Symmetry–simplicity–complexity

A number of (the 15) contributions to a theme issue ‘Making and breaking symmetries in mind and life’ have some interest to be referred.

Symmetry is a motif featuring in almost all areas of science. Symmetries appear throughout the natural world, making them particularly important in our quest to understand the structure of the world around us. Symmetries and invariances are often first principles pointing to some lawful description of an observation, with explanations being understood as both ‘satisfying’ and potentially useful in their regularity. … . The study of symmetries is so fundamental to mathematics and physics that one might ask where else it proves useful. This theme issue poses the question: what does the study of symmetry, and symmetry breaking, have to offer for the study of life and the mind?

Meditating on the 50th anniversary of the groundbreaking article by Philip Anderson, ‘More is different’, Krakauer describes in ‘Symmetry-simplicity, broken symmetry-complexity’ how emergence, frustrated random functions, autonomy, and generalized rigidity characterize the nature(s) of complexity. He describes how complex phenomena are made possible when physical symmetries are broken and selected ground states perform mechanical work and store adaptive information.

Complex phenomena are made possible when:
(i) fundamental physical symmetries are broken and
(ii) from the set of broken symmetries historically selected ground states are applied to performing mechanical work and storing adaptive information.
Philip Anderson enumerated several key principles that can follow from broken symmetry in complex systems.
The consequences of broken symmetry are multiple but of greatest interest to the study of complexity (called the four Anderson Principles) —these include:
(i) emergent properties arising through multiplicity or scaling,
(ii) the importance of ‘frustrated random functions’,
(iii) the requirement of autonomy and
(iv) the property of generalized rigidity
These four Anderson Principles are preconditions for the emergence of evolved function.
Taken together the Anderson Principles, derived largely for equilibrium macroscopic states, provide necessary foundations for understanding the emergence of quasi-equilibrium structures initiated in the non-equilibrium regime through dissipative, or driven, dynamics.
The Anderson Principles fall short of a description of adaptive function, which lies beyond any theory limited to equilibrium structure, but need be components of any such theory.

Two of the areas that Anderson did not explore deeply and that follow naturally from his inquiries into emergence are information theory and evolution.
One is arguably the most effective theoretical foundation in any effort to measure complication (beyond simple broken symmetry), and the other, the pinnacle of all domains in which broken symmetry is the foundational concept—more often described as ‘frozen accidents’.

A third transition in science?’ by Stuart Kauffman and Andrea Roli argues against the standard ‘Newtonian paradigm’ in which relevant variables and governing laws (or master equations) of systems may be clearly identified, with boundary conditions defining phase spaces over which all possible values (and their actions) are determined and fixed a priori, outside of time. These authors argue that such an approach is inadequate for the inherently time-dependent evolution of organisms in complex environments like our biosphere, wherein living cells exhibit ever-new adaptations, achieve constraint closure and construct themselves via evolutionary selection—leading to genuinely new possibilities that emerge from the edge of the adjacent possible. Their ultimate conclusion is that a ‘true’ phase space is necessarily undefinable using any mathematical or formal analytic tools, dashing hopes for theories of everything and the ‘Pythagorean dream’ which would attempt to capture the essence of all phenomena in terms of quantitative and symbolic terms. Based on these considerations, they suggest that this new major transition in the evolution of science may allow us to understand the nature(s) of emergence and the creativity of an evolving biosphere. In the context of this collection, by identifying natural systems as ‘Kantian wholes’, we may think of the evolution of parts to support the functions of wholes as self-organization in the sense described above: that of gauge forces and morphogenic fields.

we begin to understand the emergent creativity of an evolving biosphere:
emergence is not engineering.

If the evolution of life cannot be deduced and we must give up our beloved Newtonian paradigm of an entailed world, a vast new, unsuspected, world comes into view.

We achieve a new understanding of the almost miraculous emergent self-construction and emergent coherent functional organization of processes in an evolving biosphere: there is no deductive relation between the different uses of any physical thing, such as a protein in a cell that can evolve to be used to catalyse a reaction, to carry a tension load or to host a molecular motor on which it walks. Moreover, cells physically construct themselves and evolve by heritable variation and natural selection ever seizing non-deducible new affordances.

The evolving biosphere really is a propagating adapting construction, not an entailed deduction. This is ‘sustained functional integrated emergence’ in evolving Kantian wholes. It is the arrival of the fitter.

This is emergence. Emergence is not engineering. This radical emergence of a co-evolving biosphere itself emerges only beyond the Newtonian paradigm. That we are at a third transition in science, beyond Newton’s wonderful paradigm, is not a loss, rather it is an invitation to participate in this magical emergence we have not even seen before.
We hardly begin to understand this. An evolving biosphere is a self-constructing, functionally integrated blossoming emergence. This new understanding shares common ground with the old Buddhist concept of co-dependent origination

The evolving biosphere is ever-emergent and creative.
Co-evolving fungi and bacteria in the soil create ever-new ‘possibility bubbles’ that alter the phase space of the biosphere.
The third transition in science demands new tools, experiments and observations to understand how the evolving biosphere and global economy persistently create new possibilities that cannot be deduced.

Evolving biospheres are immensely creative in ways beyond our knowing or stating.
We live forward in face of mystery.
This implies that we humans are of nature, not above nature. Rather than a loss, this is, instead, an enormous invitation. We can try to understand in new ways how our or any biosphere, our global economy and even our cultures diachronically construct themselves over billions, millions and hundreds of thousands of years of non-deducible, non-entailed, ever creative, non-ergodic emergence.
We are inevitably invited to see reality anew. We are inevitably invited to live responsibly, respectfully and in wonder as we share co-creating the evolving reality of the biosphere.