Emergence, Complexity and Simplicity

"The whole is more than the sum of its parts" Aristotle

Emergence describes how novel properties can arise from lower-complexity parts, where these properties are not observed.^[12] This phenomenon is wide-spread in nature. One straight-forward example is water: molecules of H₂O are here considered as simple subparts. The liquid "water" is a system consisting of several H₂O molecules. One well-known property of this system is temperature. Nevertheless, no molecules can be characterized by such a property. Along with other properties as viscosity and pressure, temperature is an emergent property of the system.

In nature, one particular pattern formation retained our attention: some sea snail present a complex pattern on their shells. The "Cloth of Gold" observed on textile cones results from an inner computation of the neural cells of the sea snail. The complex pattern emerges from the assembly of different cells.

Figure 1 Three different taxa of cones from a [http://home.comcast.net/~edwelda/site/?/page/Seashells/ private collection ]

Pattern can be characterized by their complexity. Complexity is no synonym for randomness or for complication. Complexity absorbs two a priori opposite concepts: order and randomness. A complex pattern is random and ordered. How is it possible to merge the two concepts together? How can a scientist take it into account? Our Human Practice section is focused on those philosophical and epistemiological issues.

Emergence, Complexity and Simplicity

"The whole is more than the sum of its parts" Aristotle

When one considers an object, it is always made of sub-parts. For example, a human is made of cells. A table is made of molecules. Each sub-part has some properties. Nonetheless, the object has other properties. These global properties can, more or less directly, be linked to the sub-part properties. This is called Emergence. Another way to see it is that an object is more than only the juxtaposition of sub-parts. For instance, interactions between sub-parts have a huge influence on the property of the system.

Water is made of H₂0 molecules. Water can be hot or cold. The temperature is a property of water. However, a H₂O molecule has no temperature. It is not one of its property. Only a set of molecules can have a temperature.

In nature, emergence is a common phenomenon. For instance, those sea snails have a colorful shell. Those colors are not completely ordered. We would detect a repetitive motif on the shells. Those colors are not randomly put on the shells. We can recognize some geometrical forms. This mixture of randomness and order is a characteristic called complexity. As complexity is a buzz word in science, we chose to investigate it more in our Human Practice section and throughout our project.

Figure 1 Three different sorts of sea snails from a [http://home.comcast.net/~edwelda/site/?/page/Seashells/ private collection]

Team:ETH Zurich/project/background/casimple

Cellular Automata

This pattern formation was formalized by Neuman in the concept of cellular automata. Following a simple pre-programmed logic rule, the state of a spot on the shell, corresponding to the color (either white or brown), is determined by the states of three parent spots (from the previous computation round). Wolfram ^[11] elaborated a whole theory on these cellular automata.

According to cellular automata theory, emergent patterns offer a large panel of properties: striking examples are the rule 30 which gives an apparently random pattern and the rule 110 which has been proven to be Turing complete. With cellular automata, you cannot predict how the final pattern will look like even if you know the rule that governs its property. Thus the intricated computations of steps poses the problem of complexity.

"The whole is more than the sum of its parts" Aristotle

Emergence describes how novel properties can arise from lower-complexity parts, where these properties are not observed.^[12] This phenomenon is wide-spread in nature. One straight-forward example is water: from the molecules of H₂O, which are here considered as simple subparts, we are able to consider the liquid "water" at a higher level of complexity, with properties such as viscosity, pressure, transparency...

One particular pattern formation retained our attention: some sea snail present a complex pattern on their shells. The "Cloth of Gold" observed on textile cones results from an inner computation of the neural cells of the sea snail. This pattern appears row by row (computation after computation) and the pigments of the next row are determined by the pigments of the row before.

Cellular Automata

This pattern formation was formalized by Neuman in the concept of cellular automata. Following a simple pre-programmed logic rule, the state of a spot on the shell, corresponding to the color (either white or brown), is determined by the states of three parent spots (from the previous computation round). Wolfram ^[11] elaborated a whole theory on these cellular automata.

According to cellular automata theory, emergent patterns offer a large panel of properties: striking examples are the rule 30 which gives an apparently random pattern and the rule 110 which has been proven to be Turing complete. With cellular automata, you cannot predict how the final pattern will look like even if you know the rule that governs its property. Thus the intricated computations of steps poses the problem of complexity.

XOR Logic Gate