can also become a source of erroneous speculation and inference, of which both scholars and conscious creators, supported by phronetic critical thinking, should always be wary.

3 Levels of Cognition

What appears simple at one level may prove complex when seen from another point of view, another perspective. Nicholas of Cusa teaches that “if it were possible for someone to be situated outside of the world, the world [as such] would be invisible to him, after the fashion of an indivisible point” (Nicholas of Cusa, 2000, p. 10). Practical wisdom, what Aristotle (2011) called phronesis, makes us sensitive to the totality of the situation and allows us to act as we should. At one turn, we consider seemingly indivisible and undifferentiated points, and at another we decompose those same indivisible points into infinite structures, creating iterative contexts. In this respect, cognition and action resemble a fractal structure, whose fragments – seemingly simple at a given level – reveal, with each successive enlargement, both new and already known yet potentially and actually infinite, complexity. The graphic representation of Cantor’s set provided at the end of this Conclusion may serve as an illustration here. In this most minimalistic fractal, we always see an infinitely complex arrangement of the simplest objects, no matter what level of depth we are at. Again, in line with Aristotle’s thought, moving through these levels as one should, and not just as chance suggests, is a matter of the highest art: i.e., practical wisdom.

Complexity and simplicity, when treated solely as tools of description, may appear to be transparent entities, seemingly devoid of any effect on the reality they seek to describe. However, this is not the case. As Hutchins (2012) points out, concepts, while part of rich cognitive ecosystems, arise within a certain practice and die with that practice, just as languages or other systems for describing reality themselves perish. Concepts are part of the distributed cognition that groups of thinkers co-create. They can reinforce or weaken the intellectual mood and, in effect, function to co-create thought collectives (Fleck, 1979) – i.e., certain patterns of directed perception. In this volume, what we propose is to practice thinking and acting, in both science and art, through the lens and with the assistance of the concepts of simplicity and complexity. Why is this important, and what purpose can it serve? Hutchins (2012) has pointed to several mechanisms that increase conceptual order and thus, in a cognitive spiral of order-building and order-destruction, elevate us to a higher conceptual level. This elevation is the essence of this volume. Among these conceptual meta-tools are the aforementioned superposition of structure and mapping across conceptual spaces. In addition, we will indicate other mechanisms mentioned by Hutchins (2012), such as dimensionality reduction, filtering, and composite mechanisms of modulated positive feedback.

Simplicity and complexity make it possible to move between dimensions of cognition: on the one hand, they make it possible to reduce a dimension, and on the other, to deepen it – as in the case of successive layers in a fractal structure. In the context of his philosophy of space, Simmel would say that to move between the dimensions of cognition is, in fact, to approach one dimension and to distance oneself from another (cf. Milà, 2016). Distance and proximity not only constitute the social structure, but also allow us to dynamically approach and separate ourselves from others and, more generally, to move the objects of our cognition closer or further away. Simplicity is also that which filters what is relevant from out of complexity, and complexity is that which enriches simplicity. This is the case with complex systems that arise from the accumulation of simple structures. Such a thought resonated powerfully in ancient atomism, where all qualitative features were thought to result from accumulations of the simplest objects – atoms. Let artificial neural networks simulating their natural counterparts serve as a contemporary example in this respect.

4 The Method of Simplification

Simplification also occurs when we concretize – i.e., move from the abstract, a non-self-sufficient part of an object, to the concrete, a self-sufficient part of it. Recall that the GPT chat in the interview mentioned in Chapter 17 gave an example of a positive feedback loop when pointed in the direction of the creation of filter bubbles: “where people are only exposed to information that reinforces their existing beliefs”. Feedback loops can arise between the phenomena being studied and their models: the phenomenon influences the construction of the model, and the model, in response, like a filter, reveals just such-and-such properties of the phenomenon and not others. This is also how the concepts of simplicity and complexity work: they allow one, through feedback, to ascend the spiral of cognition.

5 The Ethics of Openness

In the introduction to this volume, we suggested that openness to the complexity of perspectives and simplicity of expression is a virtue, yet we did not indicate what exactly this virtue pertains to. It is not, after all, a naive openness to all that is complex, nor a simple delight in some engaging expression, even if that expression captures the essence of the phenomenon under study. Virtue lies somewhere in between – between the simplicity of what is vividly felt and the normative complexity of the environment, between what the context imposes and that sort of moral reasoning whose conclusion is the taking of appropriate action.

To act virtuously, as Aristotle (2011, p. 34) taught, means to act as one ought to. Openness to the complexity of perspectives and simplicity of expression is a virtue precisely inasmuch as one ought to be open both to things generally and, where specific things are concerned, to the degree that is right and appropriate. The crown of virtue understood this way – which always lies between extremes – is that phronesis mentioned above. It is thanks to it that we know how to find our way about within this tangled multitude of issues that are sometimes simple and sometimes complex. Thanks to practical wisdom, we know when cognition is overly simplistic and when too complicated. Thanks to this virtue, we also know how to choose simple means to achieve complex goals.

6 Art

The inherently simplifying principle of parsimony in thought and action that is widely accepted in science, and whose well-known manifestation is Ockham’s razor, is also valid in the art world. As Arnheim (2004, p. 59) points out, “the artist must not go beyond what is needed for his purpose”. Even seemingly complex masterpieces of art can be characterized by a kind of simplicity, which means that “they organise a wealth of meaning and form in an overall structure that clearly defines the place and function of every detail in the whole” (Arnheim, 2004, p. 60). “In the context of art, the notion of simplicity should be applied not only to the appearance of the work itself but also to the relation between the image seen and the statement it is intended to convey” (Arnheim, 2004, p. 62).

The image is a medium that is not a simple analog of spoken or written language. Therefore, artistic representations are not literal, but rather metaphorical. They are subject to multiple interpretations, affecting us on both intellectual and emotional levels. The perspective of art probably does not in any explicit way bring us closer to giving clear definitions or rigorous descriptions of the relationship between complexity and simplicity. It does, however, allow us to empathize with this relationship, and thanks to that, as a result of dynamic association, enlightenment – itself eagerly awaited by scholars and artists alike – may occur.