M. C. Escher, Hands, 1948.jpg

2. Method: Loops and Spirals



Image: Maurits Cornelis Escher, Drawing Hands, 1948, etching.

Slide 1: Our methods for reasoning about the nature of "Reality" has gone through a remarkable evolution. Before the 20th Century, Western thought, (beginning with the pre-Socratics), relied primarily on two methods: Inductive Reasoning (bottom-up) and Deductive Reasoning (to-down).

Slide 2:  During the Renaissance, Natural Philosophers tried to use logical methods to prove the existence of God and how the world came into existence, in order to develop a more "objective" description of "Reality. Francis Bacon (1561-1626) argued that "Inductive Reasoning," or the careful observation of nature, would lead to a greater understanding of Nature that would glorify God.

Slide 3: In 1637, René Descartes (1596-1550) wrote "Discourse on Method," (which is often regarded as the first book of modern philosophy). Descartes begins with a form of skepticism; he "doubts" everything. Descartes then systematically attempted to use "deductive reasoning" rebuild a body of knowledge based on deductive proofs. He famously stated that we can know with certainty that we exist because of our ability to think, "Cogito, ergo sum". Unfortunately, Descartes' philosophy reinforced a vision of our world as dualistic. Man was godly because we had reason, but we were also ungodly material stuff; reason was separate  from our animal natures (accessed by emotions) and nature (was simply mechanical) and there for our use.

Slide 3: Euclid wrote The Elements in the 3rd Century BCE. Its use of deductive reasoning held sway until the middle of the 19th Century. Although "deductive reasoning,” was a method by which logical proofs could be deduced from a small set of axioms, it was also thought to be a reliable method for finding universal truths”about Reality. Deductive Reasoning was relied on to prove universal truths about the world, mathematicians realized that Euclidean space was assumed to be flat. However, if space was curved, a proof, such as parallel lines never met, was no longer true. Was space flat or was space curved? This was now a matter of speculation; it was no longer a universal truth about Reality. 

Slide 4: Consider that learning is not a logical process. Instead, it relies on building upon what we already know; we can only build on or make room for new information, and new insights, if we are open to new possibilities. Leaning something new is not easy because we may have to re-organize what we have come to believe as settled. Slide 5: Consider that the growth of a self-organizing structure in nature appears to reveal itself as a spiral form, or a tiling pattern, or a -- slow-moving vortex -- made visible.

Slide 6: The tiling vortex pattern approximates the Fibonacci number sequence, it shows up in spiral galaxies, the tornado vortex, as well as the sunflower. It is an efficient construction process. It indicates that growth has a pattern. There has been a long-standing tension in science that began with the Greeks. Was science seeking to explain things (what it is made of) or patterns (how things interact).

Slide 7: If we believe the world is made up of things, it is easy to see how we arrived at a mechanistic universe. However, if we think of the world as engaged in relationships, we arrive at a more organic or holistic universe. For example, how do we interpret the emergence of the ratio, 1.618..., which we see over and over in nature?

Slide 8: We now know that the ratio of Phi emerges effortlessly from the Fibonacci sequence. It is sometimes referred to as "mystical." It is referred to as the Golden Mean in mathematics; Phi in science, and the Golden Section in art. It appears whenever a continuity is destabilized and seeks a new form or structure. It can appear as if an invisible hand has guided nature, however, thermodynamics provides the explanation. The ratio Phi is the most efficient way an emerging structure will manage the energy of chaos. Consider that Phi is the "visible form" of a dynamic process that shapes growth in the cosmos, life on earth, and the processes we use to learn and understand.

Slide 6: A Tornado or a hurricane vortex is both a closed and an open system, (we need constraints to turn energy into work).  A vortex will maintain its form (or boundaries) as long as the energy of chaos feeds the system from the outside. Similarly learning in science or art is a way to find an order (or to make sense) of what we do not know.

Slide 7: We cam say that learning, like a hurricane, thrives at the edge of chaos.

Slide 8: The concentrated energy of a storm (or knowledge) can produce a destructive force that destroys other patterns of order, or create the possibility of new constructive forms.

Slide: 9: The Positivist view considered that the focus of knowledge was on the relationships between things. Complexity seeks to understand the processes that generates things or meanings. Complexity focuses on a dynamic universe that is always interacting; always trembling with energy, far from equilibrium. There are worlds within worlds that evolve and take on new forms (new meanings) on the macro and the micro level. If we live in a non-deterministic world that has different meanings at different scales, we need to develop a method that for understanding that is more complex.

Slide 10: Since the early Greeks 2,300 years ago, the Deductive Method of reasoning was considered to be a reliable method for determining the "true" nature of the world. Euclidean Geometry was the gold standard: no parallel lines can ever meet. However, in the 19th Century, mathematics showed that if space was curved, not flat, parallel lines will meet. Deductive Reasoning can start logically from different assumptions. So Deductive Reasoning doesn't tell us what is "true" about the world?

Slide 11: Another form of reasoning was developed in the 17th Century that relied on empirical experiments and the collection of data. The Inductive Method, relied on gathering trusted bottom-up information to arrive at a trustworthy conclusion. This method focused our attention of reducing matter to its smallest unit. However, when in the 20th C, the smallest bit of matter seemed to have no mass and appeared to be a form of energy, the Reductive Method became problematic.

Slide 12: In the second half of the 20th Century, an old form of reasoning, borrowed from the humanities, came into use. The Hermeneutic Method is in some ways a mash-up of deductive and inductive reasoning, as well as lateral, spiraling, or unfolding thought that is inseparable from feeling. This approach is an embodied approach. It involves metaphoric processes to arrive at a phenomenological "understanding". It does not propose that literal, objective Truth that is certain and universal is possible.

Slide 13: Similar to the growth patterns of a plant, the Hermeneutic Method involves circular feedback loops, as well as spiraling part-to-part, and part-to-whole interpretations. This suggests that minor disturbances and chance events can play a significant role in generating our best "understanding". There is no attempt to claim that an interpretation is objectively or literally true. However, this form of complex understanding is reasoned, seeks understanding, and is open to revision.

Slide 14: How can we make sense of Duchamp's anonymous submission of Fountain, 1917?